Keywords:Networked control systems, Nonlinear output feedback, Observers for nonlinear systems Abstract: In this paper, we investigate output feedback based control strategy for bilateral shared autonomous system with delay. The proposed design has two parts. In first part, we design state feedback based shared input interface provided that all the states are available for feedback. In second part, we replace the unknown velocity signals by using observer to develop output feedback based shared input under delay. The convergence condition with observer based output feedback design is shown by using the singularly perturbed method. The analysis shows that the performance achieved under state feedback can be recovered by using output feedback as the values of observer gains converge to zero. Finally, Experimental results are given to demonstrate the validity of the theoretical argument of the proposed design for real-time applications.

Keywords:Large-scale systems, Optimal control, Networked control systems Abstract: In this paper, we deal with the problem of finding optimal control/observation points of large-scaled multi-agent systems. We consider a kind of reference following of the systems with a support of external optimal output feedback control called ``weak control'' under a limitation of the number of control/observation points and show that the optimal control/observation points for it can be obtained by the left/right zero eigenvectors of the network matrix. By employing this result, the computation complexity for finding the optimal control/observation points in the large-scaled multi-agent systems is drastically reduced compared to a brute-force searching method. We also remark that ``a separation principle'' holds in this optimal control/observation points problem.

Keywords:Networked control systems, Optimal control, Model/Controller reduction Abstract: In this paper we present a Linear Quadratic Regulator (LQR) control design for large-scale consensus networks. When such networks have tens of thousands of nodes spread over a wide geographical span, the design and implementation of conventional LQR controllers become very challenging. Consider an n-node consensus network with both node and edge weights. Given any positive integer r, our objective is to develop a strategy for grouping the states of this network into r distinct non-overlapping groups. The criterion for this partitioning is defined as follows. First, an LQR state-feedback controller is defined over the n-node network for any given Q >= 0. Then, an r-dimensional reduced-order network is created by imposing a projection matrix P on the open-loop network, and a reduced-order r-dimensional LQR controller is constructed. The resulting controller is, thereafter, projected back to its original coordinates, and implemented in the n-node network. The problem, therefore, is to find a grouping strategy or P that will minimize the difference between the closed-loop transfer matrix of the original network with the full-order controller and that with the projected controller in the sense of H2 norm. We derive an upper bound on this difference in terms of P, and, thereby propose a design for P using weighted k-means that tightens the bound. The weighting of k-means arises due to the node weights in the network, and the resulting asymmetry in its Laplacian matrix.

Keywords:Networked control systems, Sensor networks, Estimation Abstract: In this work, a problem of event-based state estimation for hidden Markov models is investigated. We consider the scenario that the transmission of the sensor measurement is decided by a dynamic event-trigger, the state of which depends on both the sensor measurement and the previous triggering state. An independent and identically distributed Bernoulli process is utilized to model the effect of packet dropout. Using the reference probability measure approach, expressions for the unnormalized and normalized conditional probability distributions of the states on the event-triggered measurement information are derived, based on which optimal event-based state estimates can be obtained. The effectiveness of the proposed results is illustrated through a numerical example together with comparative simulations.

Keywords:Networked control systems, Power systems, Distributed control Abstract: Smart power grids are currently equipped with open communication infrastructures to improve efficiency, reliability and sustainability of supply. Although technologically cost-effective, this makes them vulnerable to cyber attacks with potentially catastrophic consequences. In this paper an overlapping networked control architecture is investigated for addressing the problem of Load Frequency Control (LFC) under possible malicious attacks in multi-area power grids. Besides providing a certain level of redundancy, this architecture can easily be recast into leader-follower configurations with time-varying hierarchy. Here we propose a reachability analysis for such a class of systems that is instrumental to a model predictive control scheme (see Part II of this paper) able to isolate the nodes under attacks.

Keywords:Networked control systems, Power systems, Distributed control Abstract: In this paper, we present a novel control architecture capable to deal with the constrained Load Frequency Control (LFC) problem in a distributed way and to jointly manage time-delay attacks on the communication links existing amongst power areas and a set of high level controllers located at remote sides. The starting idea consists in abstractly modeling the power grid as a leader-follower configuration so that a first input -first output protocol can be adopted to compute adequate control actions. The latter is achieved by resorting to an overlapping system description which prescribes that several areas of the power grid concur to obtain a single element of the leader follower structure. The approach is based on to the reachability analysis developed in [4] where sequences of one-step ahead controllable sets have been formally derived by taking into account existing state/input constraints, distributed structure of the problem and data loss occurrences due to possible cyber attacks. Simulations put in light the reconfiguration capabilities of the proposed framework that allow one to “isolate” the attacked power units which in principle could compromise the overall operation mode of the power grid.

Keywords:Autonomous robots, Agents-based systems, Cooperative control Abstract: Recently it has been reported that biased range-measurements among neighboring agents in the gradient distance-based formation control can lead to predictable collective motion. In this paper we take advantage of this effect and by introducing distributed parameters to the prescribed inter-distances we are able to manipulate the steady-state motion of the formation. This manipulation is in the form of inducing simultaneously the combination of constant translational and angular velocities and a controlled scaling of the rigid formation. While the computation of the distributed parameters for the translational and angular velocities is based on the well-known graph rigidity theory, the parameters responsible for the scaling are based on some recent findings in bearing rigidity theory. We carry out the stability analysis of the modified gradient system and simulations in order to validate the main result.

Keywords:Autonomous robots, Autonomous systems, Control over communications Abstract: In this paper we propose a Communication-Aware Navigation (CAN) controller to safely guide an agent to a target position in a cluttered environment while maintaining a reliable Wireless Communication Link (WCL). The CAN controller is based on the Harmonic Potential Field (HPF) approach to motion planning. The navigator can generate a communication-aware navigation control signal that is able to safely steer an agent with non-trivial dynamics to a target point along a direct trajectory that avoids obstacles and Dead Communication Zones (DCZ). The approach is developed and basic proofs are provided. The capabilities of the method are demonstrated using simulation results.

Keywords:Autonomous robots, Robotics, Adaptive systems Abstract: This paper emphasizes reliability in designing controllers to enable a blind, modular series-elastic hexapod robot to autonomously navigate (climb over) obstacles such as steps and curbs. Specifically, we suggest that it is not only important to limit the complexity of controllers, but also to limit the number of operating controllers to reduce potential failure points. As such, this paper presents a two-tiered control scheme with a high-level behavioral and a mid-level, modified admittance controller. The behavioral controller, based on a dynamical systems approach, is easy to implement -- it is model-less, and may be realized using only analog circuitry. At its core, two oscillators coordinate the phasing of the robot's legs in open loop for nominal locomotion and climbing behaviors. A simple bistable dynamical system accepts torque feedback to decide the active mode and smoothly transition between behaviors -- an alternating tripod gait for nominal walking and a quadrupedal gait in climbing mode. Finally, the mid-level, modified admittance controller naturally generates discrete motions as a byproduct of regulating compliant interactions. The proposed controller avoids unnecessary complexities that would be required in switching between discrete motion controllers or primitives in a state machine. It allows the robot to adapt to different obstacle heights while minimizing open parameters.

Keywords:Autonomous robots, Autonomous systems Abstract: In the collision avoidance problem, it is a common practice to approximate the shapes of the robots and obstacles by circles or spheres. However, such approximations can be overly conservative when the objects are more elongated in one direction when compared to another, and/or non-convex. This paper develops two analytical collision avoidance laws, which do not require any approximations to the object shapes. These laws are based on the collision cone approach which has previously been used to develop exact collision conditions for objects with arbitrary shapes, moving on a plane. The first collision avoidance law governs the magnitude of the acceleration (applied at an arbitrary angle), while the second collision avoidance law governs the direction of the acceleration (applied with a magnitude of 0 or 1). The effect of time delays on the performance of the laws is analyzed. Simulation results are presented to demonstrate the working of these collision avoidance laws.

Keywords:Control system architecture, Autonomous robots, Robotics Abstract: For highly articulated robots, there is a trade-off between the capability to navigate complex unstructured environments and the high computational cost of coordinating many degrees-of-freedom. In this work, an approach that we refer to as shape-based control helps to balance this trade-off using shape functions, geometric abstractions that determine the coupling between multiple degrees-of-freedom during locomotion. This approach provides a way to intuitively adapt the shape of highly articulated robots using joint-level torque feedback control, allowing a robot to compliantly feel its way through unstructured terrain. In this work we specifically focus on compliance in the spatial frequency and temporal phase parameters of a snake-like robot's wave-like periodic wave-like kinematics. We show how varying the spatial frequency within the shape-based control architecture allows a single controller to vary the degree to which different degrees-of-freedom are coupled throughout a mechanism's body, i.e., the controller's degree of centralization. We experimentally find that for a snake-like robot locomoting through an irregularly spaced peg array, shape-based control results in more effective locomotion when compared to a central pattern generator-based approach.

Keywords:Human-in-the-loop control, Autonomous robots, Robotics Abstract: We propose a new shared control technique that takes into account the operator's intent to quickly relinquish control to the operator in off-nominal conditions. Human-machine shared control is an emerging area of research in which the autonomous control is utilized to augment the operator's performance. Existing work has established that shared control can improve cycle times in nominal conditions, that is, when the operating environment satisfies the assumptions made in the design of the optimal augmenting controller. However, these methods can be too slow to relinquish control in off-nominal cases, when the operator needs to deviate from the nominally optimal trajectory due to unforeseen obstacles or other uncertainties. In this paper, we attempt to address this gap by mathematically quantifying operator intent. The resulting technique provides autonomous control augmentation to the operator when they are attempting to drive the system along the suggested optimal trajectory, but offers little hindrance to the operator when they are attempting to deal with off-nominal conditions. Theoretical results show that the performance of the presented intent aware shared control technique is at least as good as existing techniques, and that it results in improved obstacle reaction time. Human interaction experiments on the Zermelo's navigation problem in the presence of a random pop-up obstacle show a significant reduction in obstacle collision with our method when compared to existing work.

Keywords:Control of networks, Multivehicle systems, Stability of linear systems Abstract: We recently showed for multiagent systems with first-order agent dynamics how information exchange rules represented by a network having multiple layers (multiplex information networks) can be designed for enabling spatially evolving multiagent formations. In this paper, we generalize our earlier results for multiagent systems with general linear dynamics. Specifically, we utilize multiplex information networks for formation density control of multiagent systems. The proposed approach allows capable agents to spatially alter density of the resulting formation while tracking a target of interest - without requiring global information exchange ability, and hence, through local interactions. We provide an illustrative numerical example to demonstrate the efficacy of the proposed distributed control architecture.

Keywords:Control of networks, Network analysis and control, Agents-based systems Abstract: Network connectivity plays an important role in the information exchange between different agents in the multi-level networks. In this paper, we establish a game-theoretic framework to capture the uncoordinated nature of the decision-making at different layers of the multi-level networks. Specifically, we design a decentralized algorithm that aims to maximize the algebraic connectivity of the global network iteratively. In addition, we show that the designed algorithm converges to a Nash equilibrium asymptotically and yields an equilibrium network. To study the network resiliency, we introduce three adversarial attack models and characterize their worst-case impacts on the network performance. Case studies based on a two-layer mobile robotic network are used to corroborate the effectiveness and resiliency of the proposed algorithm and show the interdependency between different layers of the network during the recovery processes.

Keywords:Decentralized control, Stochastic optimal control Abstract: In this paper, we consider finite model approximations of a large class of static and dynamic team problems where these models are constructed through uniform quantization of the observation and action spaces of the agents. The strategies obtained from these finite models are shown to approximate the optimal cost with arbitrary precision under mild technical assumptions. In particular, quantized team policies are asymptotically optimal. This result is then applied to the Gaussian relay channel problem. This result also applies to Witsenhausen's counterexample, which we had studied individually earlier.

Keywords:Control of networks, Networked control systems, Stochastic systems Abstract: Motivated by recent developments in random matrix theory through the study of inverse Littlewood--Offord problems, we investigate the controllability of random binary symmetric matrices. We show that, as the dimension of the state space goes to infinity, the probability of (A,b) being controllable approaches one for many choices of the vector b including elements of the standard basis, the all-one vector, and random binary vectors. In particular, we verify a conjecture of Godsil and show that most systems are controllable from single inputs.

Keywords:Control of networks, Time-varying systems, Distributed control Abstract: This paper considers regulated output synchronization for heterogeneous networks, where agents are non-introspective (i.e. agents have no access to their own states or outputs), non-minimum-phase and are subject to the external disturbances, including process disturbances and measurement noise, with known frequencies. Moreover, the communication network is directed, weighted and time-varying. A purely decentralized linear time-invariant protocol based on a high-gain observer is designed for each agent to achieve regulated output synchronization, i.e. agents’ outputs are asymptotically regulated to a given reference trajectory, even in the presence of external disturbance with known frequencies.

Keywords:Control of networks Abstract: We extend our previous study of vulnerability of a linear network synchronization process to external intrusion at a single network component. Our previous efforts on the topic were limited to undirected graphs. The principal limitation in generalizing to all graph classes is the complexity introduced by the possibility of a non-diagonalizable graph Laplacian. Here, we take a step towards overcoming this hurdle by developing closed-form expressions for the inverse reachability Gramian in cases where the Laplacian has a single nontrivial Jordan block. Our approach for handling a single Jordan block represents a path forward for the more general case of multiple Jordan blocks of varying sizes, and hence towards a complete graphical characterization of vulnerability of networked synchronization processes.

Keywords:Distributed control, Automotive control, Multivehicle systems Abstract: The topological variety significantly affects the platooning of multi-vehicle systems. This paper presents a distributed sliding mode control (SMC) method for vehicular platoons with positive definite topologies. The platoon model is assumed to be homogeneous with strict-feedback nonlinear node dynamics. The design of distributed SMC is divided into two parts, i.e., topological sliding surface design and topological reaching law design. In the former, the sliding surface is defined by weighted summation of individual error, while in the latter, a topologically structured reaching law is proposed to conform with the type of information flow exchange. The Lyapunov method is exploited to prove asymptotic stability of the multi-vehicle system. The effectiveness of this method is validated by numerical simulations.

Keywords:Distributed control, Computational methods Abstract: In this paper, we propose a distributed method to find the solution of the linear equations Ax = b with minimum energy, i.e. the minimum weighted norm associated with the weighted inner product. We first prove that for a special case when the norm is two-norm, the algorithm can make multiple agents reach the minimum two-norm solution of the global linear equations Ax = b if the agents are initialized at the minimum two-norm solutions of their local equations. We then prove that if there are bounded initialization errors, the final convergence of the algorithm is also bounded away from the minimum two-norm solution of the global linear equations. Next, we prove the case with the two-norm replaced with a weighted norm associated with the weighted inner product. Finally, simulation examples are presented to show the effectiveness of the results in this paper.

Keywords:Distributed control, Constrained control, Optimal control Abstract: This paper proposes a Distributed Model Predictive Control (DMPC) approach for a family of discrete-time linear systems with local (uncoupled) and global (coupled) constraints. The proposed approach is based on the dual problem of an overall MPC optimization problem involving all systems. This dual problem is then solved distributively by converting it into a consensus problem for the dual variables associated with the coupled constraints. As the state of convergence is difficult to ascertain, the distributed consensus algorithm yields an inexact solution. By the tightening of the coupled constraints, but not the local constraints, it is still possible to ensure recursive feasibility and exponential stability of the overall closed-loop system. The approach requires that the network of systems be connected and hence, local communications among the systems are needed. The performance of the proposed approach is demonstrated by a numerical example.

Keywords:Distributed control, Decentralized control Abstract: The distributed controllers that have been designed based on the decoupled nominal linear models of agents do not guarantee stabilization of the entire multiagent system in the presence of unknown nonlinearities or agents' interconnections. In this article, we consider a class of multiagent systems with homogeneous linear time-invariant dynamics in the presence of matched or unmatched heterogeneous interconnected unknown nonlinearity. We only measure the relative-state information and design distributed decoupling algorithms enabling agents to independently operate at their desired operating conditions. This goal is achieved by reformulating this distributed decoupling task as an equivalent leader-follower consensus problem. Finally, we investigate feasibility of the proposed ideas through simulation studies.

Keywords:Distributed control, LMIs Abstract: We consider systems that consist of infinitely many identical subsystems over an infinite undirected graph. Stability analysis for such systems is performed and embedded into multiplier theory from robust control. This allows to apply recently developed gain-scheduling methods for dynamic multipliers in order to design stabilizing controllers and yields LMI conditions for their existence that are less conservative than existing ones.

Keywords:Distributed control, Game theory, Agents-based systems Abstract: This paper presents a control technique based on distributed population dynamics under time-varying communication graphs for a multi-agent system structured in a leader-follower fashion. Here, the leader agent follows a particular trajectory and the follower agents should track it in a certain organized formation manner. The tracking of the leader can be performed in the position coordinates x; y; and z, and in the yaw angle phi. Additional features are performed with this method: each agent has only partial knowledge of the position of other agents and not necessarily all agents should communicate to the leader. Moreover, it is possible to integrate a new agent into the formation (or for an agent to leave the formation task)in a dynamical manner. In addition, the formation configuration can be changed along the time, and the distributed population-games-based controller achieves the new organization goal accommodating conveniently the information-sharing graph in function of the communication range capabilities of each UAV. Finally, several simulations are presented to illustrate different scenarios, e.g., formation with time-varying communication network, and time-varying formation.

Keywords:Cooperative control, Stability of linear systems, Agents-based systems Abstract: This paper addresses the positive consensus problem for a homogeneous multi-agent system, by assuming that the agents’ dynamics is described by a positive single-input and continuous-time system. We first provide a necessary condition for the problem solvability that refers to the Frobenius normal form of the Metzler matrix describing the agents’ unforced evolution. This result imposes quite significant constraints on the agents’ description, and it allows to reduce the general problem to the special case when the aforementioned matrix is irreducible. Under this assumption, equivalent sets of conditions that prove to be sufficient for the existence of a solution for the positive consensus problem are derived. Numerical examples illustrate the proposed results.

Keywords:Stability of nonlinear systems, Cooperative control, Distributed control Abstract: Contractive interference functions are a subclass of the standard interference functions used in the design and analysis of distributed power control algorithms for wireless networks. Their peculiarity is that for the resulting positive system the existence and global asymptotic stability of a unique positive equilibrium point is guaranteed. In this paper we give an infinitesimal characterization of nonlinear contractive interference functions in terms of the spectral radius of the Jacobian linearization at any point in the positive orthant. The condition we obtain, that the spectral radius is always less than 1, extends to the nonlinear case an equivalent property of linear interference functions, and leads to a Jacobian characterization similar to the one commonly used in contraction analysis of nonlinear systems.

Keywords:Robust control, Linear systems, Decentralized control Abstract: In this paper we consider the robust optimal con- trol problem for a class of positive systems with an application to design of optimal drug dosage for HIV therapy. We consider uncertainty modeled as a Linear Fractional Transformation (LFT) and we show that, with a suitable change of variables, the structured singular value, μ, is a convex function of the control parameters. We provide graph theoretical conditions that guarantee μ to be a continuously differentiable function of the controller parameters and an expression of its gradient or subgradient. We illustrate the result with a numerical example where we compute the optimal drug dosages for HIV treatment in the presence of model uncertainty.

Keywords:Time-varying systems, Stability of linear systems, Distributed control Abstract: Stable positive linear time-invariant autonomous systems admit diagonal quadratic Lyapunov functions. Such a property is known to be useful in distributed and scalable control of positive systems. In this paper, it is established that the same holds for exponentially stable positive discrete-time and continuous-time linear time-varying systems.

Keywords:Distributed parameter systems, H-infinity control, Linear systems Abstract: A simple form for the optimal H-infinity state feedback of linear time-invariant infinite-dimensional systems is derived. It is applicable to systems with bounded input and output operators and a closed, densely defined, self-adjoint and strictly negative state operator. However, unlike other state-space algorithms, the optimal control is calculated in one step. Furthermore, a closed-form expression for the L2-gain of the closed-loop system is obtained. The result is an extension of the finite-dimensional case, derived by the first two authors. Examples demonstrate the simplicity of synthesis as well as the performance of the control law.

Keywords:Distributed control, Large-scale systems, Game theory Abstract: Quadratic optimization subject to linear con- straints is a fundamental building-block in many other branches of applied mathematics. For large-scale systems, where a common global objective function is neither naturally de- fined nor easily computable, it is natural to view economic equilibrium theory as an alternative approach to design and analysis. Stability and robustness of equilibria can then be studied using the concept of monotonicity. In this paper we prove fundamental monotonicity properties for price dynamics with quadratic utilities. In particular, the main theorem gives quantitative bounds on the size of the monotone cone. Simple examples illustrate the ideas.

Keywords:Game theory, Queueing systems, Traffic control Abstract: We model parking in urban centers as a set of parallel queues and overlay a game theoretic structure. We model arriving drivers as utility maximizers and consider two games: one in which it is free to observe the queue length and one in which it is not. Not only do we compare the Nash induced welfare to the socially optimal welfare, confirming the usual result that Nash is worse for society, we also show that by other performance metrics more commonly used in transportation---such as occupancy and time spent circling---the Nash solution is suboptimal. We find that gains to welfare do not require everyone to observe. Through simulation, we explore a more complex scenario where drivers decide based the queueing game whether or not to enter a collection of queues over a network. Our simulated models use parameters informed by real-world data collected by the Seattle Department of Transportation.

Keywords:Game theory, Autonomous systems, Network analysis and control Abstract: A multi-agent system with uncertainty entails a set of agents intent on maximizing their local utility functions that depend on the actions of other agents and a state of the world while having partial and different information about actions of other agents and the state of the world. When agents repeatedly have to make decisions in these settings, we propose a general class of decision-making dynamics based on the Fictitious Play (FP) algorithm with inertia. We show convergence of the proposed algorithm to pure Nash equilibria for the class of weakly acyclic games---a structural assumption on local utility functions that guarantees existence of pure Nash equilibria---as long as the predictions of the agents of their local utilities satisfy a mild asymptotic accuracy condition. Using the results on the general dynamics, the paper proposes distributed implementations of the FP algorithm with inertia suited for networked multi-agent systems and shows its convergence to pure Nash equilibria. Numerical examples corroborate the analysis providing insights to convergence time.

Keywords:Optimization, Learning, Game theory Abstract: Game theory serves as a powerful tool for distributed optimization in multiagent systems in different applications. In this paper we consider multiagent systems that can be modeled as a potential game whose potential function coincides with a global objective function to be maximized. This approach renders the agents the strategic decision makers and the corresponding optimization problem the problem of learning a maximum of the potential function in the designed game. The paper deals with a emph{payoff-based} approach to such learning. Here, we assume that at each iteration agents can only observe their own played actions and experienced payoffs. To develop the corresponding algorithms guaranteeing convergence to a local maximum of the potential function, we utilize the idea of the well-known Robbins-Monro procedure based on the theory of stochastic approximation.

Keywords:Game theory, Optimization, Computational methods Abstract: The reverse Stackelberg game provides a suitable decision-making framework for hierarchical control problems like network pricing and toll design. We propose a novel numerical solution approach for systematic computation of optimal nonlinear leader functions, also known as incentives, for reverse Stackelberg games with incomplete information and general, nonconcave utility functions. In particular, we apply basis function approximation to the class of nonlinear leader functions, and treat the incentive design problem as a standard semi-infinite programming problem. A worked example is provided to illustrate the proposed solution approach and to demonstrate its efficiency.

Keywords:Game theory, Optimization algorithms, Stochastic systems Abstract: In asymmetric zero-sum games, one player has superior information about the game over the other. It is known that the informed players (maximizer) face the tradeoff of exploiting its superior information at the cost of revealing its superior information, but the basic point of the uninformed player (minimizer)'s decision making remains unknown. This paper studies the finite stage asymmetric repeated games from both players' viewpoints, and derives that not only security strategies but also the opponents' corresponding best responses depends only on the informed player's history action sequences. Moreover, efficient LP formulations to compute both player's security strategies are provided.

Keywords:Game theory, Power systems Abstract: The problem of designing Bayesian incentive compatible, individually rational and revenue maximizing auction for multiple goods and flexible customers is considered. The auctioneer has M goods and N potential customers. Customer i has a flexibility set φi which represents the set of goods the customer is equally interested in. Customer i can consume at most one good from its flexibility set. We first characterize the optimal auction for customers with arbitrary flexibility sets and then consider the case when the flexibility sets are nested. This allows us to group customers into classes of increasing flexibility. We show that the optimal auction can be simplified in this case and we provide a complete characterization of allocations and payments in terms of simple thresholds.

Keywords:Robotics, Biomedical, Optimization Abstract: The focus of this research is to consider control and energy regeneration for a robotic manipulator with both actively and semi-actively controlled joints. The semi-active joints are powered by a regenerative scheme. The problem of designing an impedance controller to track a desired joint trajectory and regenerate energy in the storage element is considered here as a multi-objective optimization problem. Nondominated sorting biogeography-based optimization is used for this purpose. To validate the performance of system, a prosthetic leg which imitates able-bodied gait is considered. A Pareto front is obtained where a pseudo-weight scheme is used to select among solutions. A solution with minimum tracking error (0.0009 rad) fails to regenerate energy (loses 21.56 J), while a solution with poor tracking (0.0288 rad) regenerates energy (gains 167.3 J). A tradeoff results in fair tracking (0.0157 rad) and fair energy regeneration (52.9 J). Results verify that it is possible to regenerate energy at the semi-active joint while still obtaining acceptable tracking. The results indicate that ultracapacitor systems and advanced controls/optimization have the potential to significantly reduce external power requirements in powered prostheses.

Keywords:Linear systems, Computational methods, Optimization Abstract: Modern mechatronic systems are often equipped with a set of redundant actuators due to different operating points and high reliability requirements. One possibility to deal with such systems incorporates a separation between the control task and the distribution of the control effort among the actuators (so-called control allocation). In case of a linear plant model a factorization of the input matrix has to be carried out. The relationship between factorizations can be described by means of invertible transformation matrices. This work investigates the impact of factorization on the computation of generalized inverses and their usage for control allocation. Based on these results a new method for generating generalized inverses, which allows a more effective usage of the available actuators, is developed.

Keywords:Constrained control, Optimization, Decentralized control Abstract: In this paper we consider the synthesis of sparse stabilizing static state feedback controllers subject to state and control constraints. The presence of information constraints renders this problem generically NP-hard. However, as we show in the paper, a convergent sequence of tractable convex relaxations with optimality certificates can be obtained by transforming the problem into a polynomial optimization form. The effectiveness of the proposed technique is illustrated with a numerical example.

Keywords:Optimization, Stochastic systems, Biological systems Abstract: We propose a method for bounding state functionals of a class of nonlinear stochastic differential equations. Given a class of state functionals of a stochastic system, the Feynman-Kac Lemma is a backward in time partial differential equation that describes the evolution of the state functional. We bound these state functionals based on a method which uses barrier functionals. We show that, under the assumption of polynomial data, the bounds can be obtained by using semi- definite programming. The proposed method is then applied to the case study of noise in genetic negative autoregulation to bound a functional of the second moment, which is of specific interest to experimental assays. The bound obtained is found to be in good agreement with experimental results in the literature.

Keywords:Optimization, Energy systems, Optimization algorithms Abstract: We propose a multi-objective optimization algorithm for optimal energy storage by residential customers using Li-Ion batteries. Our goal is to quantify the benefits of optimal energy storage to solar customers whose electricity bills consist of both Time of Use charges (/kWh, with different rates for on-peak and off-peak hours) and demand charges (/kW, proportional to the peak rate of consumption in a month). We first define our energy storage optimization problem as minimization of the monthly electricity bill subject to certain constraints on the energy level and the charging/discharging rate of the battery, while accounting for battery's degradation due to cycling and depth of discharge. We solve this problem by constructing a sequence of parameterized multi-objective dynamic programs whose sets of non-dominated solutions are guaranteed to contain an optimal solution to our energy storage problem. Unlike the standard formulation of our energy storage problem, each of the parameterized optimization problems satisfy the principle of optimality - hence can be solved using standard dynamic programming algorithms. Our numerical case studies on a wide range of load profiles and various pricing plans show that optimal energy storage using Tesla's Powerwall battery can reduce the monthly electricity bill by up to 52% relative to the case where no energy storage is used.

Keywords:Optimization, H-infinity control, Variable-structure/sliding-mode control Abstract: This paper is devoted to the problem of designing a sliding surface for an underlying system, while H2/Hinfty performance specifications of the closed-loop system are under control. This scheme is different from a large number of the existing methods in the literature for the sliding surface design, in the sense that it will penalize the required level of control effort to maintain sliding. This novel scheme consists of two stages. First, exploiting a certain partial eigenstructure assignment method, a state feedback gain is selected that ensures precise locations for some of the closed-loop system poles while minimizing the Hinfty-norm (H2-norm) of a specific closed-loop transfer function and satisfying an H2-norm (Hinfty-norm) constraint on the same or another closed-loop transfer function. Following this, the second stage derives the sliding surface and thereby the control law associated with the particular state feedback designed in the first stage by using one of an approach developed for this purpose. We present a numerical example to demonstrate the remarkable performance of the proposed scheme.

Keywords:Queueing systems, Stochastic systems, Discrete event systems Abstract: Motivated by timeouts in Internet services, we consider networks of infinite server queues in which routing decisions are based on deadlines. Specifically, at each node in the network, the total service time equals the minimum of several independent service times (e.g. the minimum of the amount of time required to complete a transaction and a deadline). Furthermore, routing decisions depend on which of the independent service times achieves the minimum (e.g. exceeding a deadline will require the customer to be routed so they can re-attempt the transaction). Because current routing decisions are dependent on past service times, much of the existing theory on product-form queueing networks does not apply. In spite of this, we are able to show that such networks have product-form equilibrium distributions. We verify our analytic characterization with a simulation of a simple network. We also discuss extensions of this work to more general settings.

Keywords:Stochastic systems, Stability of nonlinear systems, Control applications Abstract: Incremental stability is a property that ensures the uniform asymptotic stability of each trajectory rather than a fixed equilibrium point or trajectory. This makes it a stronger stability notion for dynamical systems. Here, we introduce a notion of incremental stability for stochastic control systems and provide its description in terms of a notion of incremental Lyapunov functions. Moreover, we provide a backstepping controller design scheme providing controllers along with corresponding incremental Lyapunov functions rendering a class of stochastic control systems, namely stochastic Hamiltonian systems, incrementally stable. Moreover, to illustrate the effectiveness of the design approach, we design a controller making a controlled spring pendulum system in a stochastic environment incrementally stable.

Keywords:Stochastic systems, Stability of nonlinear systems, Lyapunov methods Abstract: This paper develops Lyapunov and converse Lyapunov theorems for stochastic semistable nonlinear dynamical systems. Semistability is the property whereby the solutions of a stochastic dynamical system almost surely converge to (not necessarily isolated) Lyapunov stable in probability equilibrium points determined by the system initial conditions. Specifically, we provide necessary and sufficient Lyapunov conditions for stochastic semistability and show that stochastic semistability implies the existence of a continuous Lyapunov function whose infinitesimal generator decreases along the dynamical system trajectories and is such that the Lyapunov function satisfies inequalities involving the average distance to the set of equilibria.

Keywords:Stochastic systems, Stability of nonlinear systems, Lyapunov methods Abstract: In this paper, we deal with asymptotic stability in probability of a class of stochastic systems, which is described by a stochastic differential equation having a square root on the diffusion part. This type of equations are usually used for the modeling of some systems such as population dynamics. A sufficient condition which ensures the asymptotic stability in probability of this class of systems is given using a Lyapunov approach.

Keywords:Stochastic systems, Stochastic optimal control, Optimization Abstract: In this paper, we develop a framework for considering the problem of optimal resource capacity management in general stochastic loss network systems. The stochastic optimization problem consists of determining the capacities of different types of resources that minimize the total weighted loss probabilities over the entire time horizon. Since computing the exact (multi-dimensional) Erlang formula is #P-complete in the size of the network, we first consider the canonical Erlang fixed-point approximation for the blocking probability. We further propose a QED fixed-point approximation for blocking probability which is shown to be asymptotically exact and always outperform Erlang fixed-point approximation. We then improve the stochastic optimization problem by the QED fixed-point approximation. We also design an iterative algorithm to solve the optimization problem and show that it has a unique solution. Finally, we show that this improved optimization problem also converges to the original problem asymptotically in the limiting regime and numerically demonstrate that it yields an improved solution compared to the optimization problem based on the Erlang fixed-point approximation. Numerical experiments have be obtained to confirm and support our theoretical results.

Keywords:Stochastic optimal control, Stochastic systems, Robust control Abstract: This paper proposes a novel optimal control law to improve control performance in an average sense and to guarantee robust stability for discrete-time linear systems with time-invariant stochastic parameters. The time-invariant stochastic parameters cause difficulties in the optimal control problem: the principle of optimality does not hold, and a cost function includes the high-order moments of the parameters which are hard to be computed. The class of linear feedback controllers is focused on to simplify the problem so that it becomes solvable form. To optimize a feedback gain not using the principle of optimality, this paper derives a relation between the objective cost function and the gain. The gradient of the objective function is derived analytically without direct calculation of the high-order moments, which allows us to apply gradient-based optimization methods to the optimal control problem. Robust stability is exactly guaranteed even in the proposed stochastic optimization approach by employing a barrier function ensuring quadratic stability. A numerical simulation demonstrates the control performance and the stability of the proposed method.

Keywords:Estimation, Large-scale systems, Observers for Linear systems Abstract: Based on the same centralized moving horizon estimator (CMHE) with a scalar regularization parameter, two different sensitivity-driven and partition-based moving horizon estimators (PMHEs) are presented and compared. Both are iterative and converge towards the optimum of the underlying CMHE, but their convergence properties are different. In this paper, we discuss the effects of various tuning parameters and the partitioning scheme on their convergence and illustrate these effects with numerical experiments.

Keywords:Observers for Linear systems, Fault tolerant systems, Intelligent systems Abstract: We address the problem of output redundancy in linear plants, wherein the presence of redundant sensors is motivated by an unknown bias or fault affecting each sensor output. In this context, we address the design problem of a nonlinear observer consisting in a linear Luenberger structure augmented with an adaptive weighted pseudo-inverse combination of the available measurements. We characterize a number of properties of the proposed scheme and under certain conditions we establish local asymptotic stability of a certain attractor where the estimation error is zero and the fault is completely rejected. Simulation results are also given to show the potential behind the proposed solution.

Keywords:Observers for Linear systems, Hybrid systems, Stability of hybrid systems Abstract: This paper deals with the problem of state estimation for single-output observable linear systems. A hybrid observer is proposed to estimate the state of the system exactly and in a finite time. Moreover, the proposed hybrid observer provides fixed-time convergence of the state estimation error, i.e. there exists a convergence time that is bounded and such a bound is independent of the initial estimation error. Some simulation results illustrate the effectiveness of the proposed hybrid observer.

Keywords:Observers for Linear systems, Networked control systems, Stochastic systems Abstract: This paper addresses the problem of reliable sensor placement in large scale linear systems with potentially faulty components. The failure probabilities of individual system components are assumed to be known, and the goal is to place sensor outputs so that the network remains observable with high probability. Two different kinds of system component failures are considered in this paper: 1) the failure of arbitrary sensor devices and 2) the failure of arbitrary connections between pairs of state variables (referred to as a link). In addition, we focus on the design from an economic point of view; thus, we aim to identify the minimum number of state variables that need to be measured to meet desired reliability criteria. We recast this problem as an integer program. Although the integer programming problem is known to be NP-complete, we propose a greedy algorithm and characterize its performance with respect to the optimal solution. Consequently, the proposed approach provides an approximate solution to the problem of minimal sensor placement in the presence of stochastic component failure. Finally, we illustrate the obtained results with an example and simulation analysis.

Keywords:Observers for Linear systems, Observers for nonlinear systems, Optimal control Abstract: We address the optimal allocation of the capacity of a single server to buffers with different arrival flows and priority. The well-posedness is studied in a general setting with a state equation having a lower semicontinuous, nonlinear r.h.s. and a linear discounted cost function. The solution of the problem given by a discontinuous feedback control is presented by referring to a two-buffer system under the assumption of the perfect knowledge of the inflow rates. Such an assumption is relaxed by using an output feedback control scheme, for which a reduced-order practical observer is proposed to estimate the unknown inflow rates. Ultimate boundedness is proved for such a setup by using a different control law that takes into account the loss of observability at steady state. The effectiveness of the resulting approach is shown by means of simulations.

Keywords:Sampled-data control, Observers for Linear systems Abstract: This paper deals with the sampled-data control problem based on state estimation for linear sampled-data systems. An impulsive system approach is proposed based on a vector Lyapunov function method. Observer-based control design conditions are expressed in terms of LMIs. Some examples illustrate the feasibility of the proposed approach.

Keywords:Filtering, Estimation, Sensor fusion Abstract: Knowledge of the noise distributions is typically key for reliable state estimation. However, in many applications only the measurement noise can be determined a priori, since only this correspond to measurable quantities. Moreover, modeling of physical systems often leads to nonlinear state-space models with dependent noise sources. Here, we design a computationally-efficient marginalized particle filter for jointly estimating the state trajectory and the parameters of the process noise, assuming dependent noise sources. Our approach relies on marginalization and subsequent update of the sufficient statistics of the process-noise parameters. Results and comparisons for a benchmark example indicate that our method gives clear improvements.

Keywords:Filtering, Estimation, Stochastic systems Abstract: This paper presents theory, application, and comparisons of the feedback particle filter (FPF) algorithm for the problem of attitude estimation. The paper builds upon our recent work on the exact FPF solution of the continuous-time nonlinear filtering problem on matrix Lie groups. In this paper, the details of the FPF algorithm are presented for the problem of attitude estimation – a nonlinear filtering problem on SO(3). Quaternions are employed for computational purposes. The algorithm requires a numerical solution of the filter gain function, and two methods are applied for this purpose. Comparisons are also provided between the FPF and some popular algorithms for attitude estimation, including the multiplicative EKF, the unscented quaternion estimator, the invariant EKF, and the invariant ensemble Kalman filter. Simulation results are presented that help illustrate the comparisons.

Keywords:Filtering, Stochastic systems, Computational methods Abstract: This paper is concerned with numerical algorithms for gain function approximation in the feedback particle filter. The exact gain function is the solution of a Poisson equation involving a probability-weighted Laplacian. The problem is to approximate this solution using only particles sampled from the probability distribution. Two algorithms are presented: a Galerkin algorithm and a kernel-based algorithm. Both the algorithms are adapted to the samples and do not require approximation of the probability distribution as an intermediate step. The paper contains error analysis for the algorithms as well as some comparative numerical results for a non-Gaussian distribution. These algorithms are also applied and illustrated for a simple nonlinear filtering example.

Keywords:Filtering, Statistical learning Abstract: The feedback particle filter (FPF) is an approach to estimating the posterior distribution of the states in a process-observation model. As in other versions of the particle filter, Monte Carlo methods are used to generate and propagate a set of particles, based on the underlying model. The system is designed so that the empirical distribution of the particles approximates the posterior distribution. In contrast to other approaches, particles are propagated as a controlled system using a gain function that is similar in nature to the Kalman gain for linear Gaussian systems. The FPF gain is obtained as a solution to a version of Poisson's equation. Approximation techniques are required, since the FPF gain has no closed-form solution.

This paper presents a new approach to gain synthesis, based in part on a recent breakthrough in the theory of Poisson's equations for diffusions. The architecture begins with a finite-dimensional family of smooth densities (such as a class of Gaussian mixtures). Gain approximation proceeds in two steps: (i) An optimal choice of density is chosen, based on the histogram of particles. Computation can be performed using the expectation maximization (EM) algorithm.

(ii) Based on (i), and approximation to the FPF gain is obtain by applying the gradient-TD Learning algorithm that was recently introduced by the authors.

Keywords:Filtering, Stochastic systems, Nonlinear output feedback Abstract: This paper concerns the filtering problem of stochastic nonlinear systems that depend either on some external input (open-loop system) or on the system output (closed-loop system), through a controller. Such systems are denoted feedback systems. The following result is proven: for feedback systems, the minimum variance estimator belonging to a specific class of functions of the output in the open loop case has better or equal performance than the minimum variance estimator of the same class for the corresponding closed-loop system. Some consequences of this general result are illustrated together with a simple example.

Keywords:Filtering, Information theory and control, Time-varying systems Abstract: In this paper, we revisit the relation between Nonanticipative Rate Distortion (NRD) theory and real-time realizable filtering theory. Specifically, we give the closed form expression for the optimal nonstationary (time-varying) reproduction distribution of the Finite Time Horizon (FTH) Nonanticipative Rate Distortion Function (NRDF) and we establish its connection to real-time realizable filtering theory via a realization scheme utilizing time-varying fully observable multidimensional Gauss-Markov processes. As an application we provide the optimal filter with respect to a mean square error constraint. Unlike classical filtering theory, our filtering approach based on FTH NRDF is performed with waterfilling. We also derive a universal lower bound to the mean square error of any causal estimator to Gaussian processes based on the closed form expression of FTH NRDF. Our theoretical results are demonstrated via an illustrative example.

Keywords:Iterative learning control, Distributed control, Optimal control Abstract: This paper presents a novel approximate dynamic programming (ADP) algorithm for the optimal control of multiscale dynamical systems comprised of many interacting agents. The ADP algorithm presented in this paper is obtained using a distributed optimal control approach by which the performance of the multiscale dynamical system is represented in terms of a macroscopic state, and is optimized subject to a macroscopic description provided by the continuity equation. A value function approximation scheme is proposed and tested using a data set obtained by solving the necessary conditions for optimality for the distributed optimal control problem. The results shows that the proposed approximation method can learn the value function accurately and, thus, may be applied to adapt the optimal control law.

Keywords:Iterative learning control, Feedback linearization, Lyapunov methods Abstract: Iterative learning control laws can be applied to systems that execute the same finite duration task over and over again. Previous research for linear dynamics has used the stability theory of linear repetitive processes to design control laws that have been experimentally verified. This paper applies recently developed stability theory for nonlinear repetitive processes to differential dynamics that can be feedback linearized. The design in then completed by applying the stability theory for linear dynamics. An example using the model of a single-link flexible joint is used to illustrate the new design.

Keywords:Iterative learning control, Game theory, Optimization algorithms Abstract: There is a growing interest in applying Stackelberg games to model resource allocation for patrolling security problems in which defenders must allocate limited security resources to protect targets from attack by adversaries. In real-world adversaries are sophisticated presenting dynamic strategies. Most existing approaches for computing defender strategies calculate the game against fixed behavioral models of adversaries, and cannot ensure success in the realization of the game.

To address this shortcoming, this paper presents a novel approach for adapting preferred strategies in controlled Stackelberg security games using a reinforcement learning (RL) approach for attackers and defenders employing an average rewards. We propose a common framework that combines prior knowledge and temporal-difference method in reinforcement learning. The overall RL architecture involves two highest components: the Adaptive Primary Learning architecture and the Actor-critic architecture. In this work we consider a Stackelberg security game in case of a metric state space for a class of time-discrete ergodic controllable Markov chains games. For computing the equilibrium point we employ the extraproximal method. Finally, a game theory example illustrates the main results and the effectiveness of the method.

Keywords:Iterative learning control, Mechanical systems/robotics, Fault tolerant systems Abstract: In this paper, a novel iterative learning control (ILC) algorithm is presented for a class of joint position constrained robot manipulator systems. Unlike the traditional ILC probelms, where the reference trajectory is iteration invariant, the reference trajectory in this work can be non-repetitive over the iteration domain. A tan-type time-varying Barrier Lyapunov Function (BLF) is proposed to deal with the constraint requirements which can be both time and iteration varying. We show that under the proposed ILC scheme, uniform convergence of the full state tracking error beyond a small time interval in each iteration can be guaranteed over the iteration domain, while the constraints on the joint position vector will not be violated during operation. An illustrative example is presented in the end to demonstrate the effectiveness of the proposed control scheme.

Keywords:Iterative learning control, Mechanical systems/robotics, Linear systems Abstract: In this paper, a novel repetitive control scheme is presented and discussed, based on the so called B-spline filters. This type of dynamic filters are able to provide a B-spline trajectory if they are fed with the sequence of proper control points that define the trajectory itself. Therefore, they are ideal tools for generating online the reference signal with the prescribed level of smoothness for driving dynamic systems, e.g. with a feedforward compensator. In particular, the so-called Continuous Zero Phase Error Tracking Controller (ZPETC) can be used for tracking control of non-minimum phase systems but because of its open-loop nature cannot guarantee robustness with respect to modelling errors and exogenous disturbances. For this reason, ZPETC and trajectory generator have been embedded in a repetitive control scheme that allows to nullify interpolation errors even in non-ideal conditions, provided that the desired reference trajectory and the disturbances are periodic. The asymptotic stability of the overall control scheme has been proved and its performances have been demonstrated by considering a well-known non-minimum phase plant, i.e. a flexible link arm.

Keywords:Iterative learning control, Mechatronics, Linear systems Abstract: Iterative Learning Control (ILC) can significantly improve the performance of systems that perform repeating tasks. Typically, several decentralized ILC controllers are designed and implemented. Such ILC designs tacitly ignore interaction. The aim of this paper is to further analyze the consequences of interaction in ILC, and develop a solution framework, covering a spectrum of systematic decentralized designs to centralized designs. The proposed set of solutions differs in design, i.e., performance and robustness, and modeling requirements, which are investigated in detail. The benefits and differences are demonstrated through a simulation study.

Keywords:Stability of hybrid systems, Agents-based systems, Cooperative control Abstract: This paper investigates the asymptotic stability of a class of switched linear time-invariant discrete-time systems. Without the restriction of switching signals, a novel result is first proposed to guarantee uniform global asymptotic stability. Then, it is applied to studying some consensus problems of linear multi-agent systems under switching network topology. The proposed result modifies some insufficient condition assumed in a related paper and establishes the exponentially fast convergence rate of the multi-agent system. An interesting example illustrates the effectiveness of the derived results.

Keywords:Stability of hybrid systems, Formal verification/synthesis, Hybrid systems Abstract: In this paper, we investigate foundational questions related to the simplification based analysis of input-output stability of hybrid systems. Simulations and bisimulations are canonical notions that provide the relation between the original system and its abstraction that preserve several properties, including safety. However, recent investigations have shown that stability properties are not preserved by these notions. Hence, there have been efforts to strengthen these notions with additional requirements such as continuity on the relations, that enforce preservation of several stability notions including Lyapunov, asymptotic and input-to-state stability. Here, we continue this line of work, and propose strengthenings of simulation/bisimulation relations for preservation of two variants of input-output stability for hybrid systems that are inspired by the incremental input-output stability and incremental state-independent input-output stability for continuous dynamical systems.

Keywords:Stability of hybrid systems, Switched systems, Linear systems Abstract: This paper proposes a new methodology for stability analysis of singularly perturbed linear systems whose dynamics is affected by switches and state jumps. The overall problem is formulated in the framework of hybrid singularly perturbed systems and we use Lyapunov-based techniques to investigate its stability. We emphasize that, beside the stability of slow and fast dynamics, we need a dwell-time condition to guarantee the overall singularly perturbed system is globally asymptotically stable. Furthermore, we characterize this dwell-time as the sum of one term related to the stabilization of systems evolving on one time-scale (slow dynamics) and one term of the order of the parameter defining the ratio between the time-scales. As highlighted in the paper the second term is required to compensate the effect of the jumps introduced in the state of the boundary layer system by the switches and impulses affecting the overall dynamics. Some numerical examples illustrates our results.

Keywords:Stability of hybrid systems, Time-varying systems, Markov processes Abstract: In this work we present necessary and sufficient conditions for mean square stability (MSS) of discrete-time time-inhomogeneous Markov jump linear systems (MJLS) affected by polytopic uncertainties on transition probabilities. We also prove that deciding MSS on such systems is NP-hard and that MSS is equivalent to exponential mean square stability (EMSS) and to stochastic stability (SS).

Keywords:Switched systems, Lyapunov methods, Optimization Abstract: We study the L_p induced gain of discrete-time linear switching systems with graph-constrained switching sequences. We first prove that, for stable systems in a minimal realization, for every p geq 1, the L_p-gain is exactly characterized through switching storage functions. These functions are shown to be the pth power of a norm. In order to consider general systems, we provide an algorithm for computing minimal realizations. These realizations are rectangular systems, with a state dimension that varies according to the mode of the system. We apply our tools to the study on the of L_2-gain. We provide algorithms for its approximation, and provide a converse result for the existence of quadratic switching storage functions. We finally illustrate the results with a physically motivated example.

Keywords:Switched systems, Stability of hybrid systems Abstract: This paper addresses the issue of stabilizability of an autonomous discrete-time switched system via a switching law that is constrained to belong to a language generated by an nondeterministic finite state automaton. Firstly the automaton is decomposed into strongly connected components to reduce the problem to the stabilizability of each non trivial strongly connected component. Secondly the approach considering Lyapunov-Metzler inequalities taking into account the language constraint for a strongly connected component is proposed. Links with the current literature are discussed and a detailed example is given to illustrate our contributions.

Keywords:Stability of nonlinear systems, Stability of linear systems, Discrete event systems Abstract: Sufficient conditions for the existence and convergence to zero of numeric approximations to solutions of asymptotically stable homogeneous systems are obtained for the explicit and implicit Euler integration schemes. It is shown that the explicit Euler method has certain drawbacks for the global approximation of homogeneous systems with non-zero degrees, whereas the implicit Euler scheme ensures convergence of the approximating solutions to zero.

Keywords:Stability of nonlinear systems, Distributed control, Large-scale systems Abstract: The problem under consideration is the synthesis of a distributed controller for a nonlinear network composed of input affine systems. The objective is to achieve exponential convergence of the solutions. To design such a feedback law, methods based on contraction theory are employed to render the controller-synthesis problem scalable and suitable to use distributed optimization. The nature of the proposed approach is constructive, because the computation of the desired feedback law is obtained by solving a convex optimization problem. An example illustrates the proposed methodology.

Keywords:Stability of nonlinear systems, Lyapunov methods, Algebraic/geometric methods Abstract: We study convergence properties of nonlinear systems in the presence of ``almost Lyapunov'' functions which decrease along solutions in a given region not everywhere but rather on the complement of a set of small volume. The structure is quite general except that the system dynamics never vanishes in a region that is away from the equilibrium. It is shown that solutions starting inside the region will approach a small set around the origin as long as the volume where the Lyapunov function does not decrease fast enough is sufficiently small. The main theorem of this paper is established by tracking the change of Lyapunov function value when the solution passes through the above mentioned volume and finding an upper bound of the volume swept out by a neighborhood along the solution before it can achieve an overall gain in its Lyapunov function value. The result shows that the convergence rate is traded off against the size of such small volume that the system can have. In the end a non-trivial example where our theorem is applicable is demonstrated.

Keywords:Stability of nonlinear systems, Lyapunov methods, Iterative learning control Abstract: This paper considers nonlinear discrete and differential repetitive processes using the state-space model setting. These processes are a particular case of 2D systems that have their origins in the modeling of physical processes. Previous research has developed the exponential stability property but for some applications this property may be too strong. To address this issue, the new property of stability in a weak sense is defined and a vector Lyapunov function method was used to obtain sufficient conditions for the existence of this property. Based on these results the property of weak passivity is introduced and used, together with a vector storage function, to develop a new method for output based control law design. An example of a system with nonlinear actuator dynamics and a numerical study of iterative learning control design for a rigid single link robot are given to demonstrate the eventual effectiveness of these new results for applications.

Keywords:Stability of nonlinear systems, Lyapunov methods, LMIs Abstract: Estimating the domain of attraction (DA) of an equilibrium point is a long-standing yet still challenging issue in nonlinear system analysis. The method using the sublevel set of Lyapunov functions is proven to be efficient, but sometimes conservative compared to the estimate via invariant sets. This paper studies the estimation problem of the DA for autonomous polynomial system by using the invariance principle. The main idea is to estimate the DA via sublevel sets of a positive polynomial, which characterizes the boundary of invariant sets. This new type of invariant sets admits the condition that the derivative of Lyapunov functions is non-positive, which generalizes the sublevel set method via Lyapunov functions. An iterative algorithm is then proposed for enlarging the estimate of the DA. Finally, the effectiveness of the proposed method is illustrated by numerical examples.

Keywords:Stability of nonlinear systems, Lyapunov methods, Nonlinear output feedback Abstract: We consider finite volume numerical schemes for stabilizing dynamics governed by scalar nonlinear hyperbolic conservation laws through feedback boundary conditions. Using a discrete Lyapunov function we prove the decay of the discrete solution given by first–order finite volume schemes in conservative form to a desired stationary state up to the order of the time step. Theoretical results are accompanied by a computational example.

Keywords:Autonomous robots, Information theory and control, Closed-loop identification Abstract: Active SLAM is the task of actively planning robot paths while simultaneously building a map and localizing within. Existing work has been focused on planning paths with occupancy grid map, which does not scale well and suffers long term drifts. This work proposes a Topological Feature Graph (TFG) representation that scales well and develops an active SLAM algorithm with it. The TFG uses graphical models, which utilize independences between variables, and enables a unified quantification of exploration and exploitation gains with a single entropy metric. Hence, it facilitates a natural and principled balance between map exploration and refinement. A probabilistic roadmap path-planner is used to generate robot paths in real time. Results from a hardware experiment show that the proposed approach achieves better accuracy than the traditional grid-map based approaches while requiring orders of magnitude less computation and memory resources.

Keywords:Autonomous robots, Information theory and control, Stochastic optimal control Abstract: We study the problem of devising a closed-loop strategy to control the position of a robot that is tracking a possibly moving target. The robot is capable of obtaining noisy measurements of the target’s position. The key idea in active target tracking is to choose control laws that drive the robot to measurement locations that will reduce the uncertainty in the target’s position. The challenge is that measurement uncertainty often is a function of the (unknown) relative positions of the target and the robot. Consequently, a closed-loop control policy is desired which can map the current estimate of the target’s position to an optimal control law for the robot.

Our main contribution is to devise a closed-loop control policy for non-linear target tracking that plans for a sequence of control actions, instead of acting greedily. We seek to minimize the maximum uncertainty (trace of the posterior covariance matrix) over all possible measurements. We exploit the structural properties of an Extended Kalman Filter to build a policy tree that is orders of magnitude smaller than naive enumeration while still preserving optimality guarantees. We show how to obtain even more computational savings by relaxing the optimality guarantees. The resulting algorithms are evaluated through simulations.

Keywords:Information theory and control, Computational methods, Simulation Abstract: Numerical computation of the expected information content of a prospective experimental design is computationally expensive, requiring calculating the Kullback-Leibler divergence of the posterior distribution from the prior for simulated data from a large sample of points from the prior distribution. In this work, we investigate whether the Unscented Transform (UT) of the prior distribution can provide an adequate estimate of the expected information content in the context of experiment design for a previously validated HIV-1 2-LTR model. Three different schedules with evenly distributed time points have been used to generate the experimental data along with the incorporation of qPCR noise for the study . The UT shows promise in estimating information content by preserving the optimal ordering of 2-LTR sample collection schedules, when compared to completely stochastic sampling from the underlying multivariate distributions.

Keywords:Information theory and control, Stochastic optimal control, Linear systems Abstract: Retentive (memory-utilizing) sensing-acting agents may operate under limitations on the communication between their sensing, memory and acting components, requiring them to trade off the external cost that they incur with the capacity of their communication channels. In this paper we formulate this problem as a sequential rate-distortion problem of minimizing the rate of information required for the controller's operation under a constraint on its external cost. We reduce this bounded retentive control problem to the memoryless one, studied in Part I of this work, by viewing the memory reader as one more sensor and the memory writer as one more actuator. We further investigate the structure of the resulting optimal solution and demonstrate its interesting phenomenology.

Keywords:Information theory and control, Stochastic optimal control, Linear systems Abstract: With the increased demand for power efficiency in feedback-control systems, communication is becoming a limiting factor, raising the need to trade off the external cost that they incur with the capacity of the controller's communication channels. With a proper design of the channels, this translates into a sequential rate-distortion problem, where we minimize the rate of information required for the controller's operation under a constraint on its external cost. Memoryless controllers are of particular interest both for the simplicity and frugality of their implementation and as a basis for studying more complex controllers. In this paper we present the optimality principle for memoryless linear controllers that utilize minimal information rates to achieve a guaranteed external-cost level. We also study the interesting and useful phenomenology of the optimal controller, such as the principled reduction of its order.

Keywords:Networked control systems, Information theory and control, Control over communications Abstract: Reachability traditionally thinks about the controllability Grammian of a system, i.e.~the actuation vectors as they pass through the plant dynamics. This perspective depends on fully knowing the future plant dynamics even as we apply controls in the present, since the ability to plan is important for control.

This paper explores a toy model with uncertain random actuation vectors. Our ability to plan is modulated by how much we can anticipate about the plant's future actuation. The results here philosophically build on the concept of ``control capacity'' introduced earlier and the model itself is inspired by earlier work on intermittent Kalman filtering and problems of networked control with packet drops.

A simple greedy strategy is optimal for our toy model and we can easily characterize the informational value of knowing future actuation vectors. Furthermore, the control capacity of the toy system can be stated in a way that is suggestive of a dimensional-sense of ``signal-to-noise-ratio.''

Keywords:Distributed parameter systems, Estimation, Control applications Abstract: This article deals with the observer design problem for the simultaneous estimation of the solid Lithium concentration and of the diffusion parameter for a Single Particle Model of Lithium-Ion Batteries. The design is based on the Backstepping PDE methodology, including a modified Volterra transformation to compensate for the diffusivity uncertainty. The resulting coupled/uncoupled Kernel-PDE and Ordinary Differential Equation (ODE) are recast, via a Sum-of-Squares decomposition, in terms of a convex optimization problem and solved by semidefinite programming, allowing, at each fixed time, an efficient computation of the state and parameter observer gains. In addition, based on the Moment approach, a novel scheme of inversion of the nonlinear output mapping of the Single Particle Model is presented. The effectiveness of this approach is illustrated by numerical simulations.

Keywords:Distributed parameter systems, Delay systems Abstract: In this paper, we consider an Ordinary Differential Equation (ODE) with convection and diffusion in the actuation path. We prove that a prediction-based controller, designed to compensate for the sole convective PDE, actually achieves exponential stabilization of the complete plant, provided that diffusion is small enough. Our result is obtained in L_p norm and covers two cases, full-state feedback and boundary feedback. Simulation results emphasize the validity of this approach.

Keywords:Distributed parameter systems, Distributed control, Fault detection Abstract: This work proposes a synchronization controller for a class of networked finite and infinite dimensional systems. The leader, or reference model is assumed known and networked controllers are proposed to ensure that each networked system follows the leader and synchronize with each other. An attack, which takes the form of severing a link or reversing the sign of a synchronization gain, is assumed to occur at an unknown time, and its goal is to either desynchronize or destabilize the networked systems. Adaptive detection observers are designed to monitor the systems and at the onset of an attack, declare the presence of an attack and subsequently engage in an attack accommodation via an appropriate control reconfiguration. To enhance robustness against false alarms and minimize the detection time, time varying thresholds are introduced. When any of the residuals exceed the time varying thresholds, an attack in the networked systems is declared. Migrating to the infinite dimensional case requires additional assumptions and the corresponding stability and convergence results are not trivially extendable. A numerical example of four networked diffusion PDEs is included in order to provide an insight on the effects of a fixed threshold in detecting the presence of an attack and on the effects of accommodation in aiding the systems to recover by resynchronizing.

Keywords:Distributed parameter systems, Linear systems, H-infinity control Abstract: In this paper we present an overview/tutorial of the existing results and a constructive solution for the sub-optimal Hankel norm approximation problem for the Wiener class of infinite-dimensional systems. The presented approach is based on frequency domain techniques. The construction of a solution uses a recent result on the continuity of the J-spectral factorization in the Wiener norm. The Wiener class of systems is large enough to include many infinite-dimensional matrix-valued transfer functions used in mathematical modelling of different areas applications such as optimal control, prediction, physics-based modelling (to mention only a few). Therefore we believe that our approach should be of interest not only for systems theorists but also for control engineers when dealing with applications using infinite-dimensional system models and their approximations.

School of Automation and Electrical Engineering, Univ. of S

Keywords:Distributed parameter systems, Lyapunov methods, Constrained control Abstract: Aerial refueling systems have been widely used to extend the flying distance in the military. This paper addresses the vibration control problem for an aerial refueling system. The aerial refueling system is modeled as a distributed parameter system governed by hybrid PDE-ODEs. Two control laws applied on the receiving aircraft and the tanker, respectively, are designed cooperatively to: (i) regulate the deformation of the flexible hose, and (ii) constrain the transverse displacement of the tanker within a certain range. With the designed control, for initial conditions within the constrained range, the asymptotic stability of the closed-loop system is achieved and the constraint is not violated. Simulations are given to illustrate the control performance.

Keywords:Distributed parameter systems, Lyapunov methods, PID control Abstract: This paper addresses the multivariable PI regulation control of a class of linear systems described by hyperbolic partial differential equations. Both the input control and the output measurement are situated on the boundary. First, the system is transformed into the characteristic form of Riemann invariants, and the PI controller design is proposed for the Riemann invariant system. Then, a Lyapunov functional is constructed to prove stabilization and regulation of the closed-loop system. Finally, we apply the designed PI controller for a nonlinear Saint-Venant model and carry out numerical simulations to evaluate the performances of the designed PI controller.

Keywords:Autonomous robots, Feedback linearization Abstract: A control strategy for trajectory tracking of straight line trajectories for autonomous surface vehicles (ASV) is presented in this paper. Our control strategy is based on input-output feedback linearization with the so called hand position point as output. This is motivated by a method previously used for ground autonomous vehicles, without external disturbances. The proposed control strategy may be used also for path following. The control approach proposed in this paper is furthermore able to deal with external disturbances, e.g. unknown irrotational ocean currents, and gives an estimate of the disturbance. Using Lyapunov analysis, almost-global asymptotic stability (almost-GAS) of the closed-loop system is proven. Simulation results are included to validate the theoretical result.

Keywords:Feedback linearization, Constrained control, Stability of nonlinear systems Abstract: The tokamak is a torus-shaped machine in which a reactant ionized gas (plasma) is confined using magnetic fields for the purpose of generating energy from nuclear fusion reactions. In order to be commercially competitive, a tokamak needs to operate for long periods of time at high-performance operating points. Those high-performance scenarios are characterized by a steady-state, stable plasma operation, which is closely related to a property of the plasma that is known as the safety factor, q. Therefore, control of the q profile is one of the crucial aspects to the success of tokamaks. Significant research has been carried out by the fusion community to find control algorithms for the q profile. Most of that previous work makes use of approximate linearization and linear control techniques. In the present work, we propose a nonlinear model- based controller for the regulation of the q profile using feedback linearization. This nonlinear control approach may be applicable to a greater range of operating conditions, and may be able to reject larger perturbations than previous linear controllers. The effectiveness of the controller is demonstrated via a simulation study based on a DIII-D scenario.

Keywords:Lyapunov methods, Feedback linearization, Spacecraft control Abstract: The purpose of attitude stabilization is to stabilize a body about an equilibrium point, usually requiring at least three independent actuations. In practice, however, a control law for an underactuated system with two actuators becomes crucial when one of the three actuators fails during operation, or when the control objective is to stabilize the spin axis of the body about an arbitrary direction, possibly with a nonzero spinning velocity. In this work, we develop a feedback control law that globally and asymptotically achieves spin-axis stabilization of a rigid body about an arbitrary axis using only two reaction wheels. For this, a modified version of (z,w)- parameterization is presented for the purpose of describing attitude kinematics of a rigid body. We then introduce dynamics of the body with two reaction wheels and use a feedback linearization technique to develop a control law with the goal of achieving spin-axis stabilization of the body. We show that the developed control law is globally and asymptotically stable by using Lyapunov’s direct method in conjunction with LaSalle’s invariance principle. This controller is implemented in simulation, and results are presented that show its stabilizing behavior. While the control law presented here is suitable for general applications, we primarily focus on its application to the thrust direction regulation of tensegrity hoppers.

Keywords:Feedback linearization, Optimization algorithms, Linear systems Abstract: This paper presents a novel approach for trajectory tracking of non-minimum phase systems. Classical stable inversion is an effective method to get precise trajectory tracking but with a large enough extended time interval. The method proposed is to solve this problem of large extended time restriction. It can get precise tracking of the reference trajectory with smaller extended time interval and nice overall tracking of the extended reference trajectory. This proposed method is the optimal combination of pre-actuation, post-actuation and optimal state transition techniques. The time intervals for pre-actuation, post-actuation and optimal state transition can be chosen flexibly so as to have a very nice tracking for different extended time intervals. The effectiveness of the proposed method is validated though simulations for the non-minimum phase system.

Keywords:Feedback linearization, Stability of nonlinear systems Abstract: In this paper approximate feedback linearization is revisited by introducing a dynamic extension. It is shown that, under mild assumptions, a nonlinear system with state of dimension n can be immersed into an extended system that comprises a chain of n integrators, hence with linear input/output behavior, which contains all the components of the state of the original nonlinear system. This result is achieved systematically and without resorting to the solution of any partial differential equation. Moreover, it is not required that the nonlinear system be linearly controllable, hence feedback linearizable in the classical sense. The construction is then specialized to provide a linear design technique to define control laws that enforce (local) asymptotic stability of a desired equilibrium point or asymptotic tracking of reference signals. The performance of the design methodology are assessed by means of two numerical examples, encompassing a locally uncontrollable planar system with a non-hyperbolic equilibrium point and the celebrated Ball and Beam model.

Keywords:Predictive control for nonlinear systems, Robust control, Feedback linearization Abstract: Robust predictive control of non-linear systems under state estimation errors and input and state constraints is a challenging problem, and solutions to it have generally involved solving computationally hard non-linear optimizations. Feedback linearization has reduced the computational burden, but has not yet been solved for robust model predictive control under estimation errors and constraints. In this paper, we solve this problem of robust control of a non-linear system under bounded state estimation errors and input and state constraints using feedback linearization. We do so by developing robust constraints on the feedback linearized system such that the non-linear system respects its constraints. These constraints are computed at run-time using online reachability, and are linear in the optimization variables, resulting in a Quadratic Program with linear constraints. We also provide robust feasibility, recursive feasibility and stability results for our control algorithm. We evaluate our approach on two systems to show its applicability and performance.

Keywords:Formal verification/synthesis, Automotive control Abstract: Composing controllers designed individually for interacting subsystems, while preserving the guarantees that each controller provides on each subsystem is a challenging task. Motivated by this challenge, we consider in this paper the problem of synthesizing safety controllers for linear parameter varying subsystems, where the system matrices of each subsystem depend (possibly nonlinearly) on the states of the other subsystems. In particular, we propose a method for synthesis of controlled invariant sets and associated controllers, that is robust against affine parametric uncertainties in the system matrices. Then we show for certain classes of parameter dependencies how to quantify the uncertainty imposed on the other subsystems by convexifying, with an affine map, the effects of these parameters. An analysis of this quantification is provided. In the second part of the paper, we focus on an application of this method to vehicle safety systems. We demonstrate how controllers for lane-keeping and adaptive cruise control can be synthesized in a compositional way using the proposed method. Our simulations illustrate how these controllers keep their individual safety guarantees when implemented simultaneously, as the theory suggests.

Keywords:Formal verification/synthesis, Autonomous robots, Robotics Abstract: In this paper, we study the problem of controlling a two-dimensional robotic swarm with the purpose of achieving high level and complex spatio-temporal patterns. We use a rich spatio-temporal logic that is capable of describing a wide range of time varying and complex spatial configurations, and develop a method to encode such formal specifications as a set of mixed integer linear constraints, which are incorporated into a mixed integer linear programming problem. We plan trajectories for each individual robot such that the whole swarm satisfies the spatio-temporal requirements, while optimizing total robot movement and/or a metric that shows how strongly the swarm trajectory resembles given spatio-temporal behaviors. An illustrative case study is included.

Keywords:Formal verification/synthesis, Autonomous systems Abstract: We consider the problem of synthesizing safe-by-design control strategies for semi-autonomous systems. Our aim is to address situations when safety cannot be guaranteed solely by the autonomous, controllable part of the system and a certain level of collaboration is needed from the uncontrollable part, such as the human operator. In this paper, we propose a systematic solution to generating least-limiting guidelines, i.e. the guidelines that restrict the human operator as little as possible in the worst-case long-term system executions. The algorithm leverages ideas from 2-player turn-based games.

Keywords:Formal verification/synthesis, Computational methods, Distributed control Abstract: We present a method to decompose synthesis of controllers for safety specifications into smaller controller synthesis problems. The method applies to systems that we call decomposable, which means that their transition relations can be expressed as the meet of some number of transition relations over disjoint inputs. The method presented here is based on assume-guarantee reasoning and is shown to be correct and complete: a controller enforces the safety specification if and only if it can be obtained by this method.

Keywords:Formal verification/synthesis, Delay systems, Hybrid systems Abstract: Dead times exist in many physical plants. They degrade control performances and may make the plant unstable. A Smith predictor is a classical but commonly used approach to the improvement of the performance of the controller. On the other hand, a symbolic approach is useful for the design of an embedded controller. In this paper, we consider a control problem of a plant with a dead time, whose abstracted behaviors are given by a transition system with an FIFO queue to model the dead time. A desired behavior is also given by a transition system, and there exists a symbolic controller for the control specification in the case where there is no dead time. Then, we introduce a symbolic Smith predictor, and propose a configuration of a symbolic controller containing the symbolic Smith predictor. Using an aASR between the controller and the plant, we show that the controlled plant exhibits a desired behavior.

Keywords:Formal verification/synthesis, Discrete event systems, Linear systems Abstract: Designing control policies from complex specifications has drawn significant attention in recent years. Metric temporal logic (MTL) is a specification formalism for describing a wide range of temporal properties with specific timing constraints. In this paper, we focus on discrete time linear control systems and specifications given as MTL formulas over linear predicates in the states. We present a method based on polyhedral projection to find the set of all initial states from which all trajectories satisfying MTL formulas can be generated. An illustrative example is included.

Keywords:Model/Controller reduction, Computational methods, Algebraic/geometric methods Abstract: An algorithm is provided to reduce an unobservable rational system to an observable rational system while preserving its input-output behavior. The core of the algorithm lies in finding generators for the observation algebra generated by the unobservable rational system. Respective steps of the algorithm refer to standard operations in algebraic geometry. Examples are provided.

Keywords:Model/Controller reduction, Control of networks, Network analysis and control Abstract: In this paper, we analyze the eigenstructure of network systems having symmetrical graph motives and apply it to reduced order controller design based on their aggregated models. In the eigenstructure analysis, formulating the symmetry of graph motives as the graph automorphism, we show that particular eigenspace decomposition of network systems can be found by analyzing the common eigenspaces of all possible permutation matrices, with regard to the graph automorphism. This eigenspace decomposition explains the appearance of uncontrollable and unobservable subspaces that can be removed by aggregating, i.e., averaging, symmetrical graph motives. Furthermore, it turns out that the resultant aggregated model, whose state behavior tracks a kind of centroids of that of the original network system, has good compatibility with observer-based state feedback controller design. The efficiency of the aggregated controller design method is numerically demonstrated by output regulation of second-order oscillator networks.

Keywords:Network analysis and control, Model/Controller reduction, Statistical learning Abstract: In this paper a novel model order reduction method for nonlinear systems is proposed. Differently from existing ones, the proposed method provides a suitable nonlinear projection, which we refer to as control-oriented deep autoencoder (CoDA), in an easily implementable manner. This is done by combining noise response data based model reduction, whose control theoretic optimality was recently proven by the author, with stacked autoencoder design via deep learning.

Keywords:Networked control systems, Model/Controller reduction Abstract: In this paper, we propose the notion of controllability Gramian for linear network systems. In contrast to the conventional Gramians defined for asymptotically stable systems, the new Gramian is generalized to semi-stable systems and can be computed for network systems with imaginary axis poles. We also extend the Lyapunov equations to solve the network controllability Gramian. Based on this Gramian, we propose an efficient method to evaluate the H2-norms of network systems. The result is then applied to design a model reduction procedure for network systems using the clustering-based projection.

Keywords:Model/Controller reduction, Optimization algorithms, Optimization Abstract: In this paper, a new optimization problem formulation of the H^2 optimal model reduction problem is introduced and discussed. The optimization problem is shown to be a problem on a product manifold, which is a Riemannian submanifold of a Euclidean space. Geometry of the resultant optimization problem is investigated and the Riemannian conjugate gradient method for the problem is proposed. Solutions obtained by the proposed method realize stable reduced order systems if the original system satisfies a certain condition, which holds for example for dissipative systems. It is shown by numerical experiments that the proposed method is effective for large-scale problems.

Keywords:Model/Controller reduction, Uncertain systems Abstract: This paper considers the problem of complexity reduction for systems with affine parametric uncertainty. We are interested in the relation between model reduction for a nominal plant and dimension reduction for a parameter vector. By using linear fractional representations of the system, it is shown that a projection-based reduction approach can be applied separately to the generalized plant and the uncertainty block. The error bounds between the original system and its reduced order approximation are derived, and a case study is used to validate our findings.

Keywords:Smart grid, Decentralized control, Large-scale systems Abstract: We address the problem to control the charging schedules in a large population of plug-in electric vehicles, considered as heterogeneous noncooperative agents, with different strongly convex quadratic cost functions weakly coupled by a common pricing signal, and convex charging constraints, e.g. plug-in times, deadlines and capacity limits. We assume a minimal information structure through which a central controller can broadcast incentive signals to coordinate the decentralized optimal responses of the agents. We propose a dynamic con- troller that, based on fixed point operator theory arguments, ensures global exponential convergence to an aggregative Nash equilibrium for large population size. We build upon the recent literature, further address general convex quadratic cost func- tions and convex constraints, and show exponential convergence without imposing technical assumptions. Finally, we illustrate the benefits of the proposed control law via numerical simulations, where the aggregate charging demand tends to fill the overnight demand valley.

Keywords:Smart grid, Distributed control, Decentralized control Abstract: We consider the problem of controlling the reactive power injection of microgenerators to regulate the voltage profile in a power distribution network. We consider a large class of purely local controllers including most of the solutions proposed in the literature, and we show that these strategies do not guarantee the desired regulation; namely, that for each of them there are equilibria that are not feasible with respect to the desired voltage constraints. We then show that, by adding short range communication between microgenerators, it is possible to design control strategies that provably converge to the feasible set, and we propose one possible strategy. This fundamental performance gap between local and networked strategies is finally illustrated via simulations.

Keywords:Smart grid, Distributed control, Predictive control for linear systems Abstract: High penetration of Distributed Generation (DG) in Medium Voltage (MV) power grids usually leads to abrupt voltage raises in the presence of either low demand conditions or high power production from renewable sources. In order to cope with the possibly resulting voltage limits violation, a typical adopted approach is the disconnection of the distributed generators or the curtailment of the generated power leading to several disadvantages. To address this issue a Command Governor (CG) approach is proposed for the online management of the reactive power of distributed generators. The method is aimed at solving a constrained voltage control problem in both centralized and distributed ways. The approach envisages an active coordination between some controllable devices of the grid, e.g. distributed generators, MV/HV transformers, in order to maintain relevant system variables within prescribed operative constraints in response to unexpected adverse conditions. In the final simulation example, the proposed approach presents an increased level of effectiveness with respect to heuristic methods imposed by the current Italian norms on reactive power compensation.

Keywords:Smart grid, Distributed parameter systems, Fault tolerant systems Abstract: In this paper, the issue of data-driven modeling of a single load in a laboratory set-up is confronted with the same data-driven modeling of the same load, but in a real grid environment. As it is argued here, an aggregation effect of all of the loads in a grid endows a single load with grid-characteristics properties in addition to the usual load-specific properties. Topologically, the hidden feedback structure of a bus model reveals that the resulting digraph is strongly connected, meaning that all loads are intertwined in a single system that cannot be decomposed into islands.

Keywords:Power systems, Smart grid Abstract: Wide-area control is an effective mean to reduce inter-area oscillations of the bulk power system. Its dependence on communication of remote measurement signals makes the closed-loop system vulnerable to cyber attacks. This paper develops a framework to analyze and quantify resilience of a given wide-area controller under disruptive attacks on certain communication links. Resilience of a given controller is measured in terms of closed-loop eigenvalues under the worst possible attack strategy. The computation of such a resilience metric is challenging especially for large-scale power systems due to the discrete nature of attack strategies. In this paper, we propose an optimization-based formulation and a convex relaxation approach to facilitate the computation. Furthermore, we develop an efficient algorithm for the relaxed problem with guaranteed convergence to identify structural vulnerabilities of the system. Simulations are performed on the IEEE 39-bus system to illustrate the proposed resilience analysis and computation framework.

Keywords:Smart grid, Energy systems, Game theory Abstract: The aggregation of renewable energy has significant potential to mitigate undesirable characteristics such as intermittency and variability and thereby facilitate grid integration. Using cooperative game theory, it has been shown that aggregation is also beneficial for renewable energy producers because they can increase their expected profit by making a coalition, bidding a joint contract that maximizes the expected profit and sharing the profit in a way that keeps the game stable. However, we show that the realized (as opposed to expected) profit of the coalition, using the contract that maximizes the expected profit, cannot be suitably distributed among its members. We propose an alternative coalition contract and prove that it allows for a satisfactory distribution of the realized profit among the coalition members keeping the game stable. We design a new payoff allocation that lies in the core of the game of the realized profit.Finally, we analyze the cost of stabilizing the game by evaluating the loss of expected profit that a coalition incurs by bidding the stabilizing contract.

State Key Lab. of Management and Control for Complex Syste

Keywords:Intelligent systems, Learning, Robust adaptive control Abstract: In this paper, we study the adaptive-critic-based event-driven robust state feedback stabilization for a class of uncertain nonlinear systems. The novel idea lies in bringing adaptive dynamic programming, a self-learning optimization approach, into nonlinear robust control area under uncertain environment and event-triggering framework. Through theoretical analysis, the nonlinear robust stabilization is achieved by deriving an event-driven optimal controller of the nominal system. The adaptive-critic-based technique is adopted to facilitate the optimal control design, with a critic neural network being constructed to serve as the learning approximator. The control performance is also verified via simulation study. Significantly, combining the adaptive-critic-based design method with event-triggering formulation is a potential and promising direction of intelligent control since it can make better use of advanced learning behavior and limited computation resources.

Keywords:Robotics, Adaptive control, Learning Abstract: In this article we provide experimental results and evaluation of a compensation method which improves the tracking performance of a nominal feedback controller by means of reinforcement learning (RL). The compensator is based on the actor-critic scheme and it adds a correction signal to the nominal control input with the goal to improve the tracking performance using on-line learning. The algorithm has been evaluated on a 6 DOF industrial robot manipulator with the objective to accurately track different types of reference trajectories. An extensive experimental study has shown that the proposed RL-based compensation method significantly improves the performance of the nominal feedback controller.

Keywords:Neural networks, Intelligent systems, Learning Abstract: In this paper, a novel approximate optimal distributed control of a class of uncertain nonlinear interconnected system with event-sampled state vector is presented by using approximate dynamic programming (ADP). The event-sampled function approximation property of the neural network (NN) is utilized to generate a solution to the Hamilton-Jacobi-Bellman (HJB) equation and subsequently to obtain an optimal control policy of each subsystem in a forward-in-time manner. To relax the accurate knowledge of subsystem and interconnection dynamics, and input gain matrix, a novel NN identifier with event sampled state vector is designed at each subsystem. An adaptive event sampling condition and novel weight tuning rules for the NN identifier and NN controller using the Lyapunov stability theory are derived. To attain optimality faster, an iterative learning scheme is embedded within the inter-event part of the sampling interval along with time-driven learning at the event sampled instants. Further, the benefit of incorporating exploration in this event sampled framework to improve optimality is discussed along with the challenges involved. The state vector of the interconnected system and the weight estimation errors of the NN identifier and controller are demonstrated to be locally uniformly ultimately bounded (UUB). Finally, the analytical design is verified via simulation.

Keywords:Information theory and control, Autonomous systems, Time-varying systems Abstract: The key challenge for learning-based autonomous systems operating in time-varying environments is to predict when the learned model may lose relevance. If the learned model loses relevance, then the autonomous system is at risk of making wrong decisions. The entropic value at risk EVAR is a computationally efficient and coherent risk measure that can be utilized to quantify this risk. In this paper, we present a Bayesian model and learning algorithms to predict the state-dependent EVAR of time-varying datasets. We discuss applications of EVAR to an exploration problem in which an autonomous agent has to choose a set of sensing locations in order to maximize the informativeness of the acquired data and learn a model of an underlying phenomenon of interest. We empirically demonstrate the efficacy of the presented model and learning algorithms on four real-world datasets.

Keywords:Control of networks, Adaptive control, Networked control systems Abstract: In this paper we present a generic distributed weight adaptation framework to optimize some network observables of interest. We focus on the algebraic connectivity λ_{2},the spectral radius λ_{n}, the synchronizability λ_{n}/λ_{2}, or the total effective graph resistance Ω of undirected weighted networks, and describe distributed systems for the estimation of these functions and their derivatives for on-line adaptation of the edge weights.

Keywords:Optimal control, Linear systems, Output regulation Abstract: This paper studies the problem of adaptive optimal output regulation for discrete-time linear systems. A data-driven output-feedback control approach is developed via approximate/adaptive dynamic programming (ADP). Different from the existing literature of ADP and output regulation theory, the optimal controller design proposed in this paper does not require the knowledge of the plant and exosystem dynamics. Theoretical analysis and an application on an inverted pendulum system show that the proposed methodology serves as an effective tool for solving adaptive optimal output regulation problems.

Keywords:Systems biology, Stochastic systems, Metabolic systems Abstract: A basic (though rather general) enzymatic reaction scheme is investigated here, with a substrate that transforms into a product by means of the catalytic action of an enzyme. The aim is of quantifying the effects of feedback in noise propagation. Noise sources are twofold: one affects the enzyme production, assuming to happen according to finite bursts of molecules; the other concerns the product clearance, with the classical linear elimination rate affected by a Bernoulli random variable that can switch `on' or `off' the clearance. Two distinct feedback control schemes on enzyme production are considered here: one from the final product of the pathway activity, the other from the enzyme accumulation (negative autoregulation). Metabolic noise is defined in terms of the square of the coefficient of variation of the product, and computations are carried out by means of moment equations. Results show that, according to the type of the feedback parameter chosen to tune the feedback action, one of the two feedback schemes is preferable to the other with respect to noise reduction.

Keywords:Biomolecular systems, Cellular dynamics, Markov processes Abstract: We present a diagram technique for the derivation of cumulant equations with zero-cumulant closure for the approximate description of biomolecular reaction networks. Our approach is applicable both to the chemical master equation and to the Kramers-Moyal expansion. It allows one to "see" the structure of the equations. This facilitates the investigation of the properties of the approximation and the comparison with other approximation methods. As an example of this, we derive a transparent relation between the cumulant equations for the chemical master equation and for the Kramers-Moyal expansion.

Keywords:Cellular dynamics, Biological systems, Systems biology Abstract: A ubiquitous feature of all living cells is their growth over time followed by division into two daughter cells. How a population of genetically identical cells maintains size homeostasis, i.e., a narrow distribution of cell size, is an intriguing fundamental problem. We model size using a stochastic hybrid system, where a cell grows exponentially over time and probabilistic division events are triggered at discrete time intervals. Moreover, whenever these events occur, size is randomly partitioned among daughter cells. We first consider a scenario, where a timer (i.e., cell-cycle clock) that measures the time since the last division event regulates cellular growth and the rate of cell division. Analysis reveals that such a timer-driven system cannot achieve size homeostasis, in the sense that, the cell-to-cell size variation grows unboundedly with time. To explore biologically meaningful mechanisms for controlling size we consider two different classes of models: i) a constant growth rate and size-dependent division rate and ii) a constant growth rate and division rate that depends both on the cell size and timer. We show that each of these strategies can potentially achieve bounded intercellular size variation, and derive closed-form expressions for this variation in terms of underlying model parameters. Finally, we discuss how different organisms have adopted the above strategies for maintaining cell size homeostasis.

Keywords:Adaptive systems, Biomolecular systems, Genetic regulatory systems Abstract: In order to function reliably, synthetic molecular circuits require mechanisms that allow them to adapt to environmental disturbances. Least mean squared (LMS) schemes, such as commonly encountered in signal processing and control, provide a powerful means to accomplish that goal. In this paper we show how the traditional LMS algorithm can be implemented at the molecular level using only a few elementary biomolecular reactions. We demonstrate our approach using several simulation studies and discuss its relevance to synthetic biology.

Keywords:Systems biology, Stochastic systems, Reduced order modeling Abstract: In this paper, we focus on model reduction of biomolecular systems with multiple time-scales, modeled using the Linear Noise Approximation. Considering systems where the Linear Noise Approximation can be written in singular perturbation form, with epsilon as the singular perturbation parameter, we obtain a reduced order model that approximates the slow variable dynamics of the original system. In particular, we show that, on a finite time-interval, the first and second moments of the reduced system are within an O(epsilon)-neighborhood of the first and second moments of the slow variable dynamics of the original system. The approach is illustrated on an example of a biomolecular system that exhibits time-scale separation.

Keywords:Biological systems, Stochastic systems, Cellular dynamics Abstract: Bacteriophages - viruses that infect and replicate inside bacteria - undergo rapid degradation outside their hosts. Thus, a common expectation is that phages will minimize environmental exposure by maximizing their adsorption rate, i.e., infection rate. Here we show that, while maximized adsorption is a good strategy when bacterial host cells are healthy, situations exist where bypassing hosts may be beneficial, such as when host cells are not productive for infection. In these situations, optimal adsorption rates may take on intermediate values, thereby increasing phage dispersal. We aim to develop a theoretical understanding of the intermediate, optimal adsorption rate for phage λ, in environments where changing conditions lead to either good or poor quality hosts. We develop a Markov chain model and define optimal adsorption as the adsorption rate that maximizes the probability of survival. We impose experimentally-achievable periodicity in environmental change and derive novel analytic results for the probability of phage λ survival, from which optimal adsorption is computed. We then discuss the sensitivity of the phage survival probability to relevant biological parameters and environmental conditions. Finally, we extend these results to approximate the probability of phage λ survival when environment change is random, which better represents of natural dynamics, and show that stochasticity facilitates phage λ survival in sub-optimal conditions.

Keywords:Agents-based systems, Sensor networks, Estimation Abstract: Consider a community of agents, all performing a predefined task, but with different abilities. Each agent may be interested in knowing how well it performs in comparison with her peers. This general scenario is relevant, e.g., in Wireless Sensor Networks (WSNs), or in the context of crowd sensing applications, where devices with embedded sensing capabilities collaboratively collect data to characterize the surrounding environment, but the performance is very sensitive to the accuracy of the gathered measurements.

In this paper we present a distributed algorithm allowing each agent to self-rate her level of expertise/performance at the task, as a consequence of pairwise interactions with the peers. The dynamics of the proportions of agents with similar beliefs in their expertise are described using continuous-time state equations. The existence of an equilibrium is shown. Closed form expressions for the various proportions of agents with similar belief in their expertise is provided at equilibrium. Simulation results match well theoretical results in the context of agents equipped with sensors aiming at determining the performance of their sensors.

Keywords:Autonomous robots, Sensor networks, Optimal control Abstract: In this paper, we present a novel informative path planning algorithm using an active sensor for efficient environmental monitoring. While the state-of-the-art algorithms find the optimal path in a continuous space using sampling-based planning method, such as rapidly-exploring random graphs (RRG), there are still some key limitations, such as computational complexity and scalability. We propose an efficient information gathering algorithm using an RRG and a stochastic optimization method, cross entropy (CE), to estimate the reachable information gain at each node of the graph. The proposed algorithm maintains the asymptotic optimality of the RRG planner and finds the most informative path satisfying the cost constraint. We demonstrate that the proposed algorithm finds a (near) optimal solution efficiently compared to the state-of-the-art algorithm and show the scalability of the proposed method. In addition, the proposed method is applied to multi-robot informative path planning.

Keywords:Estimation, Sensor networks, Stochastic optimal control Abstract: In this paper, we consider a sensor scheduling and remote estimation problem over an additive noise channel. At each time, the sensor observes the state of a one-dimensional stochastic process, and then decides whether to transmit its observation to the remote estimator or not. The sensor is restricted to transmit its observations for no more than a fixed number of times. If the sensor decides to transmit its observation, it sends the observation to the encoder, who then sends an encoded message over the communication channel. The remote estimator generates real time estimates on the source based on the information received from the encoder. Different from problems considered in prior work, which assumed that the encoder has a constraint on the stagewise encoding power, we consider in this paper a more general setting where the encoder has a constraint on the total power over the time horizon. Under some technical assumptions, we obtain team optimal decision strategies. Moreover, we uncover a rather surprising result that under optimal strategies the encoding power allocated to each stage is the same.

Keywords:Sensor networks, Linear systems Abstract: We introduce the `security index' of a discrete-time, linear time-invariant system under sensor attacks as a quantitative measure on the vulnerability of an observable system. Ideas from linear coding theory are employed in providing conditions for attack detection and correction in terms of a system's security index, along with methods for its computation based on different representations of a system. Moreover, we provide conditions in which the security index of a control system can be manipulated under state feedback. Finally, algorithms for attack detection is developed, as well as discussions on attack correction.

Keywords:Sensor networks, Networked control systems, Control applications Abstract: This work addresses the boundary patrolling problem, where a smart camera network undertakes the task of monitoring the perimeter of an environment so as to detect anomalies and track possible intrusions. Here, a distributed solution is sought based on the definition of a suitable functional that accounts both for the equitable partitioning of the available space and for the quality of vision of the patrolled area, and admits a unique optimal solution. The optimization of such functional leads to the design of an algorithm relying on a symmetric gossip communication protocol among the neighboring cameras. The theoretical results prove the correctness of the approach and the numerical simulations on a realistic scenario confirm its validity.

Keywords:Sensor networks, Sensor fusion, Distributed control Abstract: We develop an environmental estimation method that allows large groups of agents to infer the value of an environmental field using measurements. Agents maintain estimates for subregions of the domain and communicate with local neighbors, so the method's communication and memory requirements do not increase with the number of agents, the size of the environment representation, or the agents' density in the environment. Despite the distributed representation, the union of individual estimates matches an estimate generated by a central computer with access to all measurements employing the variational inverse method, a finite element-based interpolation procedure. We also introduce a distributed query system, allowing users to determine an estimate anywhere in the domain without accessing all measurements or the full environment representation.

Keywords: Abstract: Controls is increasingly central to technology, science, and society, yet remains the “hidden technology.” Our appropriate emphasis on mathematical rigor and practical relevance in the past 40 years has not been similarly balanced with technical accessibility. The aim of this tutorial is to enlist the controls community in helping to radically rethink controls education. In addition to the brief 2 hour tutorial at CDC, we will have a website with additional materials, but particularly extensive online videos with mathematical details and case studies. We will also have a booth in the exhibition area at CDC with live demos and engaging competitions throughout the conference.

Keywords:Networked control systems, Robotics, Multivehicle systems Abstract: Recently, rigidity theory has emerged as an efficient tool in the control field of coordinated multi–agent systems, such as multi–robot formations and UAVs swarms that are characterized by the sensing, communication and movement capabilities. This paper aims at describing the rigidity properties for frameworks embedded in SE(3), i.e. the three–dimensional Euclidean space wherein each agent has 6DoF. In such configuration, it is assumed that the devices are able to gather bearing measurements of their neighbors, expressing them into their own body frame. Rigidity properties are mathematically formalized in the paper which differs from the previous works as it faces the extension in three–dimensional space dealing with the 3D rotations manifold. In particular, the attention is focused on the infinitesimal SE(3)–rigidity for which necessary and sufficient condition is provided.

Keywords:Networked control systems, Sampled-data control, Information theory and control Abstract: In this paper, we introduce a new vulnerability of cyber-physical systems to malicious attack. It arises when the physical system, that is modeled as a continuous-time LTI system, is controlled by a digital controller, i.e., the output is measured only at discrete sensing times. Since the anomaly detector monitors the output signal, nothing abnormal can be detected through the output if the output looks normal at sensing times. This implies that if an (actuator) attack drives the internal states passing through the kernel of the output matrix at each sensing time, then the attack compromises the system while it remains stealthy. We show that this type of attack is feasible when the control system uses multi-rate sampling, and the sampling rate for input signal is higher than that for output measurements. Simulation results for the X-38 vehicle illustrate this new attack strategy possibly brings disastrous consequences.

Keywords:Networked control systems, Sampled-data control, Uncertain systems Abstract: We address the stability of networked control systems in which a sensor and an output-feedback controller operate asynchronously, which leads to uncertainty in the sampling instants. In addition, we also consider polytopic uncertainty in the plant model. The analysis is based on transforming the closed-loop system into an impulsive system, by considering an extended state variable that includes the states of the continuous-time plant and the discrete-time controller. We provide a sufficient condition for the robust stability of the closed-loop system in terms of linear matrix inequalities. This condition is based on the construction of a continuous-time Lyapunov functional that also incorporates the discrete-time state of the digital controller. We illustrate the obtained result with numerical simulations.

Keywords:Networked control systems, Stochastic optimal control, Linear systems Abstract: We consider the problem of controlling an unstable plant over an additive white Gaussian noise (AWGN) channel with a transmit power constraint, where the signaling rate of communication is larger than the sampling rate (for generating observations and applying control inputs) of the underlying plant. Such a situation is quite common since sampling is done at a rate that captures the dynamics of the plant and which is often much lower than the rate that can be communicated. This setting offers the opportunity of improving the system performance by employing multiple channel uses to convey a single message (output plant observation or control input). Common ways of doing so are through either repeating the message, or by quantizing it to a number of bits and then transmitting a channel coded version of the bits whose length is commensurate with the number of channel uses per sampled message. We argue that such "separated source and channel coding" can be suboptimal and propose to perform joint source-channel coding. Since the block length is short we obviate the need to go to the digital domain altogether and instead consider analog joint source-channel coding. For the case where the communication signaling rate is twice the sampling rate, we employ the Archimedean bi-spiral-based Shannon-Kotel'nikov analog maps to show significant improvement in stability margins and linear-quadratic Gaussian (LQG) costs over simple schemes that employ repetition.

Keywords:Networked control systems, Stability of linear systems, LMIs Abstract: We consider networked control systems (NCSs) composed of a linear plant and a linear controller with direct-feedthrough terms, i.e., terms that directly connect the plant's input and output from/to the controller with each other and the controller's input and output from/to the plant with each other. The presence of such direct-feedthrough terms generates non-trivial difficulties in terms of the modeling and the analysis of NCSs. In particular, a novel stability analysis is required to address standard scheduling protocols such as the sampled-data (SD), try-once-discard (TOD), and round-robin (RR) protocols. Hereto, we will take a renewed look at the concept of uniformly globally exponentially stable (UGES) scheduling protocols for these standard scheduling protocols as used in literature, such that the direct-feedthrough terms can be incorporated in the system configuration. The application of our results are illustrated using the benchmark example of a batch reactor.

Keywords:Networked control systems, Stability of linear systems, Stochastic systems Abstract: In this paper, we explore the conservation-dissipation structure and balance equations for linear systems forced with white noise process. The proposed methodology bases on a Fokker-Planck operator with the analytic expression and an operator decomposition. The symmetric component accounts for a conservative dynamics and the skew-symmetric corresponds to a dissipating system. In terms of an important structural condition, the dissipation structures are correlated with the stationary equilibrium states, while the conservation structures are correlated with the stationary non-equilibrium states. We also conduct the energy and entropy flow analysis in the non-equilibrium circumstance associated with unbalanced probability circulation. Finally, the framework enables us to evidence the First and Second Law of thermodynamics by relating the dissipativity theory to entropy production, heat dissipation, and work extraction.

Keywords:Switched systems, Constrained control, Autonomous robots Abstract: We present an algorithm for steering the output of a linear system from a feasible initial condition to a desired target position, while satisfying input constraints and non-convex output constraints. The system input is generated by a collection of local linear state-feedback controllers. The path-planning algorithm selects the appropriate local controller using a graph search, where the nodes of the graph are the local controllers and the edges of the graph indicate when it is possible to transition from one local controller to another without violating input or output constraints. We present two methods for computing the local controllers. The first uses a fixed-gain controller and scales its positive invariant set to satisfy the input and output constraints. We provide a linear program for determining the scale-factor and a condition for when the linear program has a closed-form solution. The second method designs the local controllers using a semi-definite program that maximizes the volume of the positive invariant set that satisfies state and input constraints. We demonstrate our path-planning algorithm on docking of a spacecraft. The semi-definite programming based control design has better performance but requires more computation.

Keywords:Autonomous robots, Machine learning, Markov processes Abstract: Emergency situations in large public and residential buildings, earthquake, fire, flood, terrorist attacks, cause extreme physical and emotional behaviours, inter alia, anxiety, hyperactivity, anger, etc.; in these situations, people are often unable to take the right action or even unable to make a decision. This paper addresses the problem of generating a building evacuation plan with the help of a Y6 coaxial tricopter UAV in an emergency situation where GPS signal is not available. The proposed algorithm, stochastic Q-Learning, learns the shortest path to leave the building. The traditional 2D space navigation is extended to the challengeable 3D space, which makes our approach more applicable in the real world. The emergency evacuation system proposed in herein can navigate people to evacuate a building safely in the wake of an emergency situation.

Keywords:Maritime control, Autonomous robots, Constrained control Abstract: This paper investigates the nonlinear model predictive control (NMPC) method for the trajectory tracking application of an autonomous underwater vehicle (AUV). To formulate the tracking control problem into the standard MPC scheme, the desired spatial reference trajectory is augmented according to the kinematic property of the AUV motion, which facilitates the following distributed model predictive control (DMPC) implementation. Considering that the computational complexity of the nonlinear programming (NLP) problem associated to the NMPC tracking control could be prohibitively high, the DMPC implementation is proposed attempting to alleviate the computational burden. The six degree of freedom (DOF) AUV model is then decomposed into three slightly coupled subsystems, and the DMPC subproblems are well defined with the original cost function broken down appropriately. Warm start strategy is adopted to enhance the control performance. Simulation studies are carried out, which verifies the effectiveness of the proposed method.

Keywords:Autonomous robots, Multivehicle systems, Lyapunov methods Abstract: We address the problem of multiple networked robots circumnavigating a dynamic target in a three-dimensional setting. A distributed cooperative control strategy is proposed that guarantees convergence of the robots to a circular formation with prescribed radius and inter-agent distances around a moving target. The circular formation is constrained to evolve on a plane of motion that is fixed in orientation but translates along the target trajectory. The control design is carried out using three potential functions, each of which defines a control objective, with gradient fields that are orthogonal to each other. The novelty in this approach lies in the orthogonality of the vector fields, which decouples the control objectives and ensures asymptotic convergence to the desired formation, subject to some mild initial condition constraints. The convergence properties are analyzed using Lyapunov-based methods, and the control strategy is demonstrated through numerical simulations and experiments on a robotic test bed.

Keywords:Autonomous robots, Nonholonomic systems, Autonomous systems Abstract: In this paper, we address the problem of computing optimal paths through three consecutive points for the curvature-constrained forward moving Dubins vehicle. Given initial and final configurations of the Dubins vehicle, and a midpoint with an unconstrained heading, the objective is to compute the midpoint heading that minimizes the total Dubins path length. We provide a novel geometrical analysis of the optimal path, and establish new properties of the optimal Dubins' path through three points. We then show how our method can be used to quickly refine Dubins TSP tours produced using state-of-the-art techniques. We also provide extensive simulation results showing the improvement of the proposed approach in both runtime and solution quality over the conventional method of uniform discretization of the heading at the mid-point, followed by solving the minimum Dubins path for each discrete heading.

Keywords:Autonomous robots, Numerical algorithms, Robotics Abstract: Shortest paths generated through gradient descent on a value function have a tendency to chatter and/or require an unreasonable number of steps to synthesize. We demonstrate that the gradient sampling algorithm of [Burke, Lewis & Overton, 2005] can largely alleviate this problem. For systems subject to state uncertainty whose state estimate is tracked using a particle filter, we propose the Gradient Sampling with Particle Filter (GSPF) algorithm, which uses the particles as the locations in which to sample the gradient. At each step, the GSPF efficiently finds a consensus direction suitable for all particles or identifies the type of stationary point on which it is stuck. If the stationary point is a minimum, the system has reached its goal (to within the limits of the state uncertainty) and the algorithm naturally terminates; otherwise, we propose two approaches to find a suitable descent direction. We illustrate the effectiveness of the GSPF on several examples using the ROS and Gazebo robot simulation environment.

Keywords:Decentralized control, Networked control systems, Stochastic optimal control Abstract: We consider a decentralized optimal control problem for a linear plant controlled by two controllers, a local controller and a remote controller. The local controller directly observes the state of the plant and can inform the remote controller of the plant state through a packet-drop channel. We assume that the remote controller is able to send acknowledgments to the local controller to signal the successful receipt of transmitted packets. The objective of the two controllers is to cooperatively minimize a quadratic performance cost. We provide a dynamic program for this decentralized control problem using the common information approach. Although our problem is not a partially nested LQG problem, we obtain explicit optimal strategies for the two controllers. In the optimal strategies, both controllers compute a common estimate of the plant state based on the common information. The remote controller's action is a linear function of the common state estimate, and the local controller's action is a linear function of both the actual state and the common state estimate.

Keywords:Decentralized control, Observers for nonlinear systems, LMIs Abstract: This paper deals with a new decentralized observer-based controller design method for nonlinear discrete-time interconnected systems with nonlinear interconnections. Thanks to some algebraic transformations and the use of a new variant of Young's inequality, an LMI-based approach is provided to compute the observer-based controller gain matrices. Furthermore, the congruence principle is used under a judicious and new manner leading to include additional slack variables and to cancel some bilinear matrix coupling. The effectiveness of proposed methodology is shown through an illustrative example.

Keywords:Decentralized control, Optimization, Optimization algorithms Abstract: This paper considers decentralized dynamic optimization problems where nodes of a network try to minimize a sequence of time-varying objective functions in a real-time scheme. At each time slot, nodes have access to different summands of an instantaneous global objective function and they are allowed to exchange information only with their neighbors. This paper develops the application of the Exact Second-Order Method (ESOM) to solve the dynamic optimization problem in a decentralized manner. The proposed dynamic ESOM algorithm operates by primal descending and dual ascending on a quadratic approximation of an augmented Lagrangian of the instantaneous consensus optimization problem. The convergence analysis of dynamic ESOM indicates that a Lyapunov function of the sequence of primal and dual errors converges linearly to an error bound when the local functions are strongly convex and have Lipschitz continuous gradients. Numerical results demonstrate the claim that the sequence of iterates generated by the proposed method is able to track the sequence of optimal arguments.

Keywords:Decentralized control, Optimization algorithms, Cooperative control Abstract: We develop a decentralized algorithm for multi-agent, convex optimization programs, subject to separable constraints, where the constraint function of each agent involves only its local decision vector, while the decision vectors of all agents are coupled via a common objective function. We construct a variant of the so called Jacobi algorithm and show that, when the objective function is quadratic, convergence to some minimizer of the centralized problem counterpart is achieved. Our algorithm serves then as an effective alternative to gradient based methodologies. We illustrate its efficacy by applying it to the problem of optimal charging of electric vehicles, where, as opposed to earlier approaches, we show convergence to an optimal charging scheme for a finite, possibly large, number of vehicles.

Keywords:Decentralized control, Stochastic optimal control, Stochastic systems Abstract: This paper is concerned with the properties of the sets of strategic measures induced by admissible team policies in decentralized stochastic control and the convexity properties in dynamic team problems. To facilitate a convex analytical approach, strategic measures for team problems are introduced. Properties such as convexity, and compactness and Borel measurability under weak convergence topology are studied, and sufficient conditions for each of these properties are presented. These lead to existence of and structural results for optimal policies. It will be shown that the set of strategic measures for teams which are not classical is in general non-convex, but the extreme points of a relaxed set consist of deterministic team policies, which lead to their optimality for a given team problem under an expected cost criterion. Externally provided independent common randomness for static teams or private randomness for dynamic teams do not improve the team performance. The problem of when a sequential team problem is convex is studied and necessary and sufficient conditions for problems which include teams with a non-classical information structure are presented. Implications of this analysis in identifying probability and information structure dependent convexity properties are presented.

Keywords:Decentralized control, Mean field games Abstract: A class of optimal control problems with N agents where the agents have nonlinear dynamics, nonlinear cost functions and have mean field coupling in their cost functions are considered. The basic objective of the agents is to minimize a social cost which is the sum of the N individual cost functions. The exact socially optimal control policies require a centralized information structure for each agent and have high implementation complexity. Considering the mean field coupling in the cost functions and motivated by the analysis in mean field game theory, a decentralized cooperative optimization problem is formulated where each agent's control policy only depends on its own state and a function which may be computed offline. It is shown that the resulting set of strategies asymptotically achieves person-by-person optimality as N goes to infinity where the essential idea is to formulate an (inverse) control problem which yields an optimum solution to the variation in the social cost that occurs due to the variation in an individual agent's control law.

Keywords:Distributed control, Game theory, Optimization Abstract: We formulate a class of divisible resource allocation problems among a collection of suppliers and demanders as a double-sided auction game. The auction mechanism adopted in this paper inherits some properties of the VCG style auction mechanism, like the incentive compatibility and the efficiency of Nash Equilibrium (NE). In this paper, we propose a novel dynamic process to implement the efficient NE for the underlying auction game. Basically, the double- sided auction game is formulated as a pair of single-sided auction games which are coupled via a joint potential quantity such that the best responses of the players in each single- sided auction and the potential quantity are updated under certain regulations. We introduce a pair of parameters which reveal some rough information related to the valuation and cost functions of players; then, assisted with the given parameters, at each iteration step, a pair of buyer and seller update their best responses under the constrained sets of their bid profiles respectively. We show the advantage of the increase of the potential quantity and individual allocation, and hence the auction game system converges to a NE. Further by providing a specific update sequence among players, it is verified that the system converge to the efficient NE within finite iteration steps in the order of O(lg(1/ε)), where ε is the termination parameter of the algorithm.

Keywords:Distributed control, Game theory, Predictive control for linear systems Abstract: This work addresses distributed control design by using density-dependent population dynamics. Furthermore, stability of the equilibrium point under this proposed class of population dynamics is studied, and the relationship between the equilibrium point of density-dependent population games (DDPG) and the solution of constrained optimization problems is shown. Finally, a distributed predictive control is designed with the proposed density-dependent dynamics, and contemplating a time-varying communication network.

Keywords:Distributed control, Large-scale systems, Networked control systems Abstract: In this paper, a novel event-based distributed control strategy for a set of dynamically coupled discrete-time LTI plants is proposed. To avoid unnecessary communication among the distributed control system, each plant with its local controller is equipped with an event generator deciding locally whether new state measurements must be sent or not. Via a tuning parameter and a codesign of event generator and controller, the designer can adjust an eligible trade-off between control performance and communication utilization. Further state and input constraints as well as constraints on the communication topology can be included into the codesign. With a quadratic event-triggering law and the socalled S-procedure the codesign can be formulated as an LMI optimization problem which guarantees asymptotical stability of the closed-loop system and compliance with the constraints. The effectiveness of the approach is evaluated for distributed control of a set of mechanically coupled inverted pendulums.

Keywords:Distributed control, LMIs, Linear parameter-varying systems Abstract: Proposed in this note, is a method for scheduled distributed dynamic output feedback controller design. The underlying large-scale system is assumed to be the interconnection of Linear Parameter Varying (LPV) discrete time sub-systems. Following the concept of Integral Quadratic Constraints, robust LPV controller is developed aiming at L2 norm minimisation. The interconnection of the controller has been selected to be identical to the spacial distribution of the sub-systems to secure the level of sparsity in communication topology. By using agent-wise full block multipliers in the design phase, distributed output feedback controller design framework is obtained by the sequential use of elimination and dualization lemmas. In order to show the benefits of the suggested methodology, numerical simulation tests are carried out to control the traffic flow in a motorway segment by means of on-ramp input flow gating.

Keywords:Distributed control, Lyapunov methods, Robust control Abstract: In this paper, we study the finite-time consensus tracking problem for second-order multi-agent systems with input uncertain dynamics and external disturbances. Robust finite-time consensus tracking controllers are designed with reduced communication. The proposed controllers achieve finite time consensus tracking in the presence of bounded input uncertainties with only relative position information under general directed communication topologies. Both the cases of static and dynamic leaders are considered. An application in the coordinated attitude control of multiple satellites is used as an example to illustrate the effectiveness of the proposed control strategies.

Keywords:Distributed control, Network analysis and control Abstract: The connectivity between different agents is a basic requirement in the control problem of multi-agent systems. For a connected graph, the connectivity corresponding to a 2-hop neighbor graph remains uncertain. In this paper, we consider the problem of verifying the connectivity of 2-hop neighbor graph of a connected graph. The properties of 2- hop neighbor graph from certain basic graphs, such as tree and circle graphs are studied firstly, then arbitrary connected graphs are discussed to investigate the connectivity of the underlying 2-hop neighbor graphs. The necessary and sufficient condition for verifying the connectivity of 2-hop neighbor graphs is proposed. Also a systematic verification strategy is developed, which is able to verify the connectivity of the underlying 2-hop neighbor graph of an arbitrary graph with the computation complexity of O(|V|+|E|), comparing with algebraic solutions.

Keywords:Mean field games, Decentralized control, Optimal control Abstract: We consider within the framework of Mean Field Games theory a dynamic discrete choice model with an advertiser, where a large number of minor agents (e.g., consumers) are choosing between two predeﬁned alternatives while inﬂuenced by social and advertisement effects. For example, in schools, teenagers’ decisions to smoke are considerably affected by their peers (social effect), as well as the ministry of health campaigns against smoking (advertisement effect). The advertiser is “Stackelbergian”, in the sense that it makes its decision ﬁrst and then the consumers make their choices. We show for a continuum of minor agents that there exists a Stackelberg solution. Moreover, when the minor agents are initially uniformly distributed on a line segment, we give an explicit form for the solution and characterize it by a scalar describing the way the population of agents splits between the destination points.

Keywords:Mean field games, Estimation, Decentralized control Abstract: Subject to reasonable conditions, in large population stochastic dynamics games where the agents are coupled by the system's mean field through their nonlinear dynamics and cost functions, it can be shown that a best response control action for each agent exists which (i) depends only upon the individual agent's state observations and the mean field, and (ii) achieves an epsilon-Nash equilibrium for the system. In this work we formulate a class of problems where each agent has only partial observations on its individual state. The main result is that the epsilon-Nash equilibrium property holds where the best response control action of each agent depends upon the conditional density of its own state generated by a nonlinear filter, together with the system's mean field. Finally, it is worthwhile comparing this MFG state estimation problem to one found in the literature where there exists a major agent whose partially observed state process is independent of the control action of any individual agent; by contrast, in this work, the partially observed state process of any agent depends upon that agent's control action.

Keywords:Game theory, Networked control systems, Distributed control Abstract: We consider a gossip approach for finding a Nash equilibrium in a distributed multi-player network game. We extend previous results on Nash equilibrium seeking to the case when the players' cost functions may be affected by the actions of any subset of players. An interference graph is employed to illustrate the partially-coupled cost functions and the asymmetric information requirements. For a given interference graph, we design a generalized communication graph so that players with possibly partially-coupled cost functions exchange only their required information and make decisions based on them. Using a set of standard assumptions on the cost functions, interference and communication graphs, we prove almost sure convergence to a Nash equilibrium for diminishing step sizes. We then quantify the effect of the second largest eigenvalue of the expected communication matrix on the convergence rate, and illustrate the trade-off between the parameters associated with the communication and the interference graphs. Finally, the efficacy of the proposed algorithm on a large-scale networked game is demonstrated via simulation.

Keywords:Game theory, Networked control systems, Multivehicle systems Abstract: Networked control systems can often be viewed through a game theoretic lens with each agent responding to a local utility function. In this paper, we focus on the question of how to design agent utility functions to ensure that the resulting system-wide behavior is desirable. While recent research has identified all utility design methodologies that ensure the existence of a (pure) Nash equilibrium in networked resource allocation problems, it remains on open question as to what utility design optimizes the efficiency of the resulting equilibria. Our first result focuses on the recently introduced concept of smoothness and provides a characterization of how a budget anomaly, which we define as a measure of the difference between the sum of the agents' payoffs and the value of the global objective, impacts the efficiency of the resulting Nash equilibria. Using this characterization, we then propose a new methodology for utility design that is accompanied by automatic efficiency guarantees. Lastly, we illustrate the effectiveness of this methodology on two classes of resource allocation problems.

Keywords:Game theory, Distributed control, Large-scale systems Abstract: We analyse deterministic aggregative games, with large but finite number of players, that are subject to both local and coupling constraints. Firstly, we derive sufficient conditions for the existence of a generalized Nash equilibrium, by using the theory of variational inequalities together with the specific structure of the objective functions and constraints. Secondly, we present a coordination scheme, belonging to the class of asymmetric projection algorithms, and we prove that it converges R-linearly to a generalized Nash equilibrium. To this end, we extend the available results on asymmetric projection algorithms to our setting. Finally, we show that the proposed scheme can be implemented in a decentralized fashion and it is suitable for the analysis of large populations. Our theoretical results are applied to the problem of charging a fleet of plug-in electric vehicles, in the presence of capacity constraints coupling the individual demands.

Keywords:Game theory, Learning, Stability of linear systems Abstract: Evolutionary dynamics describe how the population composition changes in response to the fitness levels, resulting in a closed-loop feedback system. Recent work established a connection between passivity theory and certain classes of population games, namely so-called ``stable games''. In particular, it was shown that a combination of stable games and (an analogue of) passive evolutionary dynamics results in stable convergence to Nash equilibrium. This paper considers the converse question of necessary conditions for evolutionary dynamics to exhibit stable behaviors for all generalized stable games. Using methods from robust control analysis, we show that if an evolutionary dynamic does not satisfy a passivity property, then it is possible to construct a generalized stable game that results in instability. The results are illustrated on selected evolutionary dynamics with particular attention to replicator dynamics, which are also shown to be lossless, a special class of passive systems.

Keywords:Game theory, Aerospace, Optimal control Abstract: The paper proposes a visibility augmented proportional navigation guidance law, for maintaining visual contact with a target during the engagement in a structured environment. The well-known proportional navigation guidance law is augmented with a term based on a measure of the target visibility. The guidance law is developed using a modified pursuit-evasion differential game, that includes a measurement of the visibility into the players' objective functions.

Keywords:Game theory, Sensor fusion, Optimization Abstract: Consider a setup in which a central estimator seeks to estimate a random variable using measurements from multiple sensors. The sensors incur an effort cost through consumption of resources to obtain a measurement. The sensors are self-interested and need to be compensated to generate measurements with a low enough error covariance that allows the calculation of an estimate with sufficient accuracy. However, a simple compensation scheme based on self-reported effort taken will not be sufficient, since both the quality of measurements taken by a sensor and the measurement values are private information for the sensor. A strategic sensor can misreport these values to increase his compensation. We formulate this problem as a contract design problem between the sensors and the central estimator and present an optimal contract between the central estimator and sensors as the solution.

Keywords:Game theory, Stochastic optimal control, Kalman filtering Abstract: We consider stochastic dynamic game problems where a trajectory controller takes an action to construct an information bearing signal, namely the control input, and subsequently a tracking system takes an action, i.e., constructs a tracking output, based on the control input. The trajectory controller has access to two Gaussian processes evolving according to first order autoregressive models, e.g., desired and private states. Different from the design of a measurement or sensing scheme for a tracking system, here the trajectory controller and the tracking system have different objectives such that the trajectory controller aims the tracking output to track sum of the desired and private states while the tracking system constructs the output to track the desired state only. For finite horizon problems involving two different quadratic cost functions, we show that the optimal control input policies are linear functions of the current states when the states evolve in parallel. We then extend this result for the general case when the trajectory controller has a myopic objective and show that the optimal control input policies are also linear functions of the current states. Finally, we restrict the policy space for the control input to the set of all linear mappings of the current states and convert the finite horizon stochastic game problem into a discrete time deterministic optimal control problem. We also include some illustrative numerical examples for different strategic control scenarios.

Keywords:Game theory, Stochastic optimal control, Stochastic systems Abstract: In this work we present a sampling-based algorithm designed to solve game-theoretic control problems and risk-sensitive stochastic optimal control problems. The cornerstone of the proposed approach is the formulation of the problem in terms of forward and backward stochastic differential equations (FBSDEs). By means of a nonlinear version of the Feynman-Kac lemma, we obtain a probabilistic representation of the solution to the nonlinear Hamilton-Jacobi-Isaacs equation, expressed in the form of a decoupled system of FBSDEs. This system of FBSDEs can then be simulated by employing linear regression techniques. Utilizing the connection between stochastic differential games and risk-sensitive optimal control, we demonstrate that the proposed algorithm is also applicable to the latter class of problems. Simulation results validate the algorithm.

Keywords:Stochastic optimal control, Game theory, Stochastic systems Abstract: In this paper we derive necessary and sufficient Person by Person and Global (team) decentralized optimality conditions, for stochastic differential decision problems with multiple Decision Makers (DMs) or Agents aimed at optimizing a common pay-off.

These consist of forward and backward stochastic differential equations, and a set of conditional variational Hamiltonians with respect to the information structures of the DMs.

Keywords:Stochastic optimal control, Game theory, Stochastic systems Abstract: A Stochastic Game Theoretic Differential Dynamic Programming (SGT-DDP) algorithm is derived to solve a differential game under stochastic dynamics. We present the update law for the minimizing and maximizing controls for both players and provide a set of backward differential equations for the second order value function approximation. We find the extra terms in the backward propagation equations that arise from the stochastic assumption compared with the original GT-DDP. We present the SGT-DDP algorithm and analyze how the design of the cost function affects the feed-forward and feedback parts of the control policies under the game theoretic formulation. The performance of SGT-DDP is then investigated through simulations on three examples, namely, a first order nonlinear system, the inverted pendulum and the cart pole problems with conflicting controls. We conclude with some possible future extensions.

Keywords:Optimization, Hybrid systems, Robotics Abstract: This paper presents an optimal gait synthesis method that exploits the full body dynamics of robots using the Hybrid Zero Dynamics (HZD) control framework and---for the first time---experimentally realizes online HZD gait generation for a planar underactuated robot. Hybrid zero dynamics is an established theoretical framework that formally enables stable control of dynamic locomotion by enforcing virtual constraints through feedback controllers. An essential part of successfully realizing dynamic walking with HZD framework is determining parameters of the virtual constraints that satisfy hybrid invariant condition via nonlinear constrained optimization. Due to the complexity of the full hybrid system model of the robot, these optimization problems often suffer from slow convergence and local minima. In this paper, we improve the reliability of the HZD gait optimization and significantly increase the convergence speed by taking advantage of the direct transcription formulation and the exponential convergence of the global orthogonal collocation (a.k.a. pseudospectral) method. As a result, generating HZD gaits online becomes feasible with an average computation time less than 0.5 seconds, as will be demonstrated experimentally on a bipedal robot.

Keywords:Chemical process control, Manufacturing systems, Process Control Abstract: Robust optimization has been widely used in the scheduling of multipurpose batch processes under uncertainty. However, traditional robust scheduling methods make simple assumptions about uncertainty, such as independence and symmetry. This paper proposes a novel scheduling approach of batch processes based on a data-driven robust mixed-integer linear programming (MILP) model. The Dirichlet process mixture model is adopted to construct an uncertainty set via variational inference from the historical data of uncertainty parameters. A data-driven robust counterpart of a general MILP is then derived as a conic quadratic mixed-integer programming based on this uncertain set. A specific data-driven robust MILP model is further developed to address multipurpose batch process scheduling problem under various uncertainties. An industrial case study is presented to demonstrate the effectiveness of the proposed method.

Keywords:Optimization, Networked control systems, Communication networks Abstract: We study the use of approximate Lagrange multipliers in the stochastic subgradient method for the dual problem in constrained convex optimisation. The use of approximate Lagrange multipliers in the optimisation (instead of the true multipliers) is motivated by the fact that it is possible to accurately approximate some non-convex control problems as convex optimisations. For example, it is possible to solve certain stochastic discrete decision problems by solving a sequence of convex optimisations. We show how the analysis can be used in networking problems with queues, and present a wireless example that has constraints on how control actions can be selected which illustrates the power of the approach.

Keywords:Distributed parameter systems, Optimization, LMIs Abstract: We propose a novel technique to solve optimization problems subject to a class of integral inequalities whose integrand is quadratic and homogeneous with respect to the dependent variables, and affine in the parameters. We assume that the dependent variables are subject to homogeneous boundary conditions. Specifically, we derive rigorous relaxations of such integral inequalities in terms of semidefinite constraints, so a strictly feasible and near-optimal point for the original problem can be computed using semidefinite programming. Simple examples arising from the stability analysis of partial differential equations illustrate the potential of our method compared to existing techniques.

Keywords:Optimization, Optimal control, Variational methods Abstract: Fully convex optimal control problems contain a Lagrangian that is jointly convex in the state and velocity variables. Problems of this kind have been widely investigated by Rockafellar and collaborators if the Lagrangian is coercive and without state constraints. A lack of coercivity implies the dual has nontrivial state constraints, and vice versa (that is, they are dual concepts in convex analysis). We consider a framework using Goebel's self-dualizing technique that approximates both the primal and dual problem simultaneously and maintains the duality relationship. Previous results are applicable to the approximations, and we investigate the limiting behavior as the approximations approach the original problem. A specific example is worked out in detail.

Keywords:Predictive control for nonlinear systems, Stochastic optimal control, Optimization Abstract: We consider the Chance Constrained Model Predictive Control problem for polynomial systems subject to disturbances. In this problem, we aim at finding optimal control input for given disturbed dynamical system to minimize a given cost function subject to probabilistic constraints, over a finite horizon. The control laws pro- vided have a predefined (low) risk of not reaching the desired target set. Building on the theory of measures and moments, a sequence of finite semidefinite programmings are provided, whose solution is shown to converge to the optimal solution of the original problem. Numerical examples are presented to illustrate the computational performance of the proposed approach.

Keywords:Optimization, Randomized algorithms, Optimization algorithms Abstract: We investigate an approach to the approximation of ambiguous chance constrained programs (ACCP) in which the underlying distribution of the random parameters is itself uncertain. We model this uncertainty with the assumption that the unknown distribution belongs to a closed ball centered around a fixed and known distribution. Using only samples drawn from the central distribution, we approximate ACCP with a robust sampled convex program (RSCP), and establish an upper bound on the probability that a solution to the RSCP violates the original ambiguous chance constraint, when the uncertainty set is defined in terms of the Prokhorov metric. Our bound on the constraint violation probability improves upon the existing bounds for RSCPs in the literature. We also consider another approach to approximating ACCP by means of a sampled convex program (SCP), which is built on samples drawn from the central distribution. Again, we provide upper bounds on the probability that a solution to the SCP violates the original ambiguous chance constraint for uncertainty sets defined according to a variety of metrics.

Keywords:Optimization algorithms, Randomized algorithms, Uncertain systems Abstract: One of the major risks associated with rivers is flooding, and a desirable way to manage rivers is to reduce the risk of severe floods without affecting the normal river operations. The flood risks are mainly contributed by uncertain inflows from tributaries. Due to uncertain in- and out-flows, the river control problem is formulated in this paper as a Multiple Chance-Constrained optimisation Problem (M-CCP), within a Stochastic MPC setting. M-CCPs are difficult to solve and this paper proposes an optimisation and testing algorithm to find approximate solutions of such problems. The algorithm is a significantly improved version of our previous proposal in [1]. Each step of the algorithm is supported with rigorous probabilistic bounds, and the usefulness of the algorithm is demonstrated on a simulated river example.

Keywords:Randomized algorithms, Network analysis and control, Adaptive control Abstract: In the last years, the study of complex networks grows rapidly and search of tightly connected groups of nodes, or community detection, has proved to be a powerful tool for analyzing the real systems. Randomized algorithms are effective for detecting communities but there is no set of optimal parameters that makes these algorithms create a good partitions into communities for every input complex network. In this paper we consider two randomized algorithms and, based on the stochastic approximation, propose two new adaptive modifications that adjust parameters to the input data and create a good partitions for wider range of input networks.

Keywords:Randomized algorithms, Optimization, Uncertain systems Abstract: Repetitive Scenario Design (RSD) is a randomized approach to robust design based on iterating two phases: a standard scenario design phase that uses N scenarios (design samples), followed by randomized feasibility phase that uses N_o test samples on the scenario solution. We give a full and exact probabilistic characterization of the number of iterations required by the RSD approach for returning a solution, as a function of N, N_o, and of the desired levels of probabilistic robustness in the solution. This novel approach broadens the applicability of the scenario technology, since the user is now presented with a clear tradeoff between the number N of design samples and the ensuing expected number of repetitions required by the RSD algorithm. The plain (one-shot) scenario design becomes just one of the possibilities, sitting at one extreme of the tradeoff curve, in which one insists in finding a solution in a single repetition: this comes at the cost of possibly high N. Other possibilities along the tradeoff curve use lower N values, but possibly require more than one repetition.

Keywords:Randomized algorithms, Predictive control for linear systems, Uncertain systems Abstract: We propose a randomized implementation of stochastic model predictive control (MPC). As a proxy for the expected cost, which may not be efficiently computable, the algorithm minimizes the empirical average cost under N random samples of the uncertain influences on the system. The setting is an imperfectly-observed linear system with multiplicative and additive uncertainty, convex, deterministic control constraints, and convex costs that may include penalties on state constraint violations. In this setting, each sample-average MPC subproblem is a feasible convex program that, under mild regularity conditions, yields consistent estimators of the stochastic MPC subproblem's optimal value and minimizers. Under stronger assumptions, the full sample-average MPC control trajectory is asymptotically optimal for stochastic MPC as N tends to infinity. A numerical example shows that even for small N, sample-average MPC can significantly improve performance relative to certainty-equivalent MPC.

Keywords:Stochastic systems, Control of networks, Randomized algorithms Abstract: The control of stochastic growth processes has attracted a large amount of interest recently, motivated, for instance, by the desire to control and contain the spread of epidemic diseases. In this paper, we consider the control of stochastic growth processes on lattices.Throughout the paper, we present our results using the forest wildfire as an example, in which the control is exerted by a limited number of autonomous vehicles that can be assigned to extinguish fires on individual trees planted in a grid formation. However, our results are broadly applicable to problems that involves nodes connected into lattice-like structures, such as control of transportation networks on a Manhattan grid. In this context, we define a notion of stability for stochastic growth processes on lattices, and we derive analytical bounds for control effort that guarantees stability. The lattice structure allows us to analytically characterize stabilizing control policies with the help of certain recent results from the statistical mechanics literature. This analysis leads to randomized policies that stabilize originally unstable stochastic growth processes on lattices almost surely, and guarantee asymptotic optimality both in terms of the allocation and the utilization of control effort.

Keywords:Large-scale systems, Observers for nonlinear systems, Uncertain systems Abstract: In this paper, a class of nonlinear interconnected systems is considered in the presence of structured and unstructured uncertainties. The bounds on the uncertainties are nonlinear and are employed in the observer design to reject the effect of the uncertainties. Under the condition that the structure matrices of the uncertainties are known, a robust sliding mode observer is designed and a set of sufficient conditions is developed such that the error dynamics are asymptotically stable. If the structure of the uncertainties is unknown, an untimately bounded observer is developed using sliding mode techniques. The obtained results are applied to a multimachine power system to demonstrate the effectiveness of the developed methods.

Keywords:Observers for nonlinear systems, Algebraic/geometric methods Abstract: Rational observers are to be constructed for rational systems while polynomial observers are to be constructed for polynomial systems. An observer synthesis procedure is formulated. First an output-based rational realization is synthesized for the considered rational system. Then a perturbation technique creates an observer. Finite algebraic observability of the rational system implies the existence of an output-based rational realization. A local convergence result is proven. Examples are provided.

Keywords:Observers for nonlinear systems, Automotive control, Stability of nonlinear systems Abstract: The side slip angle of a vehicle as well as the tire-road friction coefficient are important inputs for vehicle dynamics control system and automated driving modules. However measurement of these parameters are difficult and costly in mass production vehicles and need to be reliably and accurately estimated. We address the observer design problem for simultaneously estimating side slip angle and tire-road friction utilizing information from vehicle Electric Power Steering System (EPS). A key observation is that the vehicle dynamics can be transformed into a lower-triangular form. For non-affine parametrized systems in such a form we propose a nonlinear adaptive observer and prove the uniform exponential stability of the estimation error by constructing a strict Lyapunov function. The design procedure is subsequently applied to the vehicle observer design problem. Simulations demonstrate the robustness of the proposed observer against modeling error and measurement noise.

Keywords:Observers for nonlinear systems, Autonomous robots, Estimation Abstract: The problem of relative attitude estimation for a formation of three mobile platforms is addressed in this paper. In previous work by the authors rate gyro bias has been considered for two of the three platforms. This paper proposes an extended framework that includes rate gyro bias estimation for all platforms. In order to do so, two additional vector observations of constant inertial vectors are assumed available, which may be distributed among the platforms. Cascade observers are then proposed, where the first stage acts as a bias observer and the second allows to filter attitude estimates directly on the special orthogonal group. The first is globally exponentially stable and the second is locally input-to-state stable with respect to the errors of the first, with the region of convergence for the initial attitude estimate better described as semi-global. Lastly, simulation results are presented that exemplify the performance of the proposed estimators in the presence of sensor noise.

Keywords:Observers for nonlinear systems, Genetic regulatory systems, Systems biology Abstract: In this paper, we propose an approach to design state observer for Boolean control networks (BCNs) by applying the semi-tensor product (STP). At first, the relationship between observability and reconstructibility is studied. Then explicit and recursive methods are proposed to check reconstructibility. After that for reconstructible BCN an approach for observer design is given. The Luenberger-like observer is introduced to facilitate an online implementation, which converges within the minimal reconstructibility index. Finally, illustrative examples are given to show the proposed approaches.

Keywords:Observers for nonlinear systems, LMIs, Estimation Abstract: An enhanced high-gain observer is proposed to estimate the state variables of dynamic systems with Lipschitz nonlinearities. Such an observer has a more general structure as compared with the standard high-gain observer, which can be regarded as a particular case of enhanced high-gain observer because of a special choice of the design parameters. The more general structure allows for additional degrees of freedom in the selection of the observer parameters, which however entails some difficulties in the design. To overcome such difficulties, a convenient design procedure is presented that is based on the use of the Young inequality and linear matrix inequalities. Numerical results are reported to evaluate the effectiveness of the proposed observer and its related design tools as compared with the high-gain observer.

Keywords:Kalman filtering, Aerospace, Simulation Abstract: Preliminary results on the design of a precision positioning system for planes landing on an aircraft carrier in the absence of Global Positioning System (GPS) are discussed. This system relies on a set of radio transmitters similar to GPS satellite transmitters that are placed on the deck of the ship. These transmitters along with the receiver on the aircraft are fitted with specially designed antennas which allow additional directional information to be gained with each transmission. Similar to GPS, this system is capable of measuring the Pseudo-Range (PR) between the transmitter and receiver and additionally measures the Angle of Arrival (AoA) and Angle of Transmission (AoT). To achieve positioning accuracy levels necessary to autonomously land a plane on the deck of a ship requires a tight coupling of the Inertial Measurement Unit (IMU) of the aircraft and the Radio Frequency (RF) sensing designs. We present and compare two navigation filters for this application, an Unscented Kalman Filter (UKF) as well as a Nonlinear Maximum Likelihood Estimator (NLMLE). We report on extensive numerical simulations that suggest that the NLMLE approach overcomes the poor geometrical conditions of placing the transmitters on the deck of the ship to achieve the necessary accuracy levels.

Keywords:Kalman filtering, Estimation, Fault detection Abstract: In this paper, an attack detection problem in cyber-physical systems is studied. In a scenario of remote state estimation, the measurement innovation sent by a sensor through a wireless communication channel may be modified by a malicious attacker deceptively. To avoid using an approximate minimum mean squared error (MMSE) estimator introduced by the traditional chi^2 detector with a fixed threshold, and inspired by the ideas of event-based sensor schedules, we propose a stochastic detector with a random threshold for the remote estimator to determine whether to fuse the received data or not. The corresponding effect of the proposed detector on the estimation performance under linear deception attacks is analyzed explicitly. Simulations are provided to illustrate the developed results.

Keywords:Networked control systems, Kalman filtering, Game theory Abstract: This paper considers security issues of a cyber-physical system (CPS) under denial-of-service (DoS) attacks. The measurements of multiple sensors are transmitted to a remote estimator over a multi-channel network which may be congested by an intelligent attacker. Aiming at improving the estimation accuracy, we first propose a novel aggregation scheme for the estimator to produce accurate state estimates, from which we obtain a closed-form expression of the expected estimation error covariance. We further develop a sensor-attacker game to design a cooperative and defensive channel-selection strategy, which is an energy efficient way to avoid the sensors being attacked. Numerical examples are provided to illustrate the developed results.

Keywords:Networked control systems, Kalman filtering, Sensor networks Abstract: In this paper, a security problem in remote estimation scenario is studied. We consider a multi-sensor system where each sensor transmits its local innovation to a remote estimator through a wireless communication network. A centralized residue-based detection criterion is adopted to monitor system anomalies. We propose a linear attack strategy and present the corresponding feasibility constraints to guarantee stealthiness. For a resource-limited attacker, who is able to listen to all the channels while only launches an attack on one sensor at each time instant, we investigate which sensor should be attacked and what strategy should be used such that the remote estimation error covariance is maximized. A closed-form expression of the optimal linear attack strategy is obtained. Simulation examples are provided to illustrate the theoretical results.

Keywords:Kalman filtering, Optimal control, Distributed control Abstract: This paper studies a design and analysis of distributed Kalman-Bucy filter in sensor networks. When observability of the target system from each sensor is lost, boundedness of the covariance matrices for the individual Riccati equations are not guaranteed. In order to overcome this difficulty and to recover the optimality of the centralized Kalman-Bucy filter, we introduce exchange of covariance matrices with other agents. Then, since those Riccati equations and estimators are heterogenous, achieving consensus among them becomes the question. We employ the recently introduced notion of averaged dynamics, which is the average of all distributed Kalman-Bucy filters’ dynamics, and show that sufficiently strong coupling gains guarantee arbitrarily precise recovery of optimality and the estimation error converges to zero when there is no noise. Numerical simulations show the performance of the proposed scheme.

Keywords:Kalman filtering, Sensor networks, Estimation Abstract: We consider the problem of multiple sensor scheduling for remote state estimation over a shared link. A number of sensors monitor different dynamical processes simultaneously but only one sensor can access the shared channel at each time instant to transmit the data packet to the estimator. We propose a stochastic event-based sensor scheduling framework in which each sensor makes transmission decisions based on both the channel accessibility and the self event-triggering condition. The corresponding optimal estimator is explicitly given. By ultilizing the realtime information, the proposed schedule is shown to be a generalization of the time-based ones and outperform the time-based ones in terms of the estimation quality. By formulating an Markov decision process (MDP) problem with average cost criterion, we can find the optimal parameters for the event-based schedule. For practical use, we also design a simple suboptimal schedule to mitigate the computational complexity of solving an MDP problem. We also propose a method to quantify the optimality gap for any suboptimal schedules.

Keywords:Statistical learning, Large-scale systems, Optimization algorithms Abstract: We consider a distributed learning setup where a network of agents sequentially access realizations of a set of random variables with unknown distributions. The network objective is to find a parametrized distribution that best describes their joint observations in the sense of the Kullback-Leibler divergence. We analyze the case of countably many hypotheses and the case of a continuum of hypotheses. We provide non-asymptotic bounds for the concentration rate of the agents' beliefs around the correct hypothesis in terms of the number of agents, the network parameters, and the learning abilities of the agents. Additionally, we provide a novel motivation for a general set of distributed non-Bayesian update rules as instances of the distributed stochastic mirror descent algorithm.

Keywords:Statistical learning, Learning, Game theory Abstract: We describe a new method of parametric utility learning for non-cooperative, continuous games using a probabilistic interpretation for combining multiple utility functions; thereby creating a mixture of utilities under non-spherical noise terms. This framework allows for the estimated parameters of the learned utility functions to depend on the historical actions of the players and allows us to capture the fact that players' utility functions are not static. In particular, we present an adaptation of mixture of regression models that takes in to account heteroskedasticity. We show the performance of the proposed method by estimating the utility functions of players using data from a social game experiment designed to encourage energy efficient behavior amongst building occupants. Using occupant voting data we simulate the new game defined by the estimated mixture of utilities and show that the resulting forecast is more accurate than robust utility learning methods such as constrained Feasible Generalized Least Squares (cFGLS), ensemble methods such as bagging, and classical methods such as Ordinary Least Squares (OLS).

Keywords:Statistical learning, Machine learning, Numerical algorithms Abstract: The problem of mining a network of time series data naturally arises in many research areas including energy system, quantitative finance, bioinformatics, environmental monitoring, traffic monitoring, etc. Among others, two emerging challenges shared by manifold applications are (1) the modeling of temporal-spatial dependence with contextual information and (2) the design of efficient learning algorithms for big data (exceedingly long sequence) analytics. In this paper, we study a Contextual Hidden Markov Model (CHMM) that describes infinite temporal dependence and contextual spatial relations in an unified framework. More importantly, to make model training feasible for growing number of data samples, we develop an Online Expectation-Maximization (OEM) algorithm that avoids the usual forward-backward pass of the entire time sequence. Two typical applications, missing value recovery and novelty detection, are considered to test CHMM and the online algorithm. Experiments are conducted on real world data collected from power distribution network monitoring. We compare CHMM with other popular methods and the results not only justify the benefit of incorporating temporal-spatial and contextual information, but also demonstrate the effectiveness of the proposed OEM algorithm.

Keywords:Statistical learning, Pattern recognition and classification Abstract: Wind speed forecasting is critical to and challenging for wind energy industry. We present a combined AR-kNN regression model for short-term wind speed forecasting. Historical samples are selected to train the coefficients of a k-nearest-neighbor (kNN) regression model in order to capture the current variation pattern of wind speed. The training samples of the kNN model are combined with the recent samples of an autoregressive (AR) model tracking recent correlation of wind speed. To verify the performance of the proposed model, we apply it to the data of 10-min wind speed, and compare it with the persistence model, the single AR model and the single kNN regression model. The simulation results demonstrate that the combined AR-kNN model is effective and generates the most accurate forecasting of wind speed in several cases.

Keywords:Stochastic optimal control, Statistical learning, Markov processes Abstract: Value functions arise as a component of algorithms as well as performance metrics in statistics and engineering applications. Computation of the associated Bellman equations is numerically challenging in all but a few special cases.

A popular approximation technique is known as Temporal Difference (TD) learning. The algorithm introduced in this paper is intended to resolve two well-known problems with this approach: In the discounted-cost setting, the variance of the algorithm diverges as the discount factor approaches unity. Second, for the average cost setting, unbiased algorithms exist only in special cases. It is shown that the gradient of any of these value functions admits a representation that lends itself to algorithm design. Based on this result, the new differential TD method is obtained for Markovian models on Euclidean space with smooth dynamics.

Numerical examples show remarkable improvements in performance. In application to speed scaling, variance is reduced by two orders of magnitude.

Keywords:Stochastic systems, Statistical learning, Uncertain systems Abstract: Gaussian Process State Space Models (GP-SSM) are a data-driven stochastic model class suitable to represent nonlinear dynamics. They have become increasingly popular in non-parametric modeling approaches since they provide not only a prediction of the system behavior but also an accuracy of the prediction. For the application of these models, the analysis of fundamental system properties is required. In this paper, we analyze equilibrium distributions and stability properties of the GP-SSM. The computation of equilibrium distributions is based on the numerical solution of a Fredholm integral equation of the second kind and is suitable for any covariance function. Besides, we show that the GP-SSM with squared exponential covariance function is always mean square bounded and there exists a set which is positive recurrent.

Keywords:Switched systems, Automata, Discrete event systems Abstract: We study discrete time linear switching systems subject to additive disturbances. We consider two types of constraints, namely on the states and on the switching signal. A switching sequence is admissible if it is accepted by an automaton. Contrary to the arbitrary switching case, stability does not imply the existence of an invariant set. In this article, we propose a generalization of a bounded invariant set, namely, the notion of an invariant multi-set and show its significance in terms of dynamical systems. Under standard assumptions, we provide an iterative algorithm to approximate the minimal invariant multi-set with a guarantee of accuracy and an algorithm to compute the maximal invariant multi-set. Application of the established framework to switching systems with minimum dwell time reveals potential computational benefits and allows formulations of more refined notions.

Keywords:Robotics, Mechanical systems/robotics, Switched systems Abstract: This paper presents a framework for navigation of 3D dynamically walking bipeds. The framework is based on extracting gait primitives in the form of limit-cycle locomotion behaviors, which are then composed by a higher-level planning algorithm with the purpose of navigating the biped to a goal location while avoiding obstacles. By formulating motion planning as a discrete-time switched system with multiple equilibria - each corresponding to a gait primitive - we provide analytical conditions that constrain the frequency of the switching signal so that the biped is guaranteed to stably execute a suggested plan. Effectively, these conditions distill the stability limitations of the system dynamics in a form that can be readily incorporated to the planning algorithm. We demonstrate the feasibility of the method in the context of a 3D bipedal model, walking dynamically under the influence of a Hybrid Zero Dynamics (HZD) controller. It is shown that the dimensional reduction afforded by HZD greatly facilitates the application of the method by allowing certificates of stability for gait primitives using sums-of-squares programming.

Keywords:Switched systems, Direct adaptive control, Linear systems Abstract: We investigate the problem of designing an adaptive performance enhancement control law for an arbitrarily fast switching linear plant given a switching compensator. Switching is assumed to be uncontrolled and the characteristics of the reference or disturbance signals are changing over time. Stability despite switching and adaptation are given by construction, using a parameterization of all quadratically stabilizing compensators. We show that the adaptive-Q control methodology is well suited to enhance performance online for the switching linear case. A simulation example of an unstable switching plant illustrates the efficacy of the method and the performance enhancement when tracking a bounded reference signal with unknown characteristics.

Keywords:Switched systems, Filtering, Lyapunov methods Abstract: This paper is concerned with the finite-time H_{infty} filter design problem for a class of switched linear systems. A more general persistent dwell-time (PDT) switching is invoked rather than the dwell time or average dwell time switching widely studied in the literature. The sensor failures with output-measurement errors are also taken into account. A kind of proper Lyapunov-like functions and switching signals for the filter are designed, which are not only mode-dependent but also quasi-time-dependent. Certain techniques effectively contribute to the filter design procedures. Sufficient conditions on finite-time boundedness and finite-time H_{infty} performance are presented and the corresponding filter is also designed in the finite-time sense. Performance of the potential of the developed filter is illustrated by an illustrative example of mass-spring system.

Keywords:Switched systems, Formal verification/synthesis, Computational methods Abstract: Safety control constitutes an important aspect of hybrid systems and control. Invariance controllers guarantee that a system can stay within a given safe set for all future time. While abstraction-based approach to control synthesis takes the advantages of formal methods in automatic synthesis, abstractions often introduce spurious transitions that can lead to failure of controller synthesis for a given specification, even though the original system can be controlled to satisfy this specification. For discrete-time switched systems, this paper presents an interval arithmetic-based approach for invariance control synthesis. The main synthesis algorithms rely on partition refinement techniques and backward reachable set computation using interval analysis. The use of rigorous numerics allow us to prove formal guarantees of finding an invariance controller via abstraction refinement, provided that a robustly invariant condition is satisfied for the original switched system. The results are illustrated with polynomial dynamics.

Keywords:Switched systems, Linear systems, Fault tolerant systems Abstract: We propose a new switching L2 gain for analyzing the magnitude of a switch between two linear time-invariant systems. It focuses on the difference between the actuality that a switch occurs and the virtual situation where it does not occur. Furthermore, we present the L2 gain conditions that enable us to compute the value of the proposed switching L2 gain. From the multiple aspects by using the multiple quantitative indices, such as the proposed switching L2 gain and the existing ones for analyzing the fluctuations in actual transient responses, we can evaluate the severity of an undesirable switch in fault-tolerant control systems more appropriately than ever before.

Keywords:Stability of nonlinear systems, Lyapunov methods, Robust control Abstract: In this paper, we study robustness analysis of systems' safety with respect to external input (or disturbance) signals. To this end, we introduce a new notion of input-to-state safety (ISSf) which allows us to quantify the systems' safety robustness, in the same way as the application of input-to-state stability (ISS) notion for analyzing robustness of systems' stability. In particular, ISSf prescribes the relationship between the evolution of state distance to the unsafe set with the initial conditions and the bounded external input signals. Finally, we discuss how to combine this notion with ISS for analyzing the robustness of both systems' stability and safety.

Keywords:Stability of nonlinear systems, Lyapunov methods Abstract: Interconnection and damping assignment passivity-based control (IDA-PBC) relies on the solution of a partial differential equation (PDE) that identifies the assignable storage function, thus the difficulties in solving the PDE are usually the main stumbling block that hampers the application method. The main objective of this paper is to propose a new IDA-PBC to simplify the solution of the PDE, in particular, we extend this method in the following directions. First, we allow the desired interconnection and damping matrices to depend on the control signal, giving the possibility to simplify the PDE to ensure its solvability. Second, the PDE directly generates the control signal that has, in general, a simpler expression. Third, it is applicable for general nonlinear systems possibly not affine in the control. The technique is validated with two illustrative examples.

Keywords:Stability of nonlinear systems, Lyapunov methods Abstract: There are several notions of output stability that are intrinsically different. We present in this work a Lyapunov characterization for the so called robust output Lagrange stability for nonlinear delay systems. This output stability property requires that the overshoots of the output variables be bounded by the magnitudes of their initial values. As in the case for systems without delays, it is expected that the results in this work will lead to equivalent Lyapunov characterizations for several input-to-output stability properties. Furthermore, for delay systems, the notion of Lyapunov functions extends to Lyapunov-Krasovskii functionals, and some new features arise in the decay estimations of these functionals. In this work our objective is to provide equivalent Lyapunov descriptions for robust output Lagrange stability in terms of different types of decay estimations.

Keywords:Stability of nonlinear systems, Optimal control, Lyapunov methods Abstract: Pointwise asymptotic stability, or semistability, is a property of a set of equilibria of a dynamical system, where every equilibrium is Lyapunov stable and every solution is convergent to some equilibrium. Under an assumption that the property can be achieved, in a discrete-time nonlinear control system, through open-loop controls, it is shown that the property can be achieved by optimal or sub-optimal feedback.

Keywords:Robotics, PID control, Stability of nonlinear systems Abstract: The new generation of robots should coexist with our human beings in every walk of life. As a result, physical Human-Robot Interaction (pHRI) is ubiquitous and robot safety is quintessential. One solution to safety demand is to voluntarily put the series elasticity into joints for shock absorbing. However, side effects in terms of increased oscillations and long settling time occur.

To alleviate this predicament, a compliant joint with two rotary position sensors measuring both the link side and motor side positions is devised. Then, a cascade control consisting of the outer position loop with the joint end position measurement and the inner torque loop is posed to improve the robot performance, and its stability is rigorously analyzed by the singular perturbation theory. Finally, experiments are conducted to verify the effectiveness of the suggested control scheme.

Keywords:Stability of nonlinear systems, Constrained control, Lyapunov methods Abstract: Our aim in this paper is the study of the global asymptotic stabilization (GAS) of an affine control system, when the control value set (CVS) is a compact (convex) set U subseteq mathbb{R}^{m} with 0 in U. Hence, we allow the null-control input to be in its boundary, 0 in partial U, i.e. a mix of signed/positive bounded control input components. First, we study the geometry of the control Lyapunov function (CLF) theory (due to Artstein and Sontag) in order to address the GAS of a system using signed/positive feedback controls valued in a CVS U. Then, we propose a control formula for admissible (bounded and regular) controls. Finally, we design an explicit admissible control formula that renders a system GAS, but having at most one positive input component, and small overflows in the signed input component values.

Keywords:Variable-structure/sliding-mode control, Mechatronics, Uncertain systems Abstract: This paper presents a novel continuous fixed-time convergent control algorithm applied to the cart inverted pendulum stabilization problem in the presence of unbounded disturbances. A continuous fixed-time convergent control is designed to drive the cart inverted pendulum states to the origin for a finite pre-established (fixed) time using a scalar input. The fixed-time convergence is established and the uniform upper bound of the settling time is computed.

Keywords:Variable-structure/sliding-mode control, Autonomous systems Abstract: In this paper, a circular formation of autonomous vehicles is deployed such that the centroid tracks a temperature contour in the region of a tidal mixing front. Only local temperature measurements at the vehicles positions are taken for this purpose. The European north-west continental shelf sea surface temperature forecast data, provided by the Met Office, UK, has been used for this study as ‘prior information’. A probabilistic ‘belief’ model of the temperature profile over the region of operation is developed using instantaneous measurements from the vehicles and the available forecast information. While tracking a contour, the ‘belief’ model is updated and used for predicting local temperature gradient information. A quasi-continuous sliding mode contour following algorithm, which relies on local temperature measurements and the predicted temperature gradient, is proposed to steer the centroid of the formation.

Keywords:Variable-structure/sliding-mode control, Decentralized control, Stability of nonlinear systems Abstract: In this paper, a decentralised control strategy based on sliding mode techniques is proposed for a class of nonlinear interconnected systems in regular form. All the isolated subsystems and interconnections are fully nonlinear. It is not required that the nominal isolated subsystems are either linearizable or partially linearizable. The uncertainties are nonlinear and bounded by nonlinear functions. Specifically, uncertainties in the input distribution and interconnections are considered. Under mild conditions, sliding mode controllers for each subsystem are designed by only employing local information. Sufficient conditions are developed under which information on the interconnections is employed for decentralised controller design to reduce conservatism. The bounds on the uncertainties have more general forms compared with previous work. A simulation example is used to demonstrate the effectiveness of the proposed method.

Keywords:Variable-structure/sliding-mode control, Electrical machine control, Power systems Abstract: This work deals with the discrete-time modeling and control design for synchronous generators by means of a variational integrator and sliding modes. First, a continuous non-conservative Lagrangian is formulated for the plant, then, the respective discrete Lagrangian is determined. Based on this, discrete-time rules are derived for synchronous generators. Second, a sliding-mode controller is proposed for the velocity stabilization of the system, and a nonlinear observer is designed for the non-measurable states. Simulations show the good performance of the synchronous generator when closed-loop with the novel discrete-time controller.

Keywords:Variable-structure/sliding-mode control, Fault detection, Nonlinear output feedback Abstract: In this paper an underactuated 3-DOF laboratory helicopter is considered as test bed for fault detection and isolation. First, a sliding mode control strategy is suitably designed. The performance and robustness issues of the closed-loop system are illustrated in both the cases of the state-feedback control and the dynamic output-feedback control, when a nonlinear observer is exploited. Then, the fault detection and isolation problem for the 3-DOF helicopter is considered. The developed residual-based fault detection and isolation relies on the measurable output, some of its derivatives, which are provided exactly by a second-order sliding-mode differentiator, and the observer's state. The proposed methodology is able to detect and to isolate, under some mild conditions, some possible actuators faults.Simulation results illustrate the feasibility of the proposed approach.

Keywords:Fault detection, Observers for Linear systems, LMIs Abstract: In this paper, we consider the problem of robust fault detection for linear time-invariant positive systems. Although positive observers have been designed for positive systems, they are unable to estimate the states when unknown inputs (disturbances or faults) are present in the systems. The first goal of this paper is to show how a positive unknown input observer (PUIO) can be designed for positive systems. The PUIO design can be performed with the aid of a positive stabilization scheme via LMI in which the positivity of the generalized inverse of a certain design matrix is required. Then, we take advantage of PI observer combined with PUIO structure to estimate the faults in positive systems. The main contribution of this paper is to design a PI-based unknown input observer (PIUIO) which is capable of decoupling the unknown input disturbance while estimating the fault. Design procedures with high PI gains are outlined through parametrized eigenvalue assignment and LMI for the case of nonlinear fault. We also demonstrate that the PIUIO with a fading term achieves the same goal with low proportional and integral gains. Finally, illustrative examples are included to support the theoretical results.

Keywords:Algebraic/geometric methods, Hybrid systems Abstract: We apply an operator-theoretic viewpoint to a class of non-smooth dynamical systems that are exposed to event-triggered state resets. The considered benchmark problem is that of a pendulum which receives a downward kick at certain fixed angles. The pendulum is modeled as a hybrid automaton and is analyzed from both a geometric perspective and the formalism of Koopman operator theory. A connection is drawn between these two interpretations of a dynamical system by establishing a link between the spectral properties of the Koopman operator and the geometric properties in the state-space.

Important remark: the authors T. Matchen, L. van Blargian, and H. Arbabi do not have PINs, hence I was not able to add their names officially.

Keywords:Numerical algorithms, Reduced order modeling, Subspace methods Abstract: Dynamic Mode Decomposition (DMD) has attracted a fair amount of attention in recent years. Applications of DMD have ranged from fluid mechanics, thermal dynamics in a building, power systems, and so on. Connections to the so-called Koopman operator have been highlighted, and variants of DMD have been called the Koopman Mode Decomposition (KMD). In many applications, these techniques are used as an attempt to derive a reduced-order system or to identify coherent dynamic structures characterized by modes oscillating with single frequencies. Therefore, they become highly relevant to control applications via the data-derived system modeling. However, in many utilizations other than within computational fluid dynamics, the spatial dimension, here defined as the number of measurement locations, of dynamic data becomes low, or even singular in the case of just one measurement sensor. Thus, the question arises on how well the different variants of DMD/KMD suggested in the literature work in this setting. In this paper, we apply three different DMD/KMD algorithms to experimental data and evaluate how well they identify modes in terms of their frequency, and show how the sampling frequency and temporal length of the data window affects the decompositions. We interpret the results with support from a new unified interpretation of the algorithms. It is shown that the so-called vector Prony analysis works well for a small spatial dimension, where DMD is not suitable.

Keywords:Observers for nonlinear systems Abstract: We propose a new observer form based on Koopman operator theoretic framework for input-output nonlinear systems with control affine inputs. Based on this observer form, we describe an observer synthesis framework which exploits estimation techniques developed for Lipschitz systems and bilinear systems. We also formulate nonlinear observability rank condition in terms of the Koopman observer form, and numerically illustrate the benefits of the proposed framework.

Keywords:Nonlinear systems identification, Computational methods, Algebraic/geometric methods Abstract: We exploit the key idea that nonlinear system identification is equivalent to linear identification of the so-called Koopman operator. Instead of considering nonlinear system identification in the state space, we obtain a novel linear identification technique by recasting the problem in the infinite-dimensional space of observables. This technique can be described in two main steps. In the first step, similar to the so-called Extended Dynamic Mode Decomposition algorithm, the data are lifted to the infinite-dimensional space and used for linear identification of the Koopman operator. In the second step, the obtained Koopman operator is “projected back” to the finite-dimensional state space, and identified to the nonlinear vector field through a linear least squares problem. The proposed technique is efficient to recover (polynomial) vector fields of different classes of systems, including unstable, chaotic, and open systems. In addition, it is robust to noise, well-suited to model low sampling rate datasets, and able to infer network topology and dynamics.

Keywords:Reduced order modeling Abstract: The objective of this paper is to address the selection of dominant modes of a system that can be used to construct a reduced-order model. This work is motivated by high-fidelity computational models that capture fluid and/or structural dynamics, which are prohibitively complex for real-tome control. A variety of techniques for obtaining simplified control-oriented models have been developed, e.g. proper orthogonal decomposition (POD) and dynamic mode decomposition. In this paper, we address the challenge of selecting a few dominant Koopman modes for systems with exogenous inputs. We use a linear channel flow example to demonstrate the utility of our approach and illustrate the advantages relative to alternative techniques for control-oriented modeling.

Keywords:Lyapunov methods Abstract: Linear monotone systems admit Lyapunov functions that are separated into a sum or a maximum over functions depending on one state only, which is a useful feature for large-scale system analysis. Under certain conditions these functions can be constructed using the leading eigenvectors (i.e., the eigenvectors corresponding to the eigenvalue with the largest real part) of the drift matrix. In this paper, our goal is to extend some of these results to the nonlinear setting. In order to do so, we employ the Koopman operator, which allows for a linear infinite-dimensional description of a nonlinear system. Since the Koopman operator is linear, we can compute its eigenfunctions, which can be seen as infinite-dimensional eigenvectors. We show that the leading eigenfunction of a Koopman operator associated with a monotone system is a Lyapunov function. However, this Lyapunov function is not necessarily sum-separable in contrast to the linear case. We also show that a recently proposed max-separable Lyapunov function can be written in terms of the leading eigenfunction under certain conditions. This allows to characterize a subset of monotone systems for which these functions exist, thus further developing the existing results. We illustrate our theoretical findings on examples, which in particular show that global monotonicity is not necessary for existence of max-separable Lyapunov functions, and discuss future research directions.

Keywords:Computational methods, Numerical algorithms, Uncertain systems Abstract: This paper presents a multi-dimensional method to compute forward invariant sets (FIS) that are tight approximations of the smallest FIS of nonlinear perturbed systems modeled by differential inclusions. We formulate the problem as a discretized optimal boundary search, using methods from computational topology and non-smooth analysis to ensure invariance constraints for piecewise linear boundaries of FIS. We solve this optimal boundary search problem using a greedy search method with backtracking to find the optimal boundary, which defines the smallest FIS that can be represented in the discretized search space.

Keywords:Computational methods Abstract: We study problems arising when attempting to apply classical input-output techniques for controller design to systems from which one only drew finitely many (input-output) samples. Such problems arise in controller design for big data applications. In particular, we derive overestimates on the operator norm, the shortage of passivity, and the cone containing the input-output tuples, all solely from our finite input-output data. This allows for application of the small-gain theorem, the feedback theorem for passive systems, and the feedback theorem for conic relations.

Keywords:Modeling, Differential-algebraic systems, Algebraic/geometric methods Abstract: This paper aims to be, first of all, a short survey on the topic of the Exact Quadratization (EQ) of nonlinear control systems, mainly related to our article on the same subject recently issued (2015) in the SIAM Jou. on Cont. & Opt.. Secondly, it aims to yield some additional material, further improvements and new insights, not present or not enough discussed in the main article, such as a new shorter proof for EQ in the basic case of σπ-systems, and a detailed description of the relationship between solutions of the original and quadratized representations.

Keywords:Computational methods, Numerical algorithms Abstract: This paper presents a new heuristic solution to the traveling salesman problem (TSP). Inspired by an existing technique that employs the task swap mechanism to solve the multi-agent task allocation, we exploit the adaptive k-swap based searching process and take into account the newly introduced subtour constraint, and propose a new variant of k-opt method for incrementally improving suboptimal but feasible TSP tours. Different from existing k-opt methods, a unique feature of the proposed method is that the parameter k is adjusted adaptively as the tour improvement proceeds. We show that by combining with existing TSP approximation techniques, the hybrid approaches can further improve the solution quality with negligible extra running time.

Keywords:Computational methods, Optimization, Optimization algorithms Abstract: In this paper, the rank-constrained matrix feasibility problem is considered, where an unknown positive semidefinite (PSD) matrix is to be found based on a set of linear specifications. First, we consider a scenario for which the number of given linear specifications is at least equal to the dimension of the corresponding space of rank-constrained matrices. Given a nominal symmetric and PSD matrix, we design a convex program with the property that every arbitrary matrix could be recovered by this convex program based on its specifications if: i) the unknown matrix has the same size and rank as the nominal matrix, and ii) the distance between the nominal and unknown matrices is less than a positive constant number. It is also shown that if the number of specifications is nearly doubled, then it is possible to recover all rank-constrained PSD matrices through a finite number of convex programs. The results of this paper are demonstrated on many randomly generated matrices.

Keywords:Computational methods, Numerical algorithms, Switched systems Abstract: This paper presents a new method for numerical integration of a class of non-smooth systems in the presence of resets in position. The hard non-linearity introduced by resets due to a unilateral constraint on position poses a challenge for traditional numerical integration schemes which invariably result in oscillations in discrete-time. The results of this paper utilize the recently developed implicit numerical integration schemes of non-smooth systems to the systems with resets via employing the method of Zhuravlev-Ivanov transformation. The contribution lies in attaining existence of discretization solutions in the presence of the Zeno mode of impacts where infinite number of events are accumulated in finite time. We illustrate the effectiveness of the method on regulation and tracking problems. The good results presented here will motivate the theoretical study of those control strategies.

Keywords:Formal verification/synthesis, Robotics, Switched systems Abstract: Contact-based decision and planning methods are increasingly being sought for task execution in humanoid robots. However, formal methods from the verification and synthesis communities have not been yet incorporated into the motion planning sequence for complex mobility behaviors in humanoid robots. This study takes a step toward formally synthesizing high-level reactive task planners for whole-body locomotion in unstructured environments. We formulate a two-player temporal logic game between the contact planner and its possibly adversarial environment. The resulting discrete planner satisfies the given task specifications expressed in a fragment of temporal logic. The resulting commands are executed by a low-level 3D phase-space motion planner algorithm. We devise various low-level locomotion modes based on centroidal momentum dynamics. Provable correctness of the low-level execution of the synthesized discrete task planner is guaranteed through the so-called simulation relations. Simulations of dynamic locomotion in unstructured environments support the effectiveness of the hierarchical planner protocol.

Keywords:Formal verification/synthesis, Learning Abstract: This paper addresses the problem of learning optimal policies for satisfying signal temporal logic (STL) specifications by agents with unknown stochastic dynamics. The system is modeled as a Markov decision process, in which the states represent partitions of a continuous space and the transition probabilities are unknown. We formulate two synthesis problems where the desired STL specification is enforced by maximizing the probability of satisfaction, and the expected robustness degree, that is, a measure quantifying the quality of satisfaction. We discuss that Q-learning is not directly applicable to these problems because, based on the quantitative semantics of STL, the probability of satisfaction and expected robustness degree are not in the standard objective form of Q-learning. To resolve this issue, we propose an approximation of STL synthesis problems that can be solved via Q-learning, and we derive some performance bounds for the policies obtained by the approximate approach. The performance of the proposed method is demonstrated via simulations.

Keywords:Formal verification/synthesis, Hybrid systems Abstract: Most of the existing results available in the literature concerning symbolic control design of purely continuous or hybrid systems assume full information of the state which in concrete applications may be not available. This partial information to the controller requires to revisit existing methods on symbolic control design. This paper aims at addressing this issue and deals with symbolic control design with state quantized measurements of discrete–time nonlinear control systems affected by disturbances, with specifications expressed as regular languages.

Keywords:Formal verification/synthesis, Hybrid systems, Stochastic systems Abstract: In this paper we consider continuous–time stochastic linear control systems and propose model reduction techniques which are based on the notion of equivalence via stochastic bisimulation. Starting from our earlier work on equivalences given for discrete–time stochastic control systems we first extend the notion of stochastic bisimulation equivalence and the corresponding geometric conditions to the present framework. We then define the quotient linear systems induced by the equivalence notion and show that the obtained system is equivalent via stochastic bisimulation to the original one. We finally discuss model reduction to the system with minimal dimension in the state space.

Keywords:Formal verification/synthesis, Hybrid systems, Stochastic systems Abstract: In this paper we consider continuous–time stochastic linear control systems and study the notion of stochastic external behaviour equivalence. Starting from our earlier work on equivalences given for discrete–time stochastic control systems, we first extend the notion of stochastic external behaviour equivalence and the corresponding geometric conditions to the continuous-time framework. We then address model reduction and we show that the system with minimal dimension in the state space which has equivalent stochastic external behavior of a system, can be easily obtained by factoring out the unobservable dynamics from the given system. Connections with equivalence notions given for nondeterministic linear control systems and with stochastic linear realization theory are also formally discussed.

Keywords:Formal verification/synthesis, Hybrid systems, Machine learning Abstract: Integrated Task and Motion Planning (ITMP) for mobile robots becomes a new trend. Most existing methods for ITMP either restrict to static environments or lack performance guarantees. This motivates us to use formal design methods for mobile robot’s ITMP in a dynamic environment with moving obstacles. Our basic idea is to synthesize a global integrated task and motion plan through composing simple local moves and actions, and to achieve its performance guarantee through modular and incremental verifications. The design consists of two steps. First, reactive motion controllers are designed and verified locally. Then, a global plan is built upon these certified controllers by concatenating them together. In particular, we model the controllers and verify their safety through formulating them as Differential Dynamic Logic (dL) formula. Furthermore, these proven safe controllers are abstracted in Counter Linear Temporal Logic over Constraint System CLTLB(D) and composed based on an encoding to Satisfiability Modulo Theories (SMT) that takes into account the geometric constraints. Since dL allows compositional verification, the sequential composition of the safe motion primitives also preserves safety properties. Illustrative examples are presented to show the effectiveness of the method.

Keywords:Modeling, Human-in-the-loop control Abstract: Pointing is a basic gesture performed by any user during human-computer interaction. It consists in covering a distance to select a target via the cursor in a graphical user interface (e.g. a computer mouse movement to select a menu element). In this work, a dynamic model is proposed to describe the cursor motion during the pointing task. The model design is based on experimental data for pointing with a mouse. The obtained model has switched dynamics, which corresponds well to the state of the art accepted in the human-computer interaction community. The conditions of the model stability are established. The presented model can be further used for the improvement of user performance during pointing tasks.

Keywords:Modeling, Hybrid systems, Communication networks Abstract: Video streaming traffic over the Internet has significantly grown in the recent years. Adaptive video streaming control systems are employed to provide the best user experience given the user device and the network available bandwidth. The control goal is to maximize the video bitrate while avoiding playback interruptions. In this paper, we present a complete and accurate model of a generic adaptive streaming control system in the form of a hybrid dynamical system. The model describes all the system features, differently from previous models making the fluid-flow approximation, and allows to rigorously design video streaming controllers whose performance can be analytically assessed. The high accuracy of the model has been assessed by comparing numerical simulations to experimental data obtained through real network experiments. Given its accuracy and low computation cost, the proposed model provides a promising alternative to network experiments in order to aid the design and evaluation of adaptive video streaming systems.

Keywords:Modeling, Intelligent systems, Traffic control Abstract: Automated Planning can be fruitfully exploited as a Decision Support toolkit that, given a specification of available actions (elementary decisions to be taken), an initial situation and goals to be achieved, generates a plan that represents a (partially ordered) sequence of such elementary decisions that once performed the required goals are achieved. Road Traffic Accident Management is a life-critical task that deals with effective planning of emergency response when accidents occur, in order to mitigate negative effects, especially saving human lives that might be in imminent danger.

In this paper, we exploit Automated Planning in the Road Traffic Accident Management domain. We specifically focus on providing necessary treatment for victims injured during accidents. This involves coordination of medical teams responsible for providing medical treatment to the victims and fire brigades that are required to release victims trapped in damaged vehicles. An empirical analysis, based in the region of West Yorkshire (UK) with a number of real accidents recently occurred there, shows the suitability of the proposed Automated Planning approach to be used in time-critical conditions, and confirms the effectiveness of the generated plans. We also demonstrated its usefulness as a tool for evaluating the impact of additional resources, in order to provide guidance for future investments.

Keywords:Modeling, Linear systems, LMIs Abstract: For linear time-invariant systems with nonnegative impulse responses, much research has been devoted to studying their positive realizations. However, the limitations in the eigenvalue positions of positive systems suggest that they are not adequately powerful as a modeling tool. Thus in this paper we propose a more powerful projected spectrahedral cone-invariant (PSCI) realization of a system with nonnegative impulse response. In the study of PSCI realization problem, Lorentz cones play an important role. To be specific, we successfully find minimal Lorentz cone-invariant realizations of a class of systems with nonnegative impulse responses, which may not have positive realizations or have positive realizations with large dimensions. Combining positive realizations and Lorentz cone-invariant realizations, which are still PSCI, we can address a larger class of systems with nonnegative impulse responses. Moreover, a minimal PSCI realization can be obtained whenever a non-minimal PSCI realization exists. These results exhibit the potential power of PSCI systems as a modeling tool.

Keywords:Modeling, Linear systems Abstract: We consider discrete-time (DT) systems S in which a DT input is first transformed to a continuous-time (CT) format by phase-amplitude modulation, then modified by a non-linear CT dynamical transformation F, and finally converted back to DT output using an ideal de-modulation scheme. Assuming that F belongs to a special class of CT Volterra series models with fixed degree and memory depth, we provide a complete characterization of S as a series connection of a DT Volterra series model of fixed degree and memory depth, and an LTI system with special properties. The result suggests a new, non-obvious, analytically motivated structure of digital compensation of analog nonlinear distortions (for example, those caused by power amplifiers) in digital communication systems. Results from a MATLAB simulation are used to demonstrate effectiveness of the new compensation scheme, as compared to the standard Volterra series approach.

Keywords:Modeling, Simulation, Nonholonomic systems Abstract: In the present paper is extended the study of the Kapitsa pendulum when the bouncing is taken into account. When a cable instead of a rigid rod is considered the dynamics turns incredibly rich.

The transition between the flexible and rigid Kapitsa pendulum is understood by the loose of tension in the cable. It was found that some stability regions in the rigid Kapitsa pendulum are no longer stable when bouncing is considered, and mostly the system will tend to a continuous rotation as observed in the rigid Kapitsa pendulum for certain initial conditions.

Modelling the system as a differential inclusion will provide simple dynamical equations for the study of this more detailed system model.

Keywords:Smart grid, Energy systems, Statistical learning Abstract: Physical Flow Networks are different infrastructure networks that allow the flow of physical commodities through edges between its constituent nodes. These include power grid, natural gas transmission network, water pipelines etc. In such networks, the flow on each edge is characterized by a function of the nodal potentials on either side of the edge. Further the net flow in and out of each node is conserved. Learning the structure and state of physical networks is necessary for optimal control as well as to quantify its privacy needs. We consider radial flow networks and study the problem of learning the operational network from a loopy graph of candidate edges using statistics of nodal potentials. Based on the monotonic properties of the flow functions, the key result in this paper shows that if variance of the difference of nodal potentials is used to weight candidate edges, the operational edges form the minimum spanning tree in the loopy graph. Under realistic conditions on the statistics of nodal injection (consumption or production), we provide a greedy structure learning algorithm with quasilinear computational complexity in the number of candidate edges in the network. Our learning framework is very general due to two significant attributes. First it is independent of the specific marginal distributions of nodal potentials and only uses order properties in their second moments. Second, the learning algorithm is agnostic to exact flow functions that relate edge flows to corresponding potential differences and is applicable for a broad class of networks with monotonic flow functions. We demonstrate the efficacy of our work through realistic simulations on diverse physical flow networks and discuss possible extensions of our work to other regimes.

Keywords:Smart grid, Game theory, Energy systems Abstract: The participation of renewable energy sources in energy markets is challenging, mainly because of the uncertainty associated with the renewables. Aggregation of renewable energy suppliers is shown to be very effective in decreasing this uncertainty. In the present paper, we propose a cost sharing mechanism that entices the suppliers of wind, solar and other renewable resources to form or join an aggregate. In particular, we consider the effect of a bonus for surplus in supply, which is neglected in previous work. We introduce a specific proportional cost sharing mechanism, which satisfies the desired properties of such mechanisms that are introduced in the literature, e.g., budget balancedness, ex-post individual rationality and fairness. In addition, we show that the proposed mechanism results in a stable market outcome. Finally, the results of the paper are illustrated by numerical examples.

Keywords:Smart grid, Game theory, Power systems Abstract: Systematic nonzero spreads, defined as the differences between day-ahead and real-time prices, are routinely observed in the wholesale electricity markets. Virtual bidding is a financial mechanism which aims to reduce the magnitude of spreads by allowing market participants to arbitrage on the spread. We follow a data-driven approach to develop a two-settlement market model, and consider a game-theoretic setting with virtual bidders as strategic players. We interpret the spread as a measure of the average forecast accuracy of the market and all the virtual bidders. The main results convey the implication that introducing more qualified virtual bidders into the market help the convergence of the spread.

Keywords:Power systems, Smart grid, Reduced order modeling Abstract: This paper develops a novel approach to extract the aggregate flexibility of deferrable loads with heterogeneous parameters via polytopic projection approximation. First, an exact characterization of their aggregate flexibility is derived analytically, which in general contains exponentially many inequality constraints with respect to the number of loads. In order to have a tractable solution, we develop a numerical algorithm that gives a sufficient approximation of the exact aggregate flexibility. Geometrically, the flexibility of each individual load is a polytope and their aggregation is the Minkowski sum of these polytopes. Our method is motivated by an alternative interpretation of the Minkowski sum as a projection operation. The aggregate flexibility can be viewed as the projection of a high-dimensional polytope onto the subspace representing the aggregate power. We formulate a robust optimization problem to optimally approximate the polytopic projection with respect to the homothets of a given polytope. To enable efficient and parallel computation of the aggregate flexibility for a large number of loads, a muti-stage aggregation strategy is proposed. Finally, an energy arbitrage problem is solved to demonstrate the effectiveness of the proposed method.

Keywords:Smart grid, Distributed parameter systems Abstract: In contrast to the traditional centralised power system state estimation methods, this paper investigates the interconnected optimal filtering problem for distributed dynamic state estimation considering packet losses. Specifically, the power system incorporating microgrids is modelled as a state-space linear equation where sensors are deployed to obtain measurements. Basically, the sensing information is transmitted to the energy management system (EMS) through a lossy communication network where measurements are lost. Secondly, as the system states are unavailable, so the estimation is essential to know the overall operating conditions of the electricity network. The proposed estimator is based on the mean squared error between the actual state and its estimate. To obtain the distributed estimation, the optimal local and neighbouring gains are computed to reach a consensus estimation after exchanging their information with the neighbouring estimators. Then the convergence of the developed algorithm is theoretically proved. Afterwards, a distributed controller is designed based on the semidefinite programming approach. Simulation results demonstrate the accuracy of the developed approaches under the condition of missing measurements.

Keywords:Smart grid, Machine learning, Estimation Abstract: The large-scale deployment of Advanced Metering Infrastructure among residential energy customers has served as a boon for energy systems research relying on granular consumption data. Residential Demand Response aims to utilize the flexibility of consumers to reduce their energy usage during times when the grid is strained. Suitable incentive mechanisms to encourage customers to deviate from their usual behavior have to be implemented to correctly control the bids into the wholesale electricity market as a Demand Response provider. In this paper, we present a framework for short-term load forecasting on an individual user level, and relate non-experimental estimates of Demand Response efficacy (the estimated reduction of consumption during Demand Response events) to the variability of a user’s consumption. We apply our framework on a dataset from a residential Demand Response program in the Western United States. Our results suggest that users with more variable consumption patterns are more likely to reduce their consumption compared to users with a more regular consumption behavior.

Keywords:Robotics, Feedback linearization, Mechanical systems/robotics Abstract: In this paper, we describe modeling and control techniques for series-elastic actuated hopping robots. There is an abundance of work regarding the implementation of highly simplified hopper models, the prevalent example being the SLIP model, with the hopes of extracting fundamental control ideas for running and hopping robots. However, real-world systems cannot be fully described by such simple models, as real actuators have their own dynamics including additional inertia and non-linear frictional losses. Therefore, an important step towards demonstrating high controllability and robustness to real-world, uneven terrain is in providing accurate higher-order models of real-world hopper dynamics. Additionally, implementing feedback control for real series-elastic actuators is difficult as the input variable does not instantaneously change the leg length acceleration. In this work we provide both hardware and simulation results that illustrate how high-order partial feedback linearization can be implemented directly on the leg length state, and show how to apply these results so that algorithms in the SLIP literature can be accurately implemented in more realistic hopping systems to accomplish tasks such as apex state tracking and precise step length control.

Keywords:Robotics, Nonholonomic systems, Modeling Abstract: Planar equations of motion for lateral undulation and sidewinding by snake robots are derived within a common framework. The equations use a continuous model of the snake shape kinematics. The shape curve is defined as time and arc length parametrized deviations from a fixed curve. Viscous anisotropic friction models the snake-ground interaction. Vertical lifting of the body off of the ground plane defines time and spatially varying contact profiles in the planar model, which influence the external forcing applied to the system. We demonstrate this framework facilitates intuitive and convenient formulation of traveling wave gaits, in the form of cyclically-varying backbone curves and ground contact patterns. Simulation results illustrate that both lateral undulation and sidewinding gaits are indeed modeled by this single formulation.

Keywords:Formal verification/synthesis, Robotics Abstract: We present a scalable robot motion planning algorithm for reach-avoid problems. We assume a discrete-time, linear model of the robot dynamics and a workspace described by a set of obstacles and a target region, where both the obstacles and the region are polyhedra. Our goal is to construct a trajectory, and the associated control strategy, that steers the robot from its initial point to the target while avoiding obstacles. Differently from previous approaches, based on the discretization of the continuous state space or uniform discretization of the workspace, our approach, inspired by the lazy satisfiability modulo theory paradigm, decomposes the planning problem into smaller subproblems, which can be efficiently solved using specialized solvers. At each iteration, we use a coarse, obstacle-based discretization of the workspace to obtain candidate high-level, discrete plans that solve a set of Boolean constraints, while completely abstracting the low-level continuous dynamics. The feasibility of the proposed plans is then checked via a convex program, under constraints on both the system dynamics and the control inputs, and new candidate plans are generated until a feasible one is found. To achieve scalability, we show how to generate succinct explanations for the infeasibility of a discrete plan by exploiting a relaxation of the convex program that allows detecting the earliest possible occurrence of an infeasible transition between workspace regions. Simulation results show that our algorithm favorably compares with state-of-the-art techniques and scales well for complex systems, including robot dynamics with up to 50 continuous states.

Keywords:Human-in-the-loop control, Robotics, Control applications Abstract: Our goal is to enable robots to better assist people with motor impairments in day-to-day tasks. Currently, such robots are teleoperated, which is tedious. It requires carefully maneuvering the robot by providing input through some interface. This is further complicated because most tasks are filled with constraints, e.g. on how much the end effector can tilt before the glass that the robot is carrying spills. Satisfying these constraints can be difficult or even impossible with the latency, bandwidth, and resolution of the input interface. We seek to make operating these robots more efficient and reduce cognitive load on the operator. Given that manipulation research is not advanced enough to make these robots autonomous in the near term, achieving this goal requires finding aspects of these tasks that are difficult for human operators to achieve, but easy to automate with current capabilities. We propose constraints are the key: maintaining task constraints is the most difficult part of the task for operators, yet it is easy to do autonomously. We introduce a method for inferring constraints from operator input, along with a confidence-based way of assisting the user in maintaining them, and evaluate in a user study.

Keywords:Robotics, Mechanical systems/robotics, Large-scale systems Abstract: This paper concerns an n-link underactuated revolute planar robot in a vertical plane with two or more actuators and encoders. The linear controllability and observability of such a robot around the upright equilibrium point (UEP), where all the links are in the upright position, are investigated. This paper concerns the problem of the linear controllability and observability of an n-link planar robot around the UEP with only multiple intermediate links being active and the corresponding link angles being measured. When neither the first link nor the last link of the robot is active, and the robot has two or more active intermediate links and the corresponding link angles are measured, this paper proves via a new constructive example that, if there do not exist two active intermediate adjacent links, then there always exists a set of mechanical parameters that renders the robot linearly uncontrollable and unobservable around the UEP. When neither the first link nor the last link of the robot is active, together with an existing result, this paper shows that the robot is linearly controllable and observable, regardless of its mechanical parameters, if and only if there are at least two active adjacent links among the n-2 intermediate links and the corresponding link angles are measured.

Keywords:Robotics, Biological systems, MEMs and Nano systems Abstract: Biological and bioinspired swimmers move by shape actuation. Great progress has been made in understanding the direct control of shape variables for locomotory purposes. However, indirect control and soft actuation of the shape variables via actuation of the fluid medium is less well explored. Here, we examine the nonlinear coupling between the shape variables and net locomotion in a model system that consists of a two-link deformable body in oscillating flow. That is, the actuation is applied to the fluid medium and not the swimmer. We determine effective conditions that lead to symmetric swimming in terms of four dimensionless parameters: the mass and spring stiffness of the swimmer and the amplitude of oscillations and viscosity of the background flow. We find optimal parameters that maximize swimming. We then examine the stability of these swimming motions and observe stable and unstable swimming. These results suggest that one can tune the background flow properties to control the swimmer motion, and thus, they may have profound implications on the design and employment of man-made swimmers in oscillatory flows.

Keywords:Control applications, Distributed control, Cooperative control Abstract: Cooperation of agents is imperative for information consensus in a network, but confidentiality issues might discourage certain agents from participating in the distributed consensus algorithms. This paper proposes a novel distributed average consensus algorithm which preserves the confidentiality of every cooperating agent’s initial state value from other cooperating agents in the network, while asymptotically achieving the desired average of the initial state values of the agents. The proposed algorithm requires minimal change in the widely-known graph Laplacian based linear consensus algorithm and imposes minimal additional computational load on the participating agents.

Keywords:Control applications, Energy systems, Agents-based systems Abstract: In this paper, bidirectional modified C^{u}k converters are utilized as the cell equalizing circuits for serially connected lithium-ion battery packs. The battery cell equalizing system is modeled as a multi-agent system, in which the cells are considered as the nodes and their connected converters are treated as the edges. A consensus algorithm is proposed to have the modified C^{u}k converters work efficiently to achieve SOC equalization of the cells. In order to accelerate the equalizing process, one more converter is added in the conventional topology of the cell balancing system here. Since the convergence rate of the cell balancing is proportional to the magnitude of the second smallest eigenvalue of the Laplacian matrix of the cell equalizing graph, the problem becomes how to determine the added edge that can increase the second smallest eigenvalue of its graph's Laplacian matrix at a maximum level. By solving a 0-1 programming issue, the position of the converter added within the cell balancing system can be obtained. Simulation results demonstrate that the equalizing time can be significantly reduced by just adding one converter properly in the conventional cell equalizing system.

Keywords:Control applications, Estimation, Kalman filtering Abstract: In this work, we develop a distributed state estimation scheme for wastewater treatment processes in the context of extended Kalman filtering. Specifically, we consider a wastewater treatment process that includes a five-compartment reactor and an ideal splitter. First, we present a method to design the sensor network for the process and then discuss how the process may be decomposed into subsystems for distributed state estimation. We present a detailed design of the distributed filters and a detailed distributed state estimation algorithm to coordinate the actions of the different filters. The distributed scheme is compared with a centralized extended Kalman filtering scheme under dry weather conditions. Simulation results show that the distributed scheme can give comparable estimation performance to the centralized scheme or even better performance than the centralized scheme. Also, the distributed estimation scheme is shown to have more stable performance under different noise conditions.

Keywords:Control applications, Fluid flow systems, Lyapunov methods Abstract: A proper orthogonal decomposition (POD)-based model reduction technique is utilized to develop a closed-loop nonlinear flow control system. By using POD, the Navier-Stokes partial differential equations are recast as a set of nonlinear ordinary differential equations in terms of the unknown Galerkin coefficients. A sliding mode estimator is then employed to estimate, in finite time, the unknown coefficients in the reduced-order model for the actuated flow system. The estimated coefficients are utilized as feedback measurements in a robust nonlinear control law. A rigorous analysis is utilized to analyze the convergence of the sliding mode estimator, and a Lyapunov-based stability analysis is used to prove asymptotic regulation of the flow field velocity to a desired velocity profile. The control objective of tracking a desired velocity profile presented here is a proof of concept only; the proposed methodology could be applied to various flow control objectives. Numerical simulation results are provided to demonstrate the capability of the estimator/control system to regulate the velocity of the flow field to a desired state.

Keywords:Automotive systems, Mechatronics, Modeling Abstract: In this paper, a control-oriented model for compressor mass flow rate is proposed. For this purpose, the compressor is approximated as an adiabatic nozzle with compressible fluid, driven by external work from the compressor wheel. The external work input is modeled using Euler’s turbomachinery equations, with the main flow losses estimated via a simple slip factor model. All other flow losses, that influence the mass flow, are lumped into the discharge coefficient as a function of turbocharger speed. Consequently, the mass flow rate is estimated based on mass conservation in a compact form. Only five parameters need to be identified with clear physical interpretations. Both steady-state and transient experimental test results confirm the validity of this model in terms of estimation accuracy and extrapolation capability, making it a promising candidate for control applications.

Keywords:Control applications, Transportation networks, Filtering Abstract: A measure of privacy infringement for agents (or participants) travelling across a transportation network in participatory-sensing schemes for traffic estimation is introduced. The measure is defined to be the conditional probability that an external observer assigns to the private nodes in the transportation network, e.g., location of home or office, given all the position measurements that it broadcasts over time. An algorithm for finding an optimal trade-off between the measure of privacy infringement and the expected estimation error, captured by the number of the nodes over which the participant stops broadcasting its position, is proposed. The algorithm searches over a family of policies in which an agent stops transmitting its position measurements if its distance (in terms of the number of hops) to the privacy sensitive node is smaller than a prescribed threshold. Employing such symmetric policies are advantageous in terms of the resources required for implementation and the ease of computation. The results are expanded to more general policies. Further, the effect of the heterogeneity of the population density on the optimal policy is explored. Finally, the relationship between the betweenness measure of centrality and the optimal privacy-preserving policy of the agents is numerically explored.

Keywords:Traffic control, Modeling, Transportation networks Abstract: In this paper we propose a variable speed control strategy based on a new Variable-Length cell transmission Model (VLM). The VLM differs from the standard Cell Transmission model in that only a limited number of (variable length) cells are used. Road network is subdivided into several sections which are assumed to be composed of a downstream congested cell followed by a free upstream cell. Both cells have variable lengths and are described by two lumped densities (one congested, the other free). One more state describing the length variation completes the model for each section. The paper also introduces an associated optimal speed control design based on the proposed VLM. The method is illustrated on a closed ring road and is shown to optimize the traveling time per turn.

Keywords:Traffic control, Multivehicle systems, Queueing systems Abstract: Back-pressure controllers have been recently applied to traffic signal control and demonstrate three key benefits: they are stability optimal, implementable in a completely distributed manner and do not require knowledge of traffic arrival rates. This paper focuses on the design of a back-pressure controller that both commands the phase at every traffic signal and the routing choice made by a certain ratio of controllable vehicles. The proposed controller is proved to be stability-optimal and simulations illustrate the efficiency of the approach. It remains implementable in a completely distributed manner and does not require knowledge of arrival rates. Numerical results show the benefits of controlling route choice in addition to the traditional phase control strategy.

Keywords:Traffic control, Optimization, Autonomous systems Abstract: This article presents a convex optimization approach to reduce fuel consumption of traffic flow on highways through speed limit control. By implementing Greenshields fundamental diagram, the solution to Moskowitz equations is expressed as linear equations with respect to vehicle inflow and outflow, which leads to generation of a linear traffic flow model. In addition, we build a quadratic function to estimate fuel consumption rate based on COPERT model. The energy-efficient traffic control problem is formulated as a convex quadratic optimization problem. Simulation results demonstrate significant reduction of fuel consumption, alleviation of congestion, and improved robustness using the proposed approach under high traffic demands.

Keywords:Traffic control, Predictive control for nonlinear systems, Transportation networks Abstract: We design model predictive control (MPC) schemes to improve urban mobility in heterogeneously congested large-scale traffic networks, the modeling and control of which remains a challenge. The multi-region urban network is modeled using the macroscopic fundamental diagram (MFD) of urban traffic, with each region having a well-defined MFD. For more realistic simulations of urban networks with route guidance actuation based control, we propose a new model with cyclic behavior prohibition. Furthermore, we extend upon earlier work on perimeter control based MPC schemes with MFD modeling by integrating route guidance type actuation, which distributes flows exiting a region over its neighboring regions. Performance of the proposed schemes are evaluated via simulations of a congested scenario with noise in demand estimation and measurement errors. Results show the possibility of substantial improvements in urban network performance.

Keywords:Queueing systems, Traffic control, Hybrid systems Abstract: We consider a horizontal traffic queue (HTQ) on a periodic road segment, where vehicles arrive according to a spatio-temporal Poisson process, and depart after traveling a distance that is sampled independently and identically from a spatial distribution. When inside the queue, the motion of vehicles is governed by a car following model. We consider safe first and second order car following models. In the first order models, the speed of a vehicle is proportional to a power m >0 of the distance to the vehicle in front. For the first order model, we show monotonicity of the service rate in between arrivals and departures. We extend the busy period calculations for M/G/1 queue to our setting, including for non-empty initial conditions in order to derive a probabilistic lower bound on the throughput for the m>1 case. For the m<1 case, we study throughput under a release control policy, where the additional expected waiting time caused by the release control policy is interpreted as the magnitude of the perturbation to the arrival process. We derive a lower bound on throughput for a given combination of maximum allowable perturbation and m < 1. For the second order model, we design a safe release control policy which guarantees a provable lower bound on the throughput. Illustrative simulation results are also presented.

Keywords:Traffic control, Switched systems, Observers for Linear systems Abstract: This paper proposes local ramp metering controllers to be applied in freeways in which there are not sensors measuring the traffic density close to the on-ramps. Since the ramp metering control laws to be applied are based on the value of the traffic densities upstream or downstream the on-ramps and since these densities cannot be measured, the density estimates provided by distributed consensus-based switched observers developed in a previous work are used. In particular, on the basis of the observability properties of the considered freeway system, which is modeled as a piecewise-affine state-dependent system, a switched ramp metering controller based on a distributed observer is proposed. According to the present mode of the freeway system, the local controller of each on-ramp switches between a feedback controller based on the downstream density, a feedforward controller based on the upstream density and a pre-computed control law.

Keywords: Abstract: Social learning or learning from actions of others is a key focus of microeconomics; it studies how individuals aggregate information in social networks. Following the seminal work of Aumann, a large literature studies the strategic interaction of agents in a social network, where they receive private information and act based upon that information while also observing the actions of each other. These observations are in turn informative about other agents' private signals; information that can be then used in making future decisions. By the same token, agents engage in group discussions to benefit from private information of others and come up with better decisions that aggregate every body's information as efficiently as possible.

We begin by considering the decision problems of a Bayesian agent in a social learning scenario. As the Bayesian agent attempts to infer the true state of the world from her sequence of private signals and observations of actions of others, her decision problems at every epoch can be cast recursively; curbing some of the complexities of the decision scenario, but only to a limited extent. In a group decision scenario, the initial private signals of the agents constitute a state space and the ultimate goal of the agents is get informed about the private signals of each other. The Bayesian agent is initially informed of only her own signal; however, as her history of interactions with other group members becomes enriched, her knowledge of the possible private signals that others may have observed also gets refined; thus enabling her to make better decisions.

Bayesian calculations in the social learning setting are notoriously difficult. Successive applications of Bayes rule to the entire history of past observations lead to forebodingly complex inferences: due to lack of knowledge about the global network structure, and unavailability of private observations, as well as third-party interactions that precede every decision. This has given rise to a large literature on non-Bayesian social learning that suggest the use of decision-making heuristics, not only for mathematical tractability but also on the grounds that they are better descriptors of the bounded rational behaviors that

Keywords: Abstract: We overview some results on distributed learning with focus on a family of recently proposed algorithms known as non-Bayesian social learning. We consider different approaches to the distributed learning problem and its algorithmic solutions for the case of finitely many hypotheses. The original centralized problem is discussed at first, and then followed by a generalization to the distributed setting. The results on convergence and convergence rate are presented for both asymptotic and finite time regimes. Various extensions are discussed such as those dealing with directed time-varying networks, Nesterov’s acceleration technique and a continuum sets of hypothesis.

Keywords: Abstract: We consider several problems in the field of distributed optimization and hypothesis testing. We show how to obtain convergence times for these problems that scale linearly with the total number of nodes in the network by using a recent linear-time algorithm for the average consensus problem.

Keywords:Networked control systems, Stability of nonlinear systems, Hybrid systems Abstract: We investigate the scenario where a controller communicates with a plant at discrete time instants generated by an event-triggering mechanism. In particular, the latter collects sampled data from the plant and the controller at each sampling instant, and then decides whether the control input needs to be updated, leading to periodic event-triggered control. We propose a systematic design procedure. We assume that we know a continuous-time state-feedback controller, which stabilizes the system in the absence of communication constraints. We then take into account sampling and we design an event-triggering condition, which is only updated at some of the sampling instants, to preserve stability. An explicit bound on the maximum sampling period with which the triggering rule is evaluated is provided. We show that there exists a trade-off between the latter and a parameter used to define the triggering condition. The results are applied to a van de Pol oscillator as an illustration.

Keywords:Networked control systems, Stability of nonlinear systems, Lyapunov methods Abstract: We investigate the time-triggered control of nonlinear discrete-time systems using an emulation approach. We assume that we know a controller, which stabilizes the origin of a discrete-time nonlinear system. We then provide conditions to preserve stability when the control input is no longer updated at each step, but within N steps from the previous update, where N is a strictly positive integer. We consider general output feedback controllers and we allow for various holding strategies of the control input between two updates, such as zero-input or hold-input policies for example. An easily computable bound on the maximum number of steps between two updates, i.e. N, is provided. The results are applied to linear time-invariant systems in which case the assumptions are written as a linear matrix inequality, and a nonlinear physical example is provided as an illustration. This study is relevant for networked control systems, as well as any system for which sparse or sporadically changing control inputs are advisable in view of the resource limitations for instance.

Keywords:Networked control systems, Stability of nonlinear systems, Lyapunov methods Abstract: This paper investigates the stability of nonlinear networked control systems (NCSs) with dynamic controllers that possess direct-feedthrough terms (i.e. that are of relative degree zero). The presence of the direct-feedthrough terms obstructs the application of existing stability results for NCSs. Indeed, the uniform global exponential stability (UGES) of an auxiliary system induced by the plant and the network protocol needs to be verified. In prior work, this auxiliary system depends solely on the protocol (and not on the plant or on the controller) and, consequently, the analysis is simpler. Checking UGES of this auxiliary system turns out to be non-trivial when direct-feedthrough terms are present (even for the simplest protocols). Still, we are able to show UGES of the auxiliary system for Round-Robin (RR) and Try-Once-Discard (TOD) network protocols, which, together with other requirements on the maximum allowable transmission intervals (MATIs), ensures the stability of the overall system. We also show that the analysis and proofs can be greatly simplified in cases when the control inputs are sent over one communication channel and the plant outputs over a separate channel.

Keywords:Networked control systems, Optimization algorithms, Optimal control Abstract: This paper is devoted to the problem of designing a sparsely distributed sliding mode control for networked systems. Indeed, this note employs a distributed sliding mode control framework by exploiting (some of) other subsystems' information to improve the performance of each local controller so that it can widen the applicability region of the given scheme. To do so, different from the traditional schemes in the literature, a novel approach is proposed to design the sliding surface, in which the level of required control effort is taken into account during the sliding surface design based on the H2 control. We then use this novel scheme to provide an innovative less-complex procedure that explores sparse control networks to satisfy the underlying control objective.

Keywords:Networked control systems, Stochastic systems, Estimation Abstract: In this work we consider systems where the measurements and control signals are transmitted over networks that are affected by independent and identically distributed (i.i.d.) packet losses. In this setting, we study two separate problems. The first one is the design of an offline state estimator. The second one is the design of a linear quadratic regulator (LQR). Both designs take the statistics of the network and the system into account, and are optimal in the sense of minimizing given cost functions. It turns out that these two designs, of which each has an associated Riccati equation, are dual. We show that the convergence of the Riccati equation associated to this dual system formulation is a necessary and sufficient condition for stability of the estimator and controller. Finally, we compare the performance of the proposed offline estimator with those of other estimators available from the literature.

Keywords:Networked control systems Abstract: Networked control systems pose the problem of choosing the communication structure of the controller with the aim to get an overall system with satisfactory performance. This paper shows that in multi-agent systems with leader-follower structure a small percentage p of all possible communication links suffice to ensure a quick reaction of all agents to set-point changes of the leader. It considers agents that are connected in a single path and choose additional communication links randomly with the probability p. The main result shows that for any p>0 there is an upper bound of the delay with which any agent in a network of arbitrary size reacts on leader commands. This result appears as a consequence of the property to have short paths from the leader to all followers, which is known as "six degrees of separation" in large networks and which is extended here to networked control systems in which the nodes represent dynamical systems.

Keywords:Autonomous robots, Optimization algorithms, Robotics Abstract: We propose a framework of algorithms for source seeking using stochastic optimization. We show that the infotaxis algorithm which uses information theory for source seeking can be realized using this framework. Using the framework, we developed a novel algorithm called the expected rate algorithm which has lower computational requirement. We prove that both infotaxis and expected rate algorithms generate identical optimization steps in most cases. Using simulation we show that under certain conditions the proposed algorithm generates more effective optimization steps than infotaxis and verify the computational performance of the proposed algorithm. We also demonstrate the practical applicability of the algorithm in source seeking through experiments.

Keywords:Autonomous robots, Optimization algorithms, Stability of nonlinear systems Abstract: This paper considers a class of stochastic source seeking problems to drive a mobile robot to the maximizer of a source signal by only using measurements of the signal at the robot location. Our algorithm builds on the simultaneous perturbation stochastic approximation idea to obtain information of the signal field. We prove the practical convergence of the algorithm to a ball of size depending on the step-size that contains the location of the source. The novelty of our approach is that we consider nondifferentiable convex functions, a fixed step-size, and the environment can be restricted to any compact convex set. Our proof methods employ nonsmooth Lyapunov theory, tools from convex analysis and stochastic difference inclusions. Finally, we illustrate the applicability of the proposed algorithm in a 2D scenario for the source seeking problem.

Keywords:Uncertain systems, Autonomous systems, Optimization Abstract: In this paper, we propose a reachable set based collision avoidance algorithm for unmanned aerial vehicles (UAVs). UAVs have been deployed for agriculture research and management, surveillance and sensor coverage for threat detection and disaster search and rescue operations. It is essential for the aircraft to have on-board collision avoidance capability to guarantee safety. Instead of the traditional approach of collision avoidance between trajectories, we propose a collision avoidance scheme based on reachable sets and tubes. We then formulate the problem as a convex optimization problem seeking time varying control sets for the ego aircraft given the predicted intruder reachable tube. We have applied the approach on a case study of two quadrotors collision avoidance scenario.

Keywords:Autonomous robots, Robotics, Uncertain systems Abstract: We propose a new sampling-based path planning algorithm, the Min-Max Rapidly Exploring Random Tree (MM-RRT*), for robot path planning under localization uncertainty. The projected growth of error in a robot's state estimate is curbed by minimizing the maximum state estimate uncertainty encountered on a path. The algorithm builds and maintains a tree that is shared in state space and belief space, with a single belief per robot state. Due to the fact that many states will share the same maximum uncertainty, resulting from a shared parent node, the algorithm uses secondary objective functions to break ties among neighboring nodes with identical maximum uncertainty. The algorithm offers a compelling alternative to sampling-based algorithms with additive cost representations of uncertainty, which will penalize high-precision navigation routes that are longer in duration.

Keywords:Uncertain systems, Stochastic systems, Hybrid systems Abstract: This paper reports on the benefit of including boundary interaction behaviors, specifically wall-following, in reducing the position uncertainty of mobile robots with little or no localization capacity. Assuming that the robot has some primitive wall-following capabilities, and can switch its behavior depending on whether it moves in free-space or along obstacle boundaries, the time evolution of its trajectories is modeled by a stochastic differential equation with piece-wise constant drift and diffusion terms. The probability law of this piece-wise linear time-invariant diffusion is matched at any given time instant by that of an appropriately constructed single diffusion, in what is called here a time-weighted convolution. Since the Fokker-Planck associated with the single diffusion can be solved analytically, this matching enables the exact calculation of the position distribution of the stochastic switching vehicle dynamics at any given stopping time.

Keywords:Autonomous systems, Autonomous robots, Cooperative control Abstract: In this work, the problem of maintaining and guaranteeing communication connectivity between a pair of ``client'' agents via controlling a number of ``router'' agents is considered. It is assumed that agents satisfy quadrotor dynamics. A set of controllers are proposed and it is shown that these controllers solve the problem exponentially fast under a set of mild assumptions. The simulation results illustrate the effectiveness of the proposed controllers.

Keywords:Decentralized control, Adaptive control Abstract: We apply retrospective cost adaptive control (RCAC) to a two-channel decentralized disturbance rejection problem. It is shown that the closed-loop channel zeros for each subcontroller consist of the plant zeros and poles of the remaining subcontroller. The nonminimum-phase (NMP) closed-loop channel zeros are included in the modeling information required by RCAC. Two adaptation schemes are presented. In one-controller-at-a-time adaptation, one subcontroller is adapted with the other subcontroller fixed at zero. The first subcontroller is then fixed while the second subcontroller is adapted taking into account the NMP closed-loop channel zeros. We also consider concurrent adaptation, where both controllers are updated at the same time. Finally, we consider decentralized control of the position and shape of a 2DOF lumped flexible body.

Keywords:Decentralized control, Control of networks Abstract: The passivity approach to the design of large networks is based on preserving the passivity property under different types of interconnection: parallel and negative feedback. Since the passivity property implies stability, this allows large and topologically complex networks to be constructed on the basis of simple local rules without the need for global stability analysis. In this paper we characterise two different stability implying properties that are preserved under negative feedback. The first generalises the passivity approach to electrical network design to other classes of minimum phase impedance functions. The second allows for networks with, for example, Laplacian structures in the feedback loop, to be designed using only local models.

Keywords:Decentralized control, Distributed control, Agents-based systems Abstract: A distributed system's interconnection structure emerges as a pattern in the system matrices. This pattern must be preserved through system analysis and control synthesis, and much has been written on these topics. A problem which has not received any attention to date is how to identify a pattern, given the linear system model. This paper proposes a method for identifying a pattern that is mathematically encoded through a commuting relationship with a base matrix. Our method generates the commuting relationship, when it exists. When it does not exist, our method produces the closest approximation to the commuting relationship. Further, it indicates which additional subsystem interconnections would render it achievable. We provide both an exact solution and an almost sure polynomial-time solution in the probabilistic sense. Finally, we give several examples to demonstrate the utility of this method for finding patterns in distributed systems.

Keywords:Decentralized control, Game theory, Linear systems Abstract: We consider a finite horizon dynamic game with two players who observe their types privately and take actions, which are publicly observed. Players' types evolve as independent, controlled linear Gaussian processes and players incur quadratic instantaneous costs. This forms a dynamic linear quadratic Gaussian (LQG) game with asymmetric information. We show that under certain conditions, players' strategies that are linear in their private types, together with Gaussian beliefs form a perfect Bayesian equilibrium (PBE) of the game. Furthermore, it is shown that this is a signaling equilibrium due to the fact that future beliefs on players' types are affected by the equilibrium strategies. We provide a backward-forward algorithm to find the PBE. Each step of the backward algorithm reduces to solving an algebraic matrix equation for every possible realization of the state estimate covariance matrix. The forward algorithm consists of Kalman filter recursions, where state estimate covariance matrices depend on equilibrium strategies.

Keywords:Decentralized control, Large-scale systems, Distributed control Abstract: This paper considers the problem of designing static feedback gains subject to a priori structural constraints, which is in general a non-convex problem. By exploiting the sparsity properties of the problem, and using chordal decomposition, a scalable algorithm is proposed to compute structured stabilizing feedback gains for large-scale systems over directed graphs. Specifically, we first present a chordal decomposition theorem for block-semidefinite matrices. A re- laxation is then used to recast the design of structured feedback gains into a convex problem. Combining the decomposition with the relaxation, we propose a sequential design algorithm to obtain structured feedback gains clique-by-clique over a clique tree of the underlying chordal graph. Numerical simulations demonstrate the efficiency of the proposed method.

Keywords:Control of networks, Network analysis and control, Cooperative control Abstract: The mechanisms of regular cooperative behavior in multi-agent networks, such as e.g. consensus and synchronization, have been thoroughly studied. However, many natural and engineered networks do not synchronize, exhibiting persistent disagreement or clustering. One of the reasons for this "irregular" behavior is competition among some pairs of agents. Whereas cooperative interactions are usually represented by attractive couplings, bringing the trajectories closer, competition between two agents is naturally modeled by a repulsive coupling, maintaining disagreement among the agents and preventing their trajectories from convergence. Such couplings may e.g. describe interactions of antagonistic individuals in social group, competing economic agents and repelling particles. Networks where agents can both cooperate and compete are said to be coopetitive. To study the dynamics of general coopetitive networks, in particular, mechanisms of agents’ splitting into several clusters, remains a challenging problem. A simple yet insightful model of polarization under coopetitive interactions was proposed in [1], [2]. These papers address consensustype dynamics over signed graphs, where arcs of positive and negative weight correspond, respectively, to cooperative and competitive couplings between the agents. If the graph is structurally balanced, these protocols lead to either consensus or “bipartite consensus” (polarization): the agents split into two competing “camps”, and the values (opinions) of agents from different camps agree in modulus but differ in sign. The results from [1], [2] are limited to single integrator agents, interaction over static signed graphs. In this paper, we extend these results to networks with time-varying topology and nonlinear heterogeneous agents, satisfying a relaxed passivity condition.

Keywords:Distributed control, Networked control systems, Agents-based systems Abstract: The problem of trajectory tracking of a moving leader for a directed network where each fully-actuated agent has Euler-Lagrange self-dynamics is studied in this paper using a distributed, model-independent control law. We show that if the directed graph contains a directed spanning tree, with the leader as the root node, then a model-independent algorithm semi-globally achieves the trajectory tracking objective exponentially fast. By model-independent we mean that each agent can execute the algorithm with no knowledge of the agent self-dynamics, though reasonably, certain bounds are known. For stability, a pair of control gains for each agent are required to satisfy lower bounding inequalities and so design of the algorithm is centralised and requires some limited knowledge of global information. Numerical simulations are provided to illustrate the algorithm's effectiveness.

Keywords:Distributed control, Observers for Linear systems, Linear systems Abstract: This paper presents a distributed design scheme of the Luenberger-type state observer for continuous-time linear dynamical systems. The proposed observer consists of networked local observers, and each local observer computes the estimate by the local measurements, which may not be sufficient to recover the full state. Therefore, by communicating with the neighboring observers, the proposed observer compensates for the insufficient information. The novelty of the proposed method is the design of two observer gains; one for local measurements and the other for the information exchange. By exploring the structure of gain matrices, our design can assign the injection gain only to ``detectable'' part of the estimate for the local measurements, and for the ``undetectable'' portion of the estimate, the gain of the information from neighboring observers is set to be relatively higher than others. It turns out that this intuitive idea leads to a simple design of distributed Luenberger-type observers.

Keywords:Distributed control, Optimization algorithms, Smart grid Abstract: In this paper, a fully distributed algorithm is proposed to solve the economic dispatch problem. Without a central control unit, the generators work collaboratively such that the total generation cost is minimized under the balance and capacity constraints. The proposed approach is based on consensus protocols and the saddle point dynamics. The consensus protocols are employed to estimate the global information in a distributed fashion, and the saddle point dynamics is leveraged to search for the optimal solution of the economic dispatch problem. When the capacity limits of the generators are not considered, exponential stability of the optimal solution is proved through Lyapunov stability analysis. With the capacity limits considered, practical stability of the optimal solution is proved by singular perturbation analysis. By the proposed method, no global information is needed, the initial condition of the variables is mild, and no private information is required to be communicated.

Keywords:Power systems, Distributed control, Communication networks Abstract: In this paper, we analyze the impact of communication failures on the performance of optimal distributed frequency control. We consider a consensus-based control scheme, and show that it does not converge to the optimal solution when the communication network is disconnected. We propose a new control scheme that uses the dynamics of power grid to replicate the information not received from the communication network, and prove that it achieves the optimal solution under any single communication link failure. In addition, we show that this control improves cost under multiple communication link failures.

Next, we analyze the impact of discrete-time communication on the performance of distributed frequency control. In particular, we will show that the convergence time increases as the time interval between two messages increases. We propose a new algorithm that uses the dynamics of the power grid, and show through simulation that it improves the convergence time of the control scheme significantly.

Keywords:Distributed control, Predictive control for linear systems, Networked control systems Abstract: In this paper we consider a distributed solution of the model predictive control problem (DMPC), based on the block version of the Jacobi algorithm applied to the dual problem. In order to accelerate the convergence, a Nesterov's schema can be considered, but the updating rule coming out in such way is fully distributed and parallel, but synchronous. This assumption is often unrealistic in real-life large-scale systems. For this reason an asynchronous version of the method has been proposed and the convergence properties have been studied. Numerical experiments show the effectiveness of the approach by comparing it with the methods presented in the literature.

Keywords:Distributed control, Variable-structure/sliding-mode control, Optimization algorithms Abstract: The problem of how to force the states of a network of non-identical systems to converge on a predefined function of the their initial conditions is a problematic challenge because of unknown perturbations or unmodeled dynamics shift the equilibrium of the network with respect to the expected "nominal" one. Furthermore, whenever outlier agents are considered, the well-studied averaged estimation of the agents initial conditions which find application in several field is definitely compromised due to the fragility of the mean statistical measure. In light of these considerations, in this paper we show how the integral sliding-mode control design paradigm can be usefully applied in the framework of multi-agent systems to solve the consensus on the median value problem for a network of perturbed non-identical single integrators. Lyapunov analysis is presented to support the convergence properties of the algorithm, and simulative results are discussed to corroborate the theoretical result.

Keywords:Mean field games, Stochastic optimal control, Decentralized control Abstract: This paper considers a linear-quadratic (LQ) mean field control problem involving a major agent and a large number of minor agents. The objective is to optimize a social cost as a weighted sum of the individual costs under decentralized information, and so the situation may be termed a mean field team problem. We apply the person-by-person optimality principle in team decision theory to the finite population model to construct two limiting optimal control problems whose solutions, subject to the requirement of consistent mean field approximations, yield a system of forward-backward stochastic differential equations (FBSDEs). We show the existence and uniqueness of a solution to the FBSDEs and obtain decentralized strategies nearly achieving social optimality in the original large but finite population model.

Keywords:Stochastic optimal control, Distributed control, Mean field games Abstract: The paper concerns design of control systems for Demand Dispatch to obtain ancillary services to the power grid by harnessing inherent flexibility in many loads. The role of ``local intelligence'' at the load has been advocated in prior work; randomized local controllers that manifest this intelligence are convenient for loads with a finite number of states.

The present work introduces two new design techniques for these randomized controllers: (i) The Individual Perspective Design (IPD) is based on the solution to a one-dimensional family of Markov Decision Processes, whose objective function is formulated from the point of view of a single load. The family of dynamic programming equation appears complex, but it is shown that it is obtained through the solution of a single ordinary differential equation. (ii) The System Perspective Design (SPD) is motivated by a single objective of the grid operator: Passivity of any linearization of the aggregate input-output model. A solution is obtained that can again be computed through the solution of a single ordinary differential equation.

Numerical results complement these theoretical results.

Keywords:Optimization, Optimization algorithms, Power systems Abstract: It is well-known that power networks are prone to cascading failures in the event of a network disruption. A traditional way to prevent such cascading failures is to shed some of the supportable demand from the network. Interestingly, due to the non-local nature of power flow distributions, further deliberate disconnection of lines in a disrupted power network can result in improvements in its supportable demand, the phenomenon resembling Braess' paradox. In this paper, we exploit this phenomenon to formulate a multi-stage control scheme using: a fast timescale, linear Network Stabilization Problem based on demand shedding; and a slow timescale, combinatorial Demand Maximization Problem based on link shedding. We provide a key example illustrating the paradox and some structural results demonstrating the limitations and potential of our control scheme. Using Simulated Annealing to tackle the large combinatorial problem, we also investigate the efficacy of our approach for the Polish power grid (which consists of 2383 buses and 2896 lines).

Keywords:Agents-based systems, Cooperative control, Stability of linear systems Abstract: In a network of n agents, consensus means that all n agents reach an agreement on a specific value of some quantity via local interactions. A linear consensus process can typically be modeled by a discrete-time linear recursion equation or a continuous-time linear differential equation, whose equilibria include nonzero states of the form amathbf{1} where a is a constant and mathbf{1} is a column vector in R^n whose entries all equal 1. Using a suitably defined semi-norm, this paper extends the standard notion of input-output stability from linear systems to linear recursions and differential equations of this type. Sufficient conditions for input-output consensus stability are provided. Connections between uniform bounded-input, bounded-output consensus stability and uniform exponential consensus stability are established. Certain types of additive perturbation to a linear consensus process are considered.

Keywords:Game theory, Uncertain systems, Agents-based systems Abstract: We study a general resource sharing game where overutilization by selfish decision makers leads to possible failure of the resource. Our goal is to understand the effectiveness of a taxation mechanism in reducing the utilization and fragility of the resource when players have behavioral risk preferences. In particular, we incorporate risk preferences drawn from prospect theory, an empirically validated behavioral model of human decision making. We first identify counter-intuitive behavior under prospect theory, where utilization (and hence fragility) can increase under taxation, depending on the resource characteristics. We then identify conditions under which taxation is effective in reducing the fragility of the resource. We also show that homogeneous sensitivities to taxes leads to smaller failure probability compared to the case where players have heterogeneous (player-specific) sensitivities to taxes.

Keywords:Game theory, Markov processes, Learning Abstract: In models of social learning where rational agents observe other agents’ actions, information cascades are said to occur when agents ignore their private information and blindly follow the actions of other. It is well known that in some cases, incorrect cascades happen with positive probability leading to a loss in social welfare. Having agents provide reviews in addition to their actions provides one possible way to avoid such “bad cascades.” In this paper, we study one such model where agents sequentially decide whether or not to purchase a good, whose true value is either “good” or “bad.” If they purchase, agents also leave a review, which is imperfect. We study the impact of such reviews on the asymptotic properties of cascades. For a good underlying state, we propose an algorithm that utilizes number theory principles and Markov chain analysis to solve for the probability of a wrong cascade. We discover that the probability of a wrong cascade is a non-monotonic function of the review strength. On the other hand, for a bad underlying state, the agents always eventually reach a correct cascade; we use a martingale analysis to bound the time until this happens.

Keywords:Game theory, Stochastic systems, Discrete event systems Abstract: We introduce a new class of 2 1/2-player games, the 2 1/2-player GR(1) games, that allows for solving problems of stochastic nature by adding a probabilistic component to simple 2-player GR(1) games. Further, we present an efficient approach for solving qualitative 2 1/2-player GR(1) games with polynomial-time complexity. Our approach is based on a reduction from 2 1/2-player GR(1) games to 2-player GR(1) games that allows for solving the game and constructing, from a sure winning strategy for player [] (resp. <>) in a 2-player GR(1) game, an almost-sure (resp. positively) winning strategy for its corresponding 2 1/2-player GR(1) game. Key to the effectiveness of the proposed approach is the fact that the reduction generates a 2-player game that is linearly larger than the original 2 1/2- player game, more precisely, it is linear with respect to the number of probabilistic states in the 2 1/2-player GR(1) game

Keywords:Game theory, Stochastic systems Abstract: We formulate and analyze dynamic games with d-step (d>=1) delayed sharing information structure. The resulting game is a dynamic game of asymmetric information with hidden actions, imperfect observations, and controlled and interdependent system dynamics. We adopt common information based perfect Bayesian equilibrium (CIB-PBE) as the solution concept, and provide a sequential decomposition of the dynamic game. Such a decomposition leads to a backward induction algorithm to compute CIB-PBEs. We discuss the features of our approach to the above class of games and address the existence of CIB-PBEs.

Keywords:Game theory, Transportation networks Abstract: In engineered systems whose performance depends on user behavior, it is often desirable to influence behavior in an effort to achieve performance objectives. However, doing so naively can have unintended consequences; in the worst cases, a poorly-designed behavior-influencing mechanism can create a perverse incentive which encourages adverse user behavior. For example, in transportation networks, marginal-cost tolls have been studied as a means to incentivize low-congestion network routing, but have typically been analyzed under the assumption that all network users value their time equally. If this assumption is relaxed, marginal-cost tolls can create perverse incentives which increase network congestion above un-tolled levels. In this paper, we prove that if some network users are unresponsive to tolls, any taxation mechanism that does not depend on network structure can create perverse incentives. Thus, to systematically avoid perverse incentives, a taxation mechanism must be network-aware to some extent. On the other hand, we show that a small amount of additional information can mitigate this negative result; for example, we show that it is relatively easy to avoid perverse incentives on affine-cost parallel-path networks, and we fully characterize the taxation mechanisms that minimize congestion for worst-case user populations on such networks.

Keywords:Game theory Abstract: In this paper, we investigate the effect of brand in market competition. Specifically, we propose a variant Hotelling model where companies and customers are represented by points in an Euclidean space, with axes being product features. %Here we focus our attention on 1 or 2 feature market, while our methods can be adapted to higher dimensional market space. N companies compete to maximize their own profits by optimally choosing their prices, while each customer in the market, when choosing sellers, considers the sum of product price, discrepancy between product feature and his preference, and a company's brand name, which is modeled by a function of its market area of the form -betacdottext{(Market Area)}^q, where beta captures the brand influence and q captures how market share affects the brand. By varying the parameters beta and q, we derive existence results of Nash equilibrium and equilibrium market prices and shares. In particular, we prove that pure Nash equilibrium always exists when q=0 for markets with either one and two dominating features, and it always exists in a single dominating feature market when market affects brand name linearly, i.e., q=1. % Moreover, we show that at equilibrium, a company's price is proportional to its market area over the competition intensity with its neighbors, a result that quantitatively reconciles the common belief of a company's pricing power. We also study an interesting ``wipe out'' phenomenon that only appears when q>0, which is similar to the ``undercut'' phenomenon in the Hotelling model, where companies may suddenly lose the entire market area with a small price increment. Our results offer novel insight into market pricing and positioning under competition with brand effect.

Keywords:Game theory Abstract: Two fundamental problems about finite pure harmonic games are investigated in this paper. First, the pure Nash equilibrium of finite pure harmonic games (PHGs) is investigated. For the basis games, the number and precise forms of Nash equilibria are presented. For two-player pure harmonic games, the structure of games with pure Nash equilibrium is revealed. Second, the dynamical equivalence to basis games has been discussed for evolutionary pure harmonic games. A necessary and sufficient condition is obtained.

Keywords:Control of networks, Game theory, Distributed control Abstract: We study distributed editing of network topologies from a game theoretic perspective. The nodes are the agents/players in the game and the editing decisions of each node are to add a new link to another node, remove an existing link, or maintain it. The aim of each node is to achieve a balance between the network property reward and the editing costs for changing and maintaining one's neighborhood. We study several variants of the potential game that result from repeated interactions between agents over the network and describe algorithms that ensure convergence to equilibrium topologies. Simulation results demonstrate the relevant properties of the limiting networks and its dependence on the cost structure.

Keywords:Optimization, Optimal control, Linear systems Abstract: We consider the problem of completing partially known sample statistics in a way that is consistent with underlying stochastically driven linear dynamics. Neither the statistics nor the dynamics are precisely known. Thus, our objective is to reconcile the two in a parsimonious manner. To this end, we formulate a convex optimization problem to match available covariance data while minimizing the energy required to adjust the dynamics by a suitable low-rank perturbation. The solution to the optimization problem provides information about critical directions that have maximal effect in bringing model and statistics in agreement.

Keywords:Optimization, Statistical learning, Computational methods Abstract: Graphical lasso is a popular method for learning the structure of an undirected graphical model, which is based on an l_1 regularization technique. This method aims to find the conditional independence between the entries of a random vector by learning the sparsity pattern of the inverse correlation matrix from a limited number of samples. Graphical lasso is computationally expensive for large-scale problems due to a positive semidefinite constraint. A numerically-cheap heuristic method for finding a graphical model is to simply threshold the sample correlation matrix. Recently, we observed that the computationally-heavy graphical lasso and the simple thresholding method would produce the same solution for functional MRI data, electrical circuit data and many random systems, provided that a sparse graph is sought. The objective of this work is to develop a rigorous mathematical foundation for that observation. More precisely, we systematically study the relationship between these two methods by introducing the notions of sign-consistent and inverse-consistent matrices. We prove that thresholding and graphical lasso are equivalent if: (i) a certain matrix formed based on the sample correlation matrix is both sign-consistent and inverse-consistent, (ii) the gap between the largest thresholded and the smallest un-thresholded entries of the sample correlation matrix is not too small. We demonstrate the above conditions on path and star graphs. These conditions are expected to be satisfied for sufficiently sparse graphical models.

Keywords:Optimization, Stochastic optimal control Abstract: Computation of stochastic reachable and viable sets enables assurances of safety and feasibility through the synthesis of optimal control policies. These control policies are typically generated under the assumption of accurate characterization of additive noise processes. We consider the case in which independent noise processes are not fully characterized. Specifically, we consider linear time-invariant dynamics with additive noise, with known mean and bounded (but unknown) variance. We propose a method to compute a conservative underapproximation to the stochastic viable set for problems with convex viable and target sets. We underapproximate probability values through linear transformation based on bounds on the unknown variance. We demonstrate this method (via dynamic programming) on a simple example.

Keywords:Optimization, Robust control, Uncertain systems Abstract: Robust semidefinite programs are NP-hard in general. In contrast, robust linear programs admit equivalent reformulations as finite-dimensional convex programs provided that the problem data are parameterized affinely in the uncertain parameters; and that the underlying uncertainty set is described by an affine slice of a proper cone. In this paper, we propose a hierarchy of inner and outer polyhedral approximations to the positive semidefinite (PSD) cone that are exact in the limit. We apply these polyhedral approximations to the PSD cone to obtain a computationally tractable hierarchy of inner and outer approximations to the robust semidefinite program, which are similarly exact in the limit. We investigate the strengths and limitations of the proposed approach with a detailed numerical study.

Keywords:Metabolic systems, Systems biology, Optimization Abstract: We formulate a resource allocation problem of interest to microbial ecology and to the emerging area of synthetic ecology. We consider a given number of microbial species symbiotically living in a community and a list of all metabolic reactions present in the community, expressed in terms of the metabolite proportions involved in each reaction. We are interested in allocating reactions to organisms so that each organism maintains a minimal level of growth and the community optimizes certain objectives, such as maximizing growth and/or the uptake of specific compounds from the common environment. We leverage Flux Balance Analysis (FBA) and formulate the problem as a mixed integer linear programming problem. We test our method in a toy model involving two organisms that can only survive through cross-feeding, demonstrating that the method can recover this interaction. We also test the method in a community of two simplified bacteria described in terms of their core, simplified metabolic network. We demonstrate that the method can obtain syntrophic cross-feeding species that would be very difficult to design manually.

Keywords:Optimization, Time-varying systems, Adaptive control Abstract: In this paper, we propose a perturbation amplitude adaption scheme for phasor extremum seeking control based on the plant's estimated gradient. By using phasor extremum seeking instead of classical extremum seeking, the problem of algebraic loops in the controller formulation is avoided. Furthermore, a stability analysis for the proposed method is provided, which is the first stability analysis for extremum seeking controllers using adaptive amplitudes. The proposed method is illustrated using numerical examples and it is found that changes in optimum can be tracked accurately while the steady-state perturbations can be reduced significantly.

Keywords:Markov processes, Stochastic systems, Optimization Abstract: Two-player single-controller zero-sum stochastic games are a class of zero-sum dynamic games with Markovian state dynamics, where only one player controls the state transitions. Design of optimal strategies for such games with large state and action spaces relies on computationally demanding dynamic programming. Linear programming can also be used, but the number of constraints equals the number of states. This paper presents a class of simple suboptimal strategies that can be constructed by playing a certain repeated static game where neither player observes the specific mixed strategies used by the other player at each round. We quantify the suboptimality of the resulting strategies and show that, when the two players honestly follow the prescribed protocol, each player can exploit the regularity or predictability of the moves of the other player, and thus speed up convergence to the minimax value.

Keywords:Markov processes, Formal verification/synthesis, Robust control Abstract: We study the synthesis of robust optimal control policies for Markov decision processes with transition uncertainty (UMDPs) and subject to two types of constraints: (i) constraints on the worst-case, maximal total cost and (ii) safety-threshold constraints that bound the worst-case probability of visiting a set of error states. For maximal total cost constraints, we propose a state-augmentation method and a two-step synthesis algorithm to generate deterministic, memoryless optimal policies given the reward to be maximized. For safety threshold constraints, we introduce a new cost function and provide an approximately optimal solution by a reduction to an uncertain Markov decision process under a maximal total cost constraint. The safety-threshold constraints require memory and randomization for optimality. We discuss the use and the limitations of the proposed solution.

Keywords:Machine learning, Markov processes, Optimization Abstract: We consider the problem of learning a policy used by an agent in a Markov decision process using state-action samples. We focus on a class of parameterized policies and use l1-regularized logistic regression to train a policy that best fits the observed state-action pairs (demonstrations). We bound the difference in average reward of the trained and the original policy (regret) in terms of the generalization error and sensitivity parameters of the Markov chain. Specifically, we use techniques from sample complexity theory to relate regret to the generalization error and techniques from sensitivity analysis of the stationary distribution of Markov chains to relate regret to the ergodic coefficient of the Markov chain. We demonstrate the effectiveness of our method on a synthetic example.

Keywords:Markov processes, Biomolecular systems, Numerical algorithms Abstract: The chemical master equation (CME) is often difficult to solve directly due to the curse of dimensionality. Aggregation was among the earliest ideas for addressing this challenge. It consists in coarsening the state space of the CME to make it more tractable. This reduction inevitably introduces a numerical error that is not trivial to account for, consequently only a few implementations deal with the estimation and control of this aggregation error. Here, we implement an error control by using an adaptive aggregation strategy and the concept of defect (or residual) in the numerical solution of ordinary differential equations. We embed the aggregation approach in the step-by-step matrix exponential implementation of Expokit that uses Krylov subspace approximations. We conduct numerical experiments on test problems that model the toggle switch, receptor oligomerization, and repressilator. This work is an important step toward solving problems that arise in the stochastic modeling of larger biological networks.

Keywords:Markov processes, Uncertain systems, Energy systems Abstract: Operational planning of a small and isolated energy system having a large wind farm and a battery storage device is studied. Operational planning decisions are to be made in two time-scales: daily unit commitment (UC) and hourly dispatch. For this problem, Markov decision process (MDP) and stochastic programming (SP) are combined to account for both daily and hourly changes of wind uncertainty. Two stage SP is formulated for day-ahead UC decision and dispatch decisions considering a number of scenarios regarding uncertainty with respect to hourly ramping of the wind within a day. Here, the value of the end state of daily unit commitment and battery with respect to the future beyond the day (value function), which is estimated from the MDP formulation, is included in the objective function to ensure that longer term implications of the decisions are considered. In the MDP formulation, daily evolving exogenous information on wind speed is captured, and the value function is approximated with a linear model. The coefficient vector of the linear model is recursively updated with sampled observations estimated from the daily SP model. In connection with this, a general wind model for timescales from seasonal to hourly is developed to enable seamless connection of the decision making across the scales. The results of the pro-posed integrated method are compared to those of just the two-stage SP model through a case study and real wind data.

Keywords:Mean field games, Markov processes Abstract: This paper considers mean field games in a multi-agent Markov decision process (MDP) framework. Each player has a continuum state and binary action. By active control, a player can bring its state to a resetting point. All players are coupled through their cost functions. The structural property of the individual strategies is characterized in terms of threshold policies when the mean field game admits a solution. We further introduce a stationary equation system of the mean field game and provide numerical solutions.

Keywords:Observers for nonlinear systems, LMIs, Estimation Abstract: The presence of unmeasured or uncontrolled inputs to dynamical systems can lead to instability or degraded performance. It becomes imperative, therefore, to estimate system states in conjunction with these exogenous disturbance inputs in order to design mitigative robust control strategies. In this paper, a systematic unknown input observer design methodology is proposed for discrete-time nonlinear systems with additive bounded disturbance inputs. Sufficient conditions in the form of linear matrix inequalities are proposed for constructing the observer gains, and providing levels of guaranteed state and unknown input estimation performance. The effectiveness of the proposed method is demonstrated on a numerical example.

Keywords:Observers for nonlinear systems, Hybrid systems Abstract: A method for observer design, using the concept of state immersion and auxiliary outputs, is proposed for linear mechanical systems subject to non-smooth impacts. Assuming elastic impacts, three different observers are proposed, which do not need the knowledge of the impact times.

Keywords:Observers for nonlinear systems, Robotics, Autonomous robots Abstract: We propose a nonlinear observer to estimate the state (orientation and in-plane velocity vector) of the quadrotor, based on a drag-force-enhanced model. It is a simpler and more robust alternative to recent works using a similar model together with an Extended Kalman Filter (EKF). A particular state over-parametrization leads to a linear time-varying model with a nonlinear state-constraint that serves for the observer design. The proposed observer is able to ensure the uniform semi-global asymptotic stability of zero estimation error by incorporating the nonlinear constraint into the correction terms.

Keywords:Observers for nonlinear systems, Uncertain systems, Fault detection Abstract: The problem of designing Unknown Input Observers (UIOs) for nonlinear systems is approached in this paper, in the cases of full and partial information. In the former, it is shown that the construction hinges upon the solution of a system of first-order Partial Differential Equations (PDEs). Such system admits a trivial solution that however renders the observer completely insensitive to disturbances as well as additional control inputs, which is a rather undesirable property in the application of UIOs to the context of Fault Detection. Therefore, we propose an alternative design methodology that allows to extend the set of solutions to the above PDEs by relying merely on the solution of ordinary differential equations, namely by exploiting the Theory of Characteristics. Then, in the partial information scenario, it is shown that introducing a suitable change of coordinates and considering reduced-order observers permit the decomposition of the primary task of disturbance decoupling with that of asymptotic stability, hence providing more intuitive conditions for the observer design.

Keywords:Observers for nonlinear systems, Visual servo control, Lyapunov methods Abstract: In this paper, an observer-based approach is proposed to asymptotically identify the velocity and range of feature points on a moving object using a static-moving camera system. Specifically, the system is composed of a static camera and a moving camera, and the approach is divided into two steps. Firstly, utilizing the static camera, a nonlinear observer is designed to identify the up-to-a-scale velocity of feature points. Secondly, with the moving camera and the estimated scaled velocity, the range of feature points is identified by an adaptive estimator. Owing to the introduction of the static-moving camera system, no motion constraint or a priori geometric knowledge is required for the moving object. Lyapunov-based analyses are used to prove that the estimators asymptotically identify the velocity and range of feature points. The performance of the proposed strategy is demonstrated by simulation results.

Keywords:Observers for nonlinear systems Abstract: High-gain observers proved to be a useful tool in the design of output feedback control of nonlinear systems. However, the observer faces a numerical challenge when its dimension is high. For an observer of dimension rho and a high-gain parameter k, the observer gain is of the order of k^{rho} and the observer variables could be of the order of k^{rho-1} during the transient period. This paper presents a new high-gain observer that is based on cascading lower-dimensional observers with saturation functions in between them. In the new observer, the gains and variables are of the order of k. It is shown that the cascade observer has properties similar to the standard one.

Keywords:Identification for control, Subspace methods, Linear parameter-varying systems Abstract: A common challenge associated with designing a Linear Parameter-Varying (LPV) controller for a nonlinear plant is identification of a plant model in state-space form with static parameter dependency. Till date, the two most frequently used methods to solve this problem are special canonical forms of Input-Output (IO) and subspace (SS) identification. This paper compares both identification methods on various criteria with a focus on low-complexity LPV systems. Features of both methods are illustrated by identification results on a simulated MIMO LPV system taken from the literature and by experimental results on the air-path system of a gasoline engine. Finally, some insight into the selection of an identification method for a given model class is provided.

Keywords:Identification for control, Predictive control for nonlinear systems, Stochastic systems Abstract: A fast stochastic model predictive control (SMPC) strategy using latent variable model is presented in this paper. In the first part of this paper, we introduce a novel data-driven approach to approximately linearize a nonlinear dynamical system in a latent space, and then identify a stochastic linearized system using a subspace state space system identification algorithm. The stochastic linear system is more tractable than the original nonlinear system because of its linearity and Gaussian distributions of latent states. In the second part of this paper, we discuss transformation of the stochastic problem into tractable deterministic one in the latent space. Our proposed strategy is based on the idea that we translate SMPC problem into tractable one in advance by offline calculation to reduce the online computational cost. The reformulated deterministic MPC problem can be also solved by parallel computation. The effectiveness of the proposed strategy is demonstrated by numerical simulations.

Keywords:Identification for control, Identification, Linear systems Abstract: The paper provides a comparison between noniterative direct data-driven control design approaches for non-minimum-phase systems. In particular, the most well known methods, i.e., Correlation based Tuning and Virtual Reference Feedback Tuning, are compared to the recently introduced non-iterative version of the Unfalsified Approach for control system design. The overall comparative analysis is substantiated by a thorough simulation campaign on two benchmark problems.

Keywords:Identification for control, Automotive control, Uncertain systems Abstract: In four-wheel steering vehicles, the rear wheels can be used to adjust the driver’s front action to enhance vehicle stability and performance. To the best of the authors’ knowledge, all the existing control design methods rely on a simple model of the lateral dynamics, which may lead to unsatisfactory results in case of uncertainty. In this paper, we propose to use a modified version of the (model-free) Virtual Reference Feedback Tuning approach, where probabilistic guarantees are given for operating conditions different from the identification experiment. We validate the proposed approach on a thorough simulation campaign using a multibody simulator.

Keywords:Identification, Model Validation, Identification for control Abstract: The identification of continuous-time models of dynamical systems based on sampled measurements of input and output signals is a research topic that has received much attention during the past decade. However, a framework for the correct assessment of the performance of various estimation methods, as well as their numerical reliability, is still missing due to a number of benchmarking difficulties, equally applicable to both discrete- and continuous-time identification problems. This paper revisits this topic, reports new numerical results, highlights several fundamental aspects regarding the definition of an appropriate benchmark for the evaluation of continuous-time linear model identification algorithms and discusses several means of addressing the related existing problems.

Keywords:Identification, Identification for control, Information theory and control Abstract: We consider the problem of system identification of linear time invariant systems when some of the sensor measurements are changed by a malicious adversary. We treat adversaries as omniscient and impose no restrictions (statistical or otherwise) on how they can alter the measurements of the sensors under attack. Given a bound on the number of attacked sensors, and under a certain observability condition, we show that we construct models that are useful for certain control purposes, e.g., stabilization. We also provide a precise characterization of the equivalence relation that identifies which models cannot be distinguished in the presence of attacks.

Keywords:Learning, Automata, Iterative learning control Abstract: Reinforcement Learning aims to find the optimal decision in uncertain environments on the basis of qualitative and noisy on-line performance feedback provided by the environments. During the past four decades, learning theory has grown into a vast field in which a very large number of problems have been studied. One of the primary limitations of reinforcement schemes, acknowledged by workers in the field, is their slow speed of convergence. The principal objective of this paper is to present a new approach, based on the use of multiple models (or estimates), that may alleviate this problem and increase the speed of response.

In adaptive control theory, multiple model based methods have been proposed over the past two decades, which improve substantially the performance of the system. The authors undertook to apply similar concepts in reinforcement learning as well, and this paper represents the first effort in this direction. Simple situations of learning in feed-forward networks are considered in the paper, and compared to two different schemes. It is shown that convergence speeds that are more than an order of magnitude faster than those of the first scheme, can be achieved in some cases. While the second scheme is comparable to the new approach in many situations, it is seen to exhibit undesirable behavior in others, where the new approach is more robust. The latter is currently being extended incrementally and systematically to more complex problems that have been discussed in the literature. The ultimate aim of the authors is to apply this approach to learning in discrete and continuous state dynamic environments.

Keywords:Iterative learning control, Optimal control, Mechanical systems/robotics Abstract: This paper proposes a novel control methodology to enable accurate tracking of a path profile defined in output space. No temporal requirement is specified on this movement a priori, and the proposed framework enforces path tracking while minimizing an additional objective function. The problem is solved by formulating the problem as a constrained optimization involving simultaneous spatial tracking constraints and temporal via-point constraints. Practical implementation is via a two stage iterative learning control algorithm based on norm optimal and gradient updates which embeds robustness to plant uncertainty. The algorithm is verified using a gantry robot experimental platform, whose results reveal practical efficacy.

Keywords:Learning, Optimization Abstract: In this paper, we address tracking of a time-varying parameter with unknown dynamics. We formalize the problem as an instance of online optimization in a dynamic setting. Using online gradient descent, we propose a method that sequentially predicts the value of the parameter and in turn suffers a loss. The objective is to minimize the accumulation of losses over the time horizon, a notion that is termed dynamic regret. While existing methods focus on convex loss functions, we consider strongly convex functions so as to provide better guarantees of performance. We derive a regret bound that captures the path-length of the time-varying parameter, defined in terms of the distance between its consecutive values. In other words, the bound represents the natural connection of tracking quality to the rate of change of the parameter. We provide numerical experiments to complement our theoretical findings.

Keywords:Iterative learning control, Robotics, Learning Abstract: Iterative learning control (ILC) is a strategy that allows a control system to improve its performance by making use of the error signals collected from previous iterations. A prerequisite of using ILC is that the output reference has to be repetitive from trial to trial. A full run of ILC training (taking non-negligible time) is needed when there exist small changes in the reference signal. This paper introduces a new approach to extrapolate the converged ILC policies to previously unseen tracking problems. A time-frequency domain mapping is constructed to approximate the ILC policy for a group of trajectories used in a particular task, say spot welding. We also introduce the idea of feature-frequency space, where the ILC policies from different trajectories can be encoded into a single model. This model can generate a control policy that performs comparably to the ILC policy while having the advantage of not requiring a full training for a new trajectory. The proposed method implemented on a FANUC R-2000iC robot achieved 31.6% of vibration reduction whereas the standard ILC (i.e., with a full training for each particular trajectory) achieved 34.6% of vibration reduction.

Keywords:Learning, Stochastic systems, Optimization Abstract: We describe and study a model for an Automated Online Recommendation System (AORS) in which a user's preferences can be time-dependent and can also depend on the history of past recommendations and play-outs. The three key features of the model that makes it more realistic compared to existing models for recommendation systems are (1)~user preference is inherently latent, (2)~current recommendations can affect future preferences, and (3)~it allows for the development of learning algorithms with provable performance guarantees. The problem is cast as an average-cost restless multi-armed bandit for a given user, with an independent partially observable Markov decision process (POMDP) for each item of content. We analyze the POMDP for a single arm, describe its structural properties, and characterize its optimal policy. We then develop a Thompson sampling-based online reinforcement learning algorithm to learn the parameters of the model and optimize utility from the binary responses of the users to continuous recommendations. We then analyze the performance of the learning algorithm and characterize the regret. Illustrative numerical results and directions for extension to the restless hidden Markov multi-armed bandit problem are also presented.

Keywords:Learning Abstract: This paper presents an active-learning technique for constructing a fault diagnoser for an unknown finite-state Discrete Event System (DES). The proposed algorithm actively asks some basic queries from an oracle through which the algorithm completes a series of observation tables leading to the construction of the diganoser. The resulting diagnoser is a deterministic-finite-state automaton, which detects and identifies occurred faults by monitoring the observable behaviors of the plant. An illustrative example is provided detailing the steps of the proposed algorithm.

Keywords:Switched systems, Optimal control, Optimization algorithms Abstract: This paper concerns a first-order algorithmic technique for a class of optimal control problems defined on switched-mode hybrid systems. The salient feature of the algorithm is that it avoids the computation of Fr´echet or Gˆateaux derivatives of the cost functional, which can be time consuming, but rather moves in a projected-gradient direction that is easily computable (for a class of problems) and does not require any explicit derivatives. The algorithm is applicable to a class of problems where a pointwise minimizer of the Hamiltonian is computable by a simple formula, and this includes many problems that arise in theory and applications. The natural setting for the algorithm is the space of continuous time relaxed controls, whose special structure renders the analysis simpler than the setting of ordinary controls. While the space of relaxed controls has theoretical advantages, its elements are abstract entities that may not be amenable to computation. Therefore, a key feature of the algorithm is that it computes adequate approximations to relaxed controls without loosing its theoretical convergence properties. Simulation results, including cpu times, support the theoretical developments.

Keywords:Switched systems, Optimization, Optimal control Abstract: Switching time optimization arises in finite-horizon optimal control for switched systems where, given a sequence of continuous dynamics, we minimize a cost function with respect to the switching times. In this paper we propose an efficient method for computing optimal switching times in switched linear systems. We derive simple expressions for the cost function, the gradient and the Hessian which can be computed efficiently online without performing any integration. With the proposed method, the most expensive computations are decomposed into independent scalar exponentials which can be efficiently computed and parallelized. Simulation results show that our method is able to provide fast convergence and handle efficiently a high number switching times.

Keywords:Switched systems, Uncertain systems, LMIs Abstract: This paper deals with observer-based controller design method via Linear Matrix Inequalities~(LMIs) for a class of switched discrete-time linear systems. The main contribution consists in providing different scenarios of the use of Finsler's Lemma to reduce the conservatism of some previous results in the literature. Thanks to this scenarios and the use of some other new mathematical tools, one of the objectives of this paper is to open new research directions for other control design problems. The validity and effectiveness of the proposed design methodologies are shown through a numerical example.

Keywords:Switched systems, Uncertain systems Abstract: This paper addresses the problem of determining the root mean square (RMS) gain of continuous-time switched linear systems in the case of arbitrary switching. It is shown that a sufficient condition for establishing upper bounds of the RMS gain can be given in terms of a linear matrix inequality (LMI) feasibility test by searching for a homogeneous rational Lyapunov function (HRLF) of any a priori chosen degree. Moreover, it is shown that this condition is also necessary under some assumptions by using HRLF candidates with degree sufficiently large. Some numerical examples illustrate the proposed methodology and the advantages with respect to the existing works.

Keywords:Switched systems Abstract: The reachable set estimation and control problems for continuous-time switched linear systems are addressed in this paper. First, a general result on reachable set estimation for switched system is proposed based on a Lyapunov function approach. Then, with the help of a class of time-scheduled Lyapunov functions, a numerically tractable sufficient condition ensuring the system state bounded in a prescribed set is derived for switched systems under dwell time constraint. Moreover, a time-scheduled state feedback controller is designed to ensure the state trajectories of the closed-loop system are confined in a prescribed set. Finally, a networked control system subject to packet dropouts is modeled as a switched system with dwell time constraints, and the controller design problem is studied as an application of our results.

Keywords:Switched systems Abstract: This paper presents robust stabilizability analysis and stabilizing state-feedback controller design for discrete-time piecewise affine systems in the presence of disturbance inputs. The piecewise affine plant leads to an increasing sequence of robust symbolic models by extending existing symbolic models to the case where bounded disturbance inputs, as well as control inputs, affect the state transfer. A numerical example illustrates the developed analysis and design approaches

Keywords:Robust control, Uncertain systems, Lyapunov methods Abstract: This paper considers the problem of global stabilization for a class of nonlinear systems with time-varying powers. A new design method based on the technique of adding a power integrator and the interval homogeneous domination approach, which can be thought as an evolution of the homogeneous domination approach, is developed to explicitly construct a smooth state feedback globally stabilizing controller. The novelty of this paper is the development of a systematic scheme, which provides us a new perspective to deal with the state feedback control problem for the nonlinear systems with time-varying powers.

Keywords:Robust control, Uncertain systems, Stability of nonlinear systems Abstract: This paper focusses on stability and performance analysis of feedback interconnections involving a linear time invariant and an uncertain system subject to some external disturbances. We extend the framework of integral quadratic constraints to general signal spaces and specifically apply this concept to Sobolev spaces. Our new framework offers the possibility for a natural generalization from constraints on the inputs and outputs of uncertainties to relations among derivatives thereof. In addition, it allows to impose performance criteria that put special emphasis on chosen derivatives.

Keywords:Predictive control for linear systems, Stability of nonlinear systems, Optimization algorithms Abstract: It is a well known fact that finite time optimal controllers, such as MPC does not necessarily result in closed loop stable systems. Within the MPC community it is common practice to add a final state constraint and/or a final state penalty in order to obtain guaranteed stability. However, for more advanced controller structures it can be difficult to show stability using these techniques. Additionally in some cases the final state constraint set consists of so many inequalities that the complexity of the MPC problem is too big for use in certain fast and time critical applications. In this paper we instead focus on deriving a tool for a-postiori analysis of the closed loop stability for linear systems controlled with MPC controllers. We formulate an optimisation problem that gives a sufficient condition for stability of the closed loop system and we show that the problem can be written as a Mixed Integer Linear Programming Problem (MILP)

Keywords:Stability of nonlinear systems, Stability of hybrid systems Abstract: This paper is concerned with analyzing noise-to-state stability of a class of nonlinear systems with random disturbances and impulses. It is assumed that the random noises have finite second-order moments and the random impulses have impulse ranges driven by a sequence of random variables. The Lyapunov approach is first utilized to establish the criteria on global existence and stability of solutions for the considered random nonlinear impulsive systems. Then the average impulsive interval approach is applied to develop sufficient conditions on noise-to-state stability of random nonlinear impulsive systems. A numerical example is presented to show the efficiency of the proposed theoretical results.

Keywords:Stability of nonlinear systems, Agents-based systems, Adaptive control Abstract: Self-stabilizing (asymptotically stable) distance estimation algorithms are an important building block of many distributed systems featuring in Spatial or Aggregate computing, but the dynamics of their convergence to correct distance estimates has not previously been formally analyzed. As a first step to understanding, how they behave in interconnections involving other building blocks, it is important to develop a Lyapunov framework to demonstrate their robust stability. This paper addresses this shortcoming by providing the first Lyapunov-based analysis of an adaptive Bellman-Ford algorithm, by formulating a simple Lyapunov function. This analysis proves global uniform asymptotic stability of such algorithms, a property which the classical Bellman-Ford algorithm lacks, thus demonstrating a measure of robustness to structural perturbations, empirically observed by us in a previous work.

Keywords:Stability of nonlinear systems, Uncertain systems, Variable-structure/sliding-mode control Abstract: The known results on asymptotic stability of homogeneous differential inclusions with negative homogeneity degrees and their accuracy in the presence of noises and delays are extended to arbitrary homogeneity degrees. Discretization issues are considered, which include explicit and implicit Euler integration schemes. Computer simulation illustrates the theoretical results.

Keywords:Variable-structure/sliding-mode control, Power systems, Uncertain systems Abstract: In this paper the design of sliding mode controllers for Maximum Power Point Tracking (MPPT) of a photovoltaic inverter in microgrids is presented. A master-slave configuration of the microgrid is considered in islanded operation mode where the photovoltaic Distributed Generation unit (DGu) serves as a slave. The DGu is also affected by nonlinearities, parameters and modelling uncertainties, which make the use of the sliding mode control methodology particularly appropriate. Specifically, a sliding mode controller, relying on the so-called unit vector approach, is first proposed to control the photovoltaic inverter. Then, a Second Order Sliding Mode (SOSM) controller, adopting a Suboptimal SOSM algorithm, is proposed to alleviate the chattering phenomenon and feed a continuos modulating signal into the photovoltaic inverter. Simulation tests, carried out on a realistic scenario, confirm satisfactory closed-loop performance of the proposed control scheme.