Keywords:Optimization algorithms, Optimization, Machine learning Abstract: We consider a class of nonsmooth convex com- posite optimization problems, where the objective function is given by the sum of a continuously differentiable convex term and a potentially non-differentiable convex regularizer. In [1], the authors introduced the proximal augmented Lagrangian method and derived the resulting continuous-time primal-dual dynamics that converge to the optimal solution. In this paper, we extend these dynamics from continuous to discrete time via the forward Euler discretization. We prove explicit bounds on the exponential convergence rates of our proposed algorithm with a sufficiently small step size. Since a larger step size can improve the convergence speed, we further develop a linear matrix inequality (LMI) condition which can be numerically solved to provide rate certificates with general step size choices. In addition, we prove that a large range of step size values can guarantee exponential convergence. We close the paper by demonstrating the performance of the proposed algorithm via computational experiments.

Keywords:Iterative learning control, Optimization, Robotics Abstract: This paper takes the advantage of iterative learning control (ILC) to solve spatial path following problems with high tracking accuracy. The concept of spatial path tracking is first introduced by defining a varying reference profile, which specifies the speed along the path. The task description of ILC is extended to incorporate the scope of spatial tracking by enabling its reference profile as a changing variable. Hence, a spatial ILC algorithm with monotonic convergence properties is derived, which updates the input signal and reference profile simultaneously by solving a minimum norm problem. This optimization problem is further reformulated into a second order cone programming (SOCP) problem by linear approximation, and the global optimal solution can be obtained. Based on a gantry robot model, numerical tests are undertaken to demonstrate the feasibility of the proposed algorithm.

Keywords:Optimization algorithms, Distributed control Abstract: In this paper, we consider the problem of minimizing the sum of nonconvex and possibly nonsmooth functions over a connected multi-agent network, where the agents have partial knowledge about the global cost function and can only access the zeroth-order information (i.e., the functional values) of their local cost functions. We propose and analyze a distributed primal-dual gradient-free algorithm for this challenging problem. We show that by appropriately choosing the parameters, the proposed algorithm converges to the set of first order stationary solutions with a provable global sublinear convergence rate. Numerical experiments demonstrate the effectiveness of the proposed method for optimizing nonconvex and nonsmooth problems over a network.

Keywords:Optimization algorithms, Distributed control, Large-scale systems Abstract: Submodular optimization is a special class of combinatorial optimization arising in several machine learning problems, but also in cooperative control of complex systems. In this paper, we consider agents in an asynchronous, unreliable and time-varying directed network that aim at cooperatively solving submodular minimization problems in a fully dis- tributed way. The challenge is that the (submodular) objective set-function is only partially known by agents, that is, each one is able to evaluate the function only for subsets including itself. We propose a distributed algorithm based on a proper linear programming reformulation of the combinatorial problem. Our algorithm builds on a column generation approach in which each agent maintains a local candidate basis and locally generates columns with a suitable greedy inner routine. A key interesting feature of the proposed algorithm is that the pricing problem, which involves an exponential number of constraints, is solved by the agents through a polynomial time greedy algorithm. We prove that the proposed distributed algorithm converges in finite time to an optimal solution of the submodular minimization problem and we corroborate the theoretical results by performing numerical computations on instances of the s–t minimum graph cut problem.

Keywords:Optimization algorithms, Large-scale systems, Machine learning Abstract: We study a standard distributed optimization framework where N networked nodes collaboratively minimize the sum of their local convex costs. The main body of existing work considers this problem when the underlying

network is either static or deterministically varying, and the distributed optimization algorithm is of first or second order, i.e., it involves the local costs' gradients and possibly the local Hessians. In this paper, we consider the relatively unexplored but highly relevant scenarios when: 1) only noisy function values are available (no gradients nor Hessians can be directly evaluated); and 2) the underlying network is randomly varying (according to an independent, identically distributed process). For the above random networks based zeroth order optimization setting, we develop a distributed stochastic approximation method of the Kiefer-Wolfowitz type. Furthermore, under standard smoothness and strong convexity assumptions on the local costs, we establish the O(1/k^{1/2}) mean square convergence rate for the method -- the rate that matches that of the method's centralized counterpart under equivalent conditions.

Keywords:Optimization algorithms, Computational methods Abstract: We present a novel heuristic first order method for large-scale mixed-integer programs, more specifically we focus on mixed-integer quadratically constrained quadratic programs. Our method builds on Lagrangian relaxation techniques and Hopfield Neural Networks. For illustration, we apply this method to an economic load dispatch problem and compare with two convex approximation techniques.

Keywords:Stochastic optimal control, Information theory and control, Emerging control applications Abstract: We characterize the n-finite time feedback information (FTFI) control-coding capacity of decision models (DMs) driven by correlated noise. Under information stability the per unit limit, called control-coding (CC) capacity of the DM is operational, and analogous to Shannon's coding capacity of noisy communication channels, with the encoder replaced by a controller-encoder.

We also analyze application examples of recursive linear DMs driven by correlated Gaussian noise, subject to an average cost constraint of quadratic form, called linear-quadratic Gaussian DMs (LQG-DMs). In one of the main theorems we show that the optimal randomized control strategies that achieve the n-FTFI CC capacity of the LQG-DMs, consist of multiple parts, that include control, estimation, and information transmission/signalling strategies, and that these strategies are determined using decentralized optimization techniques.

Keywords:Stochastic optimal control, Stochastic systems, Optimal control Abstract: A linear-quadratic optimal control problem with an infinite time horizon for a scalar linear stochastic differential equation with additive Rosenblatt noise is formulated and solved. The Rosenblatt process is a non-Gaussian continuous stochastic process which exhibits self-similarity and long-range dependence. The feedback form of the optimal control and the optimal cost are given explicitly. The main tool used to find the optimal control is an It^o-type formula for a Rosenblatt process with drift.

Keywords:Stochastic optimal control, Computational methods Abstract: We consider the infinite dimensional stochastic linear quadratic optimal control problem for the infinite horizon case. We provide a numerical framework for solving this prob- lem using a polynomial chaos expansion approach. By applying the method of chaos expansions to the state equation, we obtain a system of deterministic partial differential equations in terms of the coefficients of the state and the control variables. We set up a control problem for each equation, which results in a set of infinite horizon deterministic linear quadratic regulator problems. We prove the optimality of the solution expressed in terms of the expansion of these coefficients compared to the direct approach. We perform numerical experiments which validate our approach and compare the finite and infinite horizon case.

Keywords:Stochastic optimal control, Game theory, Markov processes Abstract: This paper investigates an infinite-horizon incentive Stackelberg game for discrete-time linear stochastic systems subject to Markov jump parameters and external disturbance by means of static output feedback (SOF). In contrast to the existing studies, players can only have access to local output information in designing their incentive Stackelberg strategies with H-infinity constraint. It is shown that the incentive Stackelberg strategy set is obtained by solving a set of higher-order cross-coupled Lyapunov type equations (CCLTRs). As another important contribution, a numerical algorithm is proposed based on the coordinate descent method that guarantees local convergence. A numerical example demonstrates the existence of the SOF incentive Stackelberg strategy set and the effectiveness of the proposed algorithm.

Keywords:Stochastic optimal control, Stochastic systems, Optimization Abstract: Path Integral control theory yields a sampling-based methodology for solving stochastic optimal control problems. Motivated by its computational efficiency, we extend this framework to account for systems evolving on Lie groups. Our derivation relies on recursive mappings between system poses and corresponding Lie algebra elements. This approach allows us to apply standard facts from stochastic calculus, and obtain expressions analogous to those of Euclidean problems. Our results imply that stochastic optimal control can be applied in a coordinate-free manner, even when nonlinear configuration spaces are considered. The method is tested in simulation on a simple model of a rigid satellite.

Keywords:Stochastic systems, Identification, Optimization Abstract: In this paper we propose an identification procedure of a sparse graphical model associated to a Gaussian stationary stochastic process. The identification paradigm exploits the approximation of autoregressive processes through reciprocal processes in order to improve the robustness of the identification algorithm, especially when the order of the autoregressive process becomes large. We show that the proposed paradigm leads to a regularized, circulant matrix completion problem whose solution only requires computations of the eigenvalues of matrices of dimension equal to the dimension of the process.

Keywords:Lyapunov methods, Networked control systems, Quantized systems Abstract: A secure nonlinear networked control system (NCS) design using semi-homomorphic encryption, namely, Paillier encryption is studied. Under certain assumptions, control signal computation using encrypted signal directly is allowed by semi-homomorphic encryption. Thus, the security of the NCSs is further enhanced by concealing information on the controller side. However, additional technical difficulties in the design and analysis of NCSs are induced compared to standard NCSs. In this paper, the stabilization of a nonlinear discrete time NCS is considered. More specifically, sufficient conditions on the encryption parameters that guarantee stability of the NCS are provided, and a trade-off between the encryption parameters and the ultimate bound of the state is shown.

Keywords:Control over communications, Optimal control Abstract: With the advent of cloud computing and the increasing connectivity of devices at the edge of the internet, closing feedback control loops over the cloud is becoming a reality. This is especially the case when computationally expensive algorithms, such as model-predictive control for nonlinear plants, are used to optimize performance. A major roadblock to closing feedback control loops over the cloud, however, is ensuring privacy of the exchanged data. Further exacerbating this difficulty, is the need to minimize the computational overhead of enforcing privacy so as not to degrade control performance. In this paper, we propose several methods for enforcing data privacy using symmetry transformations. We address three different scenarios: a) the cloud has no knowledge about the system being controlled; b) the cloud knows what sensors and actuators the system employs but not the system dynamics; c) the cloud knows the system dynamics, its sensors, and actuators. The proposed methods allow us, in all of these three scenarios, to successfully execute control over the cloud without revealing private information (which information is considered private depends on the considered scenario). The advantage of these methods lies in their generality, which makes them applicable to wide class of systems and with low computational overhead.

Keywords:Predictive control for linear systems, Optimization, Emerging control applications Abstract: This paper explores the privacy of cloud outsourced Model Predictive Control (MPC) for a linear system with input constraints. A client sends her private states to the cloud who performs the MPC computation and returns the control inputs. In order to guarantee that the cloud can perform this computation without obtaining anything about the client's private data, we employ a partially homomorphic cryptosystem. We propose protocols for two cloud-MPC architectures: a client-server architecture and a two-server architecture. In the first case, a control input for the system is privately computed by the cloud server with the assistance of the client. In the second case, the control input is privately computed by two independent, non-colluding servers, with no additional requirements from the client. We prove that the proposed protocols preserve the privacy of the client's data and of the resulting control input. Furthermore, we compute bounds on the errors introduced by encryption. We discuss the trade-off between communication, MPC performance and privacy.

Keywords:Emerging control applications, Computational methods, Networked control systems Abstract: Encryption of feedback controller based on homomorphic encryption techniques allows control operation on encrypted sensor measurements, to protect data secrecy of networked control systems. In this paper, we first revisit the fact that an encrypted dynamic controller based on partially homomorphic cryptosystems cannot operate for infinite time horizon in general due to the problem of the size of encrypted controller state. Then, it is highlighted that an encrypted LTI controller can operate for infinite time horizon when the denominator of its transfer function is a monic polynomial with integer coefficients. In this case, it does not utilize bootstrapping techniques from fully homomorphic encryption for resizing the controller state, and it does not assume the decryption of controller state from time to time. In this respect, we discuss potential benefits of using PID controllers and FIR filters. Then, we introduce a way how to approximately convert controllers having non-integer coefficients to have integer coefficients without losing stability.

Keywords:Networked control systems, Cooperative control, Distributed control Abstract: Cooperative control for multi-agent systems usually requires some communication between the various subsystems. In the resulting networked control system, sensitive data is transmitted and shared between the agents. We propose a novel encrypted control scheme that ensures privacy of the individual agents' data not only during transmission but also during controller evaluations at neighboring agents. Our control scheme efficiently combines the design of structured feedback laws for multi-agent systems with encrypted controllers for conventional linear systems. The underlying key technology is partial homomorphic encryption, which allows simple computations to be carried out on encrypted data.

Keywords:Linear systems, Fault detection, Quantized systems Abstract: This study proposes an encrypted control system capable of the dynamic management of the switching of public and private keys as a means of enhancing cyber-security. Dynamic management involves the selection of keys based on timestamp information that identifies the correct pairs of public and private keys. A security level index indicates the computational cost of deciphering the keys, and shows that the proposed encrypted control system is more secure than a conventional encrypted control system that uses static-key management. Furthermore, the proposed control system makes it easier to detect controller falsification attacks and replay attacks. Finally, a numerical example demonstrates that the proposed encrypted control system is more secure and can better detect the replay attacks.

Keywords:Decentralized control, Stochastic optimal control, Stochastic systems Abstract: In this paper, we introduce a topology for policies in decentralized stochastic control models to establish the existence of team-optimal policies for both static and a class of sequential dynamic teams. We first consider the static team problems and show the existence of optimal policies under the assumption that the observation channels have densities and are continuous with respect to the total variation distance. Then we consider sequential dynamic teams and establish the existence of an optimal policy via the static reduction method of Witsenhausen. We apply our findings to the well-known counterexample of Witsenhausen and the Gaussian relay channel.

Keywords:Decentralized control, Kalman filtering, Linear systems Abstract: We consider the problem of optimal decentralized estimation of a linear stochastic process by multiple agents. Each agent receives a noisy observation of the state of the process and delayed observations of its neighbors (according to a pre-specified, strongly connected, communication graph). Based on their observations, all agents generate a sequence of estimates of the state of the process. The objective is to minimize the total expected weighted mean square error between the state and the agents' estimates over a finite horizon. In centralized estimation with weighted mean square error criteria, the optimal estimator does not depend on the weight matrix in the cost function. We show that this is not the case when the information is decentralized. The optimal decentralized estimates depend on the weight matrix in the cost function. In particular, we show that the optimal estimate consists of two parts: a common estimate which is the conditional mean of the state given the common information and a correction term which is a linear function of the offset of the local information from the conditional expectation of the local information given the common information. The corresponding gain depends on the weight matrix as well as on the covariance between the offset of agents' local information from the conditional expectation of the local information given the common information. We show that the common estimate can be computed from single Kalman filter and derive recursive expressions for computing the offset covariances and the estimation gains.

Keywords:Stochastic optimal control, Decentralized control, Stochastic systems Abstract: For sequential stochastic control problems with standard Borel measurement and control action spaces, we introduce a general dynamic programming formulation, establish its well-posedness, and provide new existence results for optimal policies. Our dynamic program builds in part on Witsenhausen's standard form, but with a different formulation for the state, action, and transition dynamics. Using recent results on measurability properties of strategic measures in decentralized control, we obtain a controlled Markov model with standard Borel state and state dependent action sets. This allows for a well-posed formulation for the controlled Markov model for a general class of sequential decentralized stochastic control in that it leads to well-defined dynamic programming recursions through universal measurability properties of the value functions for each time stage. In addition, new existence results are obtained for optimal team policies in decentralized stochastic control. These state that for a static team with independent measurements, it suffices for the cost function to be continuous (only) in the actions for the existence of an optimal policy under mild compactness conditions. These also apply to dynamic teams which admit static reductions with independent measurements.

Keywords:Game theory, Stochastic optimal control, Stochastic systems Abstract: Martingale techniques are applied to derive sufficient decentralized optimality conditions for general stochastic differential games, with multiple Decision Makers (DMs), who aim at optimizing a common pay-off, based on the notion of decentralized Person-by-Person (PbP) optimality.

The methodology utilizes the value processes of each one of the DMs of the game, and relates them to solutions of backward stochastic differential equations (SDEs). The sufficient conditions for decentralized PbP optimality are expressed in terms of conditional Hamiltonians, conditioned on the information structures of the DMs.

The mathematical models are generalizations of the ones considered in [1], while the decentralized PbP optimality conditions of this paper degenerate to the ones derived in [1] via the stochastic maximum principle.

Keywords:Stochastic optimal control, Game theory, Optimization Abstract: This paper considers a zero-sum game between a team of delay-constrained encoder and decoder, and a finite state jammer, with average probability of error as the payoff. The team attempts to communicate a discrete source using a finite blocklength over a finite family of discrete channels whose state is controlled by the jammer. For each strategy of the jammer, the team's problem has nonclassical information structure and hence is nonconvex, whereby a saddle point solution may not exist for the game. Our main contributions consist of a novel lower bound on the min-max and max-min value of the game via a linear programming (LP) relaxation and a new upper bound on the min-max value. These bounds imply that for rates of transmission R satisfying RCu, where Cl,Cu are precomputable thresholds depending on the channel kernels, the min-max and max-min values of the game approach each other as the blocklength n rightarrow infty. In the intermediate range, we give a fundamental lower bound on the limiting max-min value, which for a two-state jammer is shown to be frac{1}{2}.

Keywords:Stochastic systems, Game theory, Decentralized control Abstract: We study a general class of decentralized dynamic decision-making problems with many agents, asymmetric information, and hidden actions. We propose the notion of sufficient information that provides a mutually consistent compression of the agents' private and common information for decision-making purposes. We define a class of strategies, called sufficient information-based (SIB) strategies, that are based on the agents' sufficient information. We show that restriction to SIB strategies is without loss of optimality in decentralized decision problems with non-strategic agents (i.e. teams). Accordingly, we provide a sequential decomposition of dynamic teams over time that specifies an algorithm for determining globally optimal strategies. For decentralized decision problems with strategic agents (i.e. games), we show that the class of SIB strategies is closed under the best response map. Consequently, we propose a notion of sufficient information-based equilibrium and provide a sequential decomposition of dynamic games over time that specifies an algorithm for determining Sufficient Information Based Perfect Bayesian Equilibria (SIB-PBE).

Keywords:Distributed control, Stability of linear systems, Automotive systems Abstract: This paper deals with the problem of string stability in a chain of acceleration-controlled vehicles, i.e. how input disturbances affect the distributed system for very long chains. There exist variants of string stability, like avoiding that a local disturbance gets amplified along the chain, or more strongly ensuring that the output vector's p-norm remains bounded for any bounded vector of input disturbances independently of the string length. They are all impossible to achieve with any linear controller if the vehicles only use relative information of few vehicles in front. Previous work has shown that adding absolute velocity into the controller, allows to at least avoid amplification of a local disturbance. In this paper, we consider the stronger definitions of string stability, under this same relaxation of using absolute velocity in the controller. We prove that the influence from input vector to output vector cannot be bounded independently of chain length in the most popular 2-norm sense, with any bounded stabilizing linear controller; while a proportional derivative (PD) controller can guarantee it in the practically relevant infinity-norm sense. Moreover, we identify the disturbance acting on the leader as the main issue for string stability.

Keywords:Distributed control, Cooperative control, Agents-based systems Abstract: This paper addresses the problem of bipartite output consensus of heterogeneous multi-agent systems over signed graphs. A dynamical neighbor-based consensus protocol is proposed, which consists of the solution pair of the regulation equation and a homogenous compensator. The controller parameters can be obtained by Lyapunov stability theory and matrix theory. To make the agents achieve bipartite output consensus without using any global information, a fully distributed adaptive protocol is further designed.

Keywords:Distributed control, Autonomous systems, Autonomous vehicles Abstract: In this paper, we propose a cloud-supported control framework for multi-agent circumnavigation missions. We consider a network of planar autonomous agents. Our objective is for the agents to circumnavigate a target with a desired angular speed, while forming a regular polygon around the target. We propose self-triggered rules to schedule the bearing measurements and the cloud accesses for each agent.

Keywords:Distributed control, Cooperative control Abstract: With the system-theoretic advancements in distributed control of multiagent systems, groups of agents are already able to utilize local interactions for achieving a broad class of prescribed global objectives. On the other hand, several agents forming the multiagent system are still expected to perform their own local objectives while they simultaneously achieve a given global objective. Yet, we currently do not have distributed control methods with analytic foundations that offer an effective remedy to this problem. Motivated from this standpoint, the contribution of this note is to present several distributed control solutions with comparable advantages. We provide system-theoretic stability analyses for each proposed method, where all these methods allow a subset of agents to perform their local objectives without deteriorating the overall multiagent system’s global objective.

Keywords:Distributed control, Cooperative control, Adaptive control Abstract: This paper presents a novel distributed adaptive time-varying formation tracking protocol for general linear multi-agent systems. In contrast to the existing distributed methods that require global information of the interaction graph, the proposed control strategy is fully distributed such that each agent only requires its own information and the information from its neighbors through switching directed communication networks. Then, an algorithm to determine the control parameters is presented, where feasible formation condition for the followers to accomplish the desired time-varying formation tracking is provided. Furthermore, the proposed strategy is also guaranteed to achieve an optimal control performance index by using the inverse optimal approach. Simulation results are provided to verify the effectiveness of the proposed strategy.

Keywords:Distributed control, Networked control systems, Cooperative control Abstract: This paper studies the cooperative output regulation problem of linear multi-agent systems. In contrast to the existing results where the exogenous signals are generated by a static exosystem, we consider a class of non-smooth exogenous signals generated by a switched exosystem, which are more practical in some real applications. In contrast to the traditional asymptotic tracking, in this paper, the regulated outputs are required to be bounded and decay to zero in a piecewise way. The major technical difficulty in solving this cooperative output regulation problem lies in that the switched exosystem leads to a switched nonlinear closed-loop system. In order to ensure the system stability, a lower bound on the dwell time of the switching signal is found based on the establishment of several important lemmas. Moreover, the upper bounds for the regulated outputs are also explicitly given.

Keywords:Control applications, Linear parameter-varying systems, Aerospace Abstract: In this paper, the linear parameter varying (LPV) gain-scheduled control method is applied to a two-link space manipulator (SM). The dynamic model of the SM is first derived by taking advantage of the dynamically equivalent manipulator (DEM) approach to simplify calculations and eliminate some undesirable nonlinear terms existing in the Lagrange dynamical model. Then by setting and sampling the typical scheduling parameter trajectories, an order-reducing LPV model using parameter set mapping (PSM) algorithm is obtained. The order-reducing model achieves a good trade-off between the complexity and accuracy of the LPV model, and thus diminishes the conservatism when designing the LPV model-based controller. The SM under the control of newly designed gain-scheduled controller shows reasonable end-effector tracking errors and good disturbance attenuation ability. Finally, simulations are carried out to verify the effectiveness of the proposed approach.

Univ of Illinois, Urbana-Champaign and Khalifa University

Keywords:Control applications, Control system architecture, Robust control Abstract: Computer systems are operating in environments where applications are rapidly diversifying while resources like energy and storage are becoming severely limited. These environments demand that computers dynamically manage their resources efficiently to deliver the best performance and meet many goals. An important challenge in designing computer resource management systems is that computers are structured in multiple modular layers, such as hardware, operating system, and network. Each layer is complex and designed independently without full knowledge of the other layers. Therefore, computers must have modular resource controllers for each layer that are robust to modeling limitations and the uncertainty of influence from other layers. Existing designs either rely heavily on ad hoc heuristics or lack modularity. We present a design with multiple Structured Singular Value (SSV) controllers from robust control theory for systematic and efficient computer management. On a challenging computer, we build a two-layer SSV control system that significantly outperforms state-of-the-art heuristics.

Keywords:Automotive systems, Estimation, Learning Abstract: This paper addresses the control of the clamping force provided by an Electric Parking Brake (EPB). A simple on-off strategy is implemented: the device is actuated until the actual force reaches the target value maintaining the vehicle in a steady position. The effectiveness of the control is then highly depending on the quality of the clamping force estimation. The proposed estimator relies on the sole DC motor current and voltage signals and does not require the knowledge of any physical parameters nor the measurement of the DC motor angular displacement. Extensive eperimental tests show the robustness of the proposed strategy with respect to different operating and aging conditions.

Keywords:Control applications, Mechatronics Abstract: Green production and energy efficiency in industrial environments are essential topics in recent political and scientific discussions. For realization, design processes of industrial applications such as robotic manipulators have to become energy aware. While most approaches regarding efficient design of robotic manipulators found in literature are based on complex optimization schemes, we present a novel, simply evaluable bound for the energy a kinematic structure will consume to fulfill a given motion task within a given time. The proposed estimate is based on optimal control methods for free rigid body mechanics, allowing an explicit solution in the considered case. After presenting and deriving the bound, we give numerical results for validation, yielding a deviation of only 0.1% to 7.2% compared to the numeric optimal control solution, depending on the considered kinematic structure. This confirms the proposed bound as non-conservative but suitable for estimating the energy consumption of a certain kinematic structure for a given motion task.

Keywords:Direct adaptive control, Constrained control, Control applications Abstract: Redundant actuators provide the opportunity to allocate control effort to account for saturation and other input constraints. This is especially true in wide systems, where the number of input channels is greater than the number of outputs. The present paper considers the control allocation problem within the context of adaptive control. In particular, for retrospective cost adaptive control (RCAC), the target model is shown to constrain the direction of the vector of inputs. This directional constraint is used within RCAC to enforce control allocation across the input channels of wide systems. This approach is applied to the allocation of rudder and aileron inputs for lateral flight control.

Keywords:Process Control, Fault diagnosis, Machine learning Abstract: Accurate diagnosis of operating modes for industrial processes is critical to safe and reliable operation of processes. The Hidden Markov Models (HMMs) have been widely employed to solve the real-time operating mode diagnosis problems for multi-modal processes. However, restricted by the inherent conditional independence assumptions, the operating mode diagnosis performance of HMMs tends to be degraded as these assumptions can be easily broken in reality. Alternatively, the conditional random field (CRF) model has been proposed in the context of process monitoring and proven to outperform the HMMs. In this work, we extend the CRF framework to the diagnosis of the operating modes of the processes that have multiple operating conditions, by designing a new framework, termed as, a switching CRF (SCRF). In the proposed framework, multiple linear-chain CRF models are proposed which have the capability to switch between each other in accordance with a scheduling variable that is indicative of the operating conditions. The expectation maximization (EM) algorithm is employed for parameter estimation. To validate the performance, a numerical example is employed. The results demonstrate that the proposed SCRF approach shows superior diagnosis performance to the linear-chain CRF models.

Keywords:Predictive control for linear systems, Iterative learning control, Uncertain systems Abstract: We present a Stochastic Model Predictive Controller for constrained uncertain systems. The proposed framework guarantees recursive feasibility of the controller while ensuring probabilistic constraint satisfaction. Furthermore, we show that the closed loop system converges to a neighborhood of the origin regardless of the disturbance realization. The main contribution of this work is to propose a deterministic reformulation of the chance constraints, where the constraint tightening is constant over the prediction horizon. Therefore, the proposed strategy can be integrated with the recently proposed Leaning Model Predictive Control (LMPC) scheme. The properties of the controller and its integration with the LMPC are discussed in the result section.

Keywords:Predictive control for linear systems, Time-varying systems, Stability of linear systems Abstract: The approach presented in the paper is applied for constructing a consecutive compensator in time-delay control systems. The synthesis of the consecutive compensator is performed based on the desired typical polynomial model of the «input-output» system that leads to the appearance of the advance term in its composition. The aim of the method is to determine one parameter of a closed system that provides the required quality indicators for the system. The methodology for parameter calculation is described in the paper. The method is based on the approximation of the advance term. It is proposed to use approximants in the form of differentiating link. The method eliminates the problem of the approximant stability.

Keywords:Predictive control for linear systems, Control over communications, Distributed control Abstract: Distributed model predictive control (DMPC) as a widely considered approach for large-scale systems like transportation, traffic control or power distribution systems necessitates appropriate methods for stability analysis. The quantification of a minimum prediction horizon is, among others, a pertinent method to stabilize DMPC. The finite horizon DMPC optimization problem can then be handled in a distributed way using e.g. dual decomposition. Theoretically a duality-based iterative optimization algorithm can assure primal feasibility only if the number of iterations tends towards infinity. In order to achieve feasibility with a finite number of iterations, the constraint set can be tightened. Determination of a suitable tightening factor for this purpose deserves careful consideration. While applying a very high amount of tightening destroys feasibility of the problem, a low tightening factor will result in an unnecessarily large number of iterations and communications in DMPC. The state of the art method in the literature selects an arbitrary tightening factor and iterates until it turns out that this factor is unsuitable and must be modified. Such a trial-and-error approach will indeed lead to a waste of communication resources which is undesirable especially when the communication capacity is shared out among many users. In this paper, a method to determine a suitable tightening factor will be presented which is dependent on the predefined suboptimality level and can significantly decrease communication load on the network. The efficiency of the proposed method will be studied through a numerical example.

Keywords:Predictive control for linear systems, Distributed control, Large-scale systems Abstract: In distributed model predictive control the global optimization problem is split into simpler problems through the use of decomposition methods. To enable such a decomposition, the problem is required to be separable, a property which is in general fulfilled when dealing with networks of dynamically coupled systems. The standard Linear Quadratic Regulator used to provide stability through a terminal cost function, however, destroys the problem's inherent structure and can therefore not be directly employed. In this paper an alternative suboptimal design providing both a stabilizing terminal cost function which preserves the network structure and a nominal distributed control law for the unconstrained system is presented. The proposed iterative algorithm is based on the standard Riccati iteration and on semidefinite programming. The global synthesis problem is itself amenable to distributed optimization and can hence be executed online. The controllers can therefore easily adapt to general network changes enabling full Plug&Play capabilities. The implemented method is tested numerically on a chain of inverted penduli network.

Keywords:Predictive control for linear systems, Robust control, Optimal control Abstract: We present Robust Model Predictive Control (MPC) problems with adjustable uncertainty sets. In contrast to standard Robust MPC problems with known uncertainty sets, we treat the uncertainty sets in our problems as additional decision variables. In particular, given a metric for adjusting the uncertainty sets, we address the question of determining the optimal size of those uncertainty sets, while ensuring robust constraint satisfaction. The focus of this paper is to ensure constraint satisfaction over an infinite horizon, also known as persistent feasibility. We show that, similar as in standard Robust MPC, persistent feasibility can be guaranteed if the terminal set is an invariant set with respect to both the state of the system and the adjustable uncertainty set. We also present an algorithm for computing such invariant sets, and illustrate the effectiveness of our approach in a cooperative adaptive cruise control application.

Keywords:Predictive control for linear systems, Stochastic optimal control, Stochastic systems Abstract: In this paper, we propose a stochastic model predictive control (MPC) algorithm for linear discrete-time systems affected by possibly unbounded additive disturbances and subject to probabilistic constraints. Constraints are treated in analogy to robust MPC using a constraint tightening based on the concept of probabilistic reachable sets, which is shown to provide closed-loop fulfillment of chance constraints under a unimodality assumption on the disturbance distribution. A control scheme reverting to a backup solution from a previous time step in case of infeasibility is proposed, for which an asymptotic average performance bound is derived. Two examples illustrate the approach, highlighting closed-loop chance constraint satisfaction and the benefits of the proposed controller in the presence of unmodeled disturbances.

Keywords:Robust adaptive control, Biomedical, Delay systems Abstract: Motivated by improved ways to disrupt brain oscillations linked to Parkinson's disease, we propose an adaptive output feedback strategy for the stabilization of nonlinear time-delay systems evolving on a bounded set. To that aim, using the formalism of input-to-output stability (IOS), we first show that, for such systems, internal stability guarantees robustness to exogenous disturbances. We then use this feature to establish a general result on scalar adaptive output feedback of time-delay systems inspired by the ``sigma-modification'' strategy. We finally apply this result to a delayed neuronal population model and assess numerically the performance of the adaptive stimulation.

Keywords:Biomedical, Systems biology, Optimal control Abstract: The primary factor limiting the success of chemotherapy in cancer treatment is the phenomenon of drug resistance. Resistance manifests through a diverse set of molecular mechanisms, such as the upregulation of efflux transporters on the cell membrane, enhanced DNA damage repair mechanisms, and/or the presence of cancer stem cells. Classically, these mechanisms are understood as conferred to the cell by random genetic mutations, from which clonal expansion occurs via Darwinian evolution. However, the recent experimental discovery of epigenetics and phenotype plasticity complicates this hypothesis. It is now believed that chemotherapy can produce drug-resistant clones. In this work, we study a previously introduced framework of drug-induced resistance, which incorporates both random and drug induced effects.

A time-optimal control problem is presented and analyzed utilizing differential-geometric techniques. Specifically, we seek the treatment protocol which prolongs patient’s life by maximizing the time of treatment until a critical tumor size is reached. The general control structure is determined as a combination of bang-bang and singular arcs.

Keywords:Reduced order modeling, Biomedical, Kalman filtering Abstract: In this paper, proper-orthogonal-decomposition (POD) reduced models of the body’s heat response to radio- frequency hyperthermia cancer treatment are used for recursive temperature estimation. First, efficient low-dimensional models are obtained by projecting high-resolution finite-difference discretized models on low-dimensional subspaces spanned by empirical simulation modes. These models are then used in a Kalman filter to obtain recursive 3D temperature esti- mates from noise-susceptible magnetic resonance thermometry (MRT). The strategy is tested on an experimental setup con- taining an anthropomorphic phantom. It is found that recursive estimation reduces the mean absolute temperature error for the phantom experiment by 38% when compared to MRT and may be a valuable addition to MRT, most notably in the case where high quality thermometry is temporally interleaved with thermometry of degraded quality.

Keywords:Neural networks, Agents-based systems, Healthcare and medical systems Abstract: Synchrony of neuronal ensembles is believed to facilitate information exchange among cortical regions in the human brain. Recently, it has been observed that distant brain areas which are not directly connected by neural links also experience synchronization. Such synchronization between remote regions is sometimes due to the presence of a mediating region connecting them, e.g., the thalamus. The underlying network structure of this phenomenon is star-like and motivates us to study the remote synchronization of Kuramoto oscillators, modeling neural dynamics, coupled by a directed star network, for which peripheral oscillators get phase synchronized, remaining the accommodating central mediator at a different phase. We show that the symmetry of the coupling strengths of the outgoing links from the central oscillator plays a crucial role in enabling stable remote synchronization. We also consider the case when there is a phase shift in the model which results from synaptic and conduction delays. Sufficient conditions on the coupling strengths are obtained to ensure the stability of remotely synchronized states. To validate our obtained results, numerical simulations are also performed.

Keywords:Healthcare and medical systems, Modeling, Machine learning Abstract: Women affected by pain during penetrative sexual intercourse are often treated using fixed-size vaginal dilators that are regularly perceived as uncomfortable and leading to premature treatment drop-outs. These dilators could be improved by making them adaptive, i.e., able to exert dynamically different pressures on the vaginal duct to simultaneously guarantee comfort levels and achieve the medical dilation objectives. Implementing feedback control would then benefit from models that connect the patients' comfort levels with their experienced physiological stimuli.

Here we address the problem of data-driven quantitative modelling of pain/pleasure self-assessments obtained through medical trials. More precisely, we consider time-series records of Pelvic Floor Muscles (PFM) pressure, vaginal dilation, and pain/pleasure evaluations, and model the relations among these quantities using statistical analysis tools. Besides this, we also address the important issue of the individualization of these models: different persons may respond differently, but these variations may sometimes be so small that it may be beneficial to learn from several individuals simultaneously. We here numerically validate the previous claim by verifying that clustering patients in groups may lead, from a data-driven point of view, to models with a significantly improved statistical performance.

Keywords:Identification, Optimization, Identification for control Abstract: In a market environment, there often are multiple vendors offering similar products or services. It has been observed that individuals’ decisions to adopt a product or service are influenced by the recommendations of their friends and acquaintances. Consequently, in the last few years there has been considerable interest in the research community to study the dynamics of influence propagation in social networks in competitive settings. The goal of these studies is often to identify the key individuals in a social network, whose recommendations have significant impact on adoption of a product or service by the members of that community. Using Separated Threshold Model (SepT) [1] of influence propagation, in this paper we study a problem of similar vein, where the goal of the two vendors (players) is to win the competition by having a market share that is larger than its competitor. In our model, the first player has already identified a set of key influencers when the second player enters the market. The goal of the second player is to have a larger market share, but wants to achieve the goal with least amount of investment, i.e., by incentivizing the fewest number of key individuals (influencers) in the social network. The problem is NP-hard. We provide an approximation algorithm with O(log n) bound. Detailed experimentations have been conducted to evaluate the efficacy of our algorithm. Moreover, we present an equivalent random process for the SepT model which facilitates analysis of competitive influence propagation under this model.

Keywords:Network analysis and control, Hierarchical control, Biological systems Abstract: Understanding how the complex network dynamics of the brain support cognition constitutes one of the most challenging and impactful problems ahead of systems and control theory. In this paper, we study the problem of selective recruitment, namely, the simultaneous selective inhibition of activity in one subnetwork and top-down recruitment of another by a cognitively-higher level subnetwork, using the class of linear-threshold rate (LTR) models. We first use singular perturbation theory to provide a theoretical framework for selective recruitment in a bilayer hierarchical LTR network using both feedback and feedforward control. We then generalize this framework to arbitrary number of layers and provide conditions on the joint structure of subnetworks that guarantee simultaneous selective inhibition and top-down recruitment at all layers. We finally illustrate an application of this framework in a biologically-inspired scenario where simultaneous stabilization and control of a lower level excitatory subnetwork is achieved through proper oscillatory activity in a higher level inhibitory subnetwork.

Keywords:Networked control systems, Network analysis and control, Stochastic systems Abstract: We consider exponentially stable linear systems subject to heavy-tailed noise. Based on the distributional properties of the output dynamics, we introduce novel performance and risk indexes to evaluate system's response towards the exogenous and/or structural sources of noise. We derive explicit expressions of the aforementioned indexes whenever possible, as well as general spectral-related estimates. We apply the obtained rigorous results to improve systemic performance on a case study of a distributed consensus system.

Keywords:Network analysis and control, Distributed control Abstract: We study distributed cooperative decision-making in a multi-agent stochastic multi-armed bandit (MAB) problem in which agents are connected through an undirected graph and observe the actions and rewards of their neighbors. We develop a novel policy based on partitions of the communication graph and propose a distributed method for selecting an arbitrary number of leaders and partitions. We analyze this new policy and evaluate its performance using Monte-Carlo simulations.

Keywords:Networked control systems, Network analysis and control, Sensor networks Abstract: Measures of node centrality that describe the importance of a node within a network are crucial for understanding the behavior of social networks and graphs. In this paper, we address the problem of distributed node centrality identification. In particular, we focus our attention on alpha-centrality, which can be seen as a generalization of eigenvector centrality, particularly suitable for graphs with asymmetric interactions. In this setting, our contribution is twofold: first we derive a distributed protocol where agents can locally compute their alpha-centrality index by means of local interactions; then we propose a novel consensus-algorithm running in parallel to the alpha-centrality estimator, which converges towards a weighted average of the initial conditions, where the weights are dictated by the alpha-centrality vector. The proposed algorithm finds application in social networks, where agreement protocols typically place more value on experts and influencers than on the rest of users. Simulations results are provided to corroborate the theoretical findings.

Keywords:Network analysis and control, Large-scale systems, Control of networks Abstract: Control and estimation on large-scale social networks often necessitate the availability of models for the interactions amongst the agents. However characterizing accurate models of social interactions pose new challenges due to inherent complexity and unpredictability. Moreover, model uncertainty becomes more pronounced for large-scale networks. For certain classes of social networks, the layering structure allows a compositional approach. In this paper, we present such an approach to determine performance guarantees on layered networks with inherent model uncertainties. A factorization method is used to determine robust stability and performance and this is accomplished by a layered cost-guaranteed design via a layered Riccati-type solver, mirroring the network structure. We provide an example of the proposed methodology in the context of opinion dynamics on large-scale social networks.

Keywords:Iterative learning control, Building and facility automation, Optimization Abstract: In this paper, a concurrent design of feedforward and feedback controllers is proposed for the building thermal system. The algorithm aims at finding a balance between building occupants' thermal comfort and the energy consumption. The influence of disturbance from ambient environment and inside human activities is considered. The controller design is formulated as an optimization with feedforward and feedback controllers as two decision variables. In order to take advantage of the nearly repetitive property of the disturbances, iterative learning control (ILC) technique is utilized to reject the repetitive disturbance components. This applies to building systems in the tropics such as Singapore. For the iteration varying and unpredictable disturbance components, a feedback controller with Youla-parametrized structure is selected. To guarantee that the controllers are stabilizing and implementable in practice, stability, causality and robustness requirements along with the control saturation limit are included as constraints. The optimization is convexified via introducing new variables and relaxation. The solution to the optimization simultaneously gives the feedforward and feedback controllers to be applied in the next iteration. The proposed algorithm is demonstrated on a four-room system by simulation.

Keywords:Iterative learning control, Constrained control Abstract: Feedback-based iterative learning control (ILC) has been proposed to improve the unacceptable transient performance (either in state or in output) in the iteration-domain. This paper addresses a special performance requirement of output constraints, which are motivated from the safety requirements in robotic manipulators. A barrier-function like Lyapunov function is used to design a new state feedback (or a proportional-derivative controller) to ensure that output constraints are satisfied in the finite time-domain. This state feedback is then combined with the standard feed-forward ILC to track the desired trajectory. With the help of composite energy function, it is shown that, for robotic manipulators, the proposed control method can achieve perfect tracking performance without violating output constraints in any iteration. Simulation results, which are based on the model of recently developed rehabilitation robot EMU, are presented to illustrate the effectiveness of the proposed controller.

Keywords:Iterative learning control, Distributed parameter systems, Identification Abstract: This paper develops a computational scheme to solve the optimal tracking control problem by repeated trials for distributed-parameter processes where an example from elasticity analysis in structural mechanics is used as motivation. An adaptive control scheme based on iterative learning control is used to develop an effective solution of underlying optimization task. The essential feature of the resulting approach is the efficient modelling and simulation of the distributed system under consideration using discretization based on the finite element method. Also to reduce the uncertainty of the model used for the control design, thus increasing the system performance, the iterative learning control scheme is extended by parameter estimation of mathematical model through application of one form of sequential experimental design. The related sensor location problem corresponds to situation where from among all potential sites where the sensors can be placed a subset must be selected that provide the most informative measurements to update the system parameter estimates. The new results are lustrated by an example from the area of smart materials.

Keywords:Iterative learning control, Constrained control Abstract: In this paper, we propose a model-free algorithm for global stabilization of linear systems subject to actuator saturation. The idea of gain-scheduled low gain feedback is applied to develop control laws that avoid saturation and achieve global stabilization. To design these control laws, we employ the framework of parameterized algebraic Riccati equations (AREs). Reinforcement learning techniques are developed to find the solution of the parameterized ARE without requiring any knowledge of the system dynamics. In particular, we present an iterative Q-learning algorithm that searches for an appropriate value of the low gain parameter and iteratively solves the parameterized ARE using the Bellman equation. It is shown that the proposed algorithm achieves model-free global stabilization under bounded controls and converges to the solution of the ARE. The proposed scheme neither requires an initially stabilizing policy nor is affected by any excitation noise bias. Simulation results are presented that confirm the effectiveness of the proposed method.

Keywords:Iterative learning control, Linear systems, Stability of linear systems Abstract: This paper develops novel procedures for designing of iterative learning control (ILC) schemes for both continuous-time and discrete-time systems. These procedures are developed by transforming the ILC design problem into stability problem for a two-dimensional (2D) system described by the Roesser model. Moreover, since the results are based on 2D system stability conditions that can reach necessity then the resulting design conditions are possibly characterized by a very low level of conservativeness. All conditions are derived in terms of linear matrix inequalities (LMIs), and they directly give formulas for computing the required ILC controllers. A numerical example to demonstrate the new results is also given.

Keywords:Iterative learning control, Optimal control Abstract: We propose a model-free reduced-order optimal control design for linear time-invariant singularly perturbed (SP) systems using reinforcement learning (RL). Both the state and input matrices of the plant model are assumed to be completely unknown. The only assumption imposed is that the model admits a similarity transformation that results in a SP representation. We propose a variant of Adaptive Dynamic Programming (ADP) that employs only the slow states of this SP model to learn a reduced-order adaptive optimal controller. The method significantly reduces the learning time, and complexity required for the feedback control by taking advantage of this model reduction. We use approximation theorems from singular perturbation theory to establish sub-optimality of the learned controller, and to guarantee closed-loop stability. We validate our results using two representative examples - one with a standard singularly perturbed dynamics, and the other with clustered multi-agent consensus dynamics. Both examples highlight various implementation details and effectiveness of the proposed approach.

Keywords:Aerospace, Autonomous systems, Distributed control Abstract: In this paper, we investigate the problem of simultaneously controlling both attitude and position of a network of collaborative aerospace vehicles. In particular, we use unit dual quaternions to model the coupled rotational and translational motion present in many applications. We then derive a simple PD-like feedback controller that simultaneously stabilizes the attitude and position of all vehicles in the network. The analysis reveals global asymptotic stability using LaSalle's invariance principle. We discuss various applications of the control design framework and provide a numerical example of a spacecraft landing on a moving platform. This example demonstrates the utility of the proposed approach to 6-degree-of-freedom multiagent coordination that can be achieved with a single framework.

Keywords:Aerospace, Estimation, Uncertain systems Abstract: Space object uncertainty propagation is critical to space situational awareness. However, due to a large number of space objects and limited available sensors, observations of a certain space object are sparse. As a result, short-arc orbit uncertainty propagation is common. By using various constraints, the admissible region for space objects can be identified using short-arc observations. The initial uncertainty of the space object can then be described by samples of the admissible region. The challenge is that the resultant initial uncertainty has no analytical form. Hence, the conventional generalized polynomial chaos method cannot be directly used. In this paper, an arbitrary polynomial chaos (aPC) is proposed to better represent the initial uncertainty, which requires only a finite number of moments of the initial uncertainty distribution, and does not require the complete knowledge or even existence of the probability density function. The moments can be easily calculated using sampling points in the admissible region. In addition, the multi-element aPC is utilized to improve the accuracy and computation efficiency of aPC for the long-term propagation. Simulation results demonstrate the superb performance of the proposed method to address both the short-term and long-term short-arc orbit uncertainty propagation problems.

Keywords:Aerospace, MEMs and Nano systems, Sensor fusion Abstract: The article proposes a methodology for estimating the velocity (w.r.t the air) of a high-velocity flying shell from low-cost embedded sensors. The novelty is to exploit aerodynamics models in combination with a frequency detection approach, through a state observer. Besides its main rotation (spin), the shell has gyroscopic precession and nutation motions, which are measured by inertial sensors as pseudo-periodic signals. The instantaneous frequencies of these time-varying signals give direct information on the aerodynamics of the shell, and in particular, its velocity w.r.t the air. The frequency content of the signal of the strapdown sensors is exploited by means of a two-step approach consisting of frequency detection reconciled with the aerodynamic models by an observer. A switching gain is used to deal with the transition of the shell in the transonic regime. A proof of convergence is given. Experimental results are exposed.

Keywords:Aerospace, Delay systems, Nonlinear output feedback Abstract: The problem of stabilizing a nonlinear system when the variables are not accurately mea- sured and cannot be differentiated arises when it comes to use direction measurements to one point in the environment. We here propose to adapt a recent backstepping technique with delay to the specificity of this problem. The proposed method was first mo- tivated and thus finally applied to the vision based control problem of a landing airliner.

Keywords:Filtering, Aerospace, Stochastic systems Abstract: A matrix Fisher distribution on the special orthogonal group is a compact, global form of attitude uncertainty distribution that has been successfully utilized for Bayesian attitude estimations in an intrinsic fashion. This paper addresses two computational issues in implementing matrix Fisher distributions, namely numerical stability and computational efficiency. More precisely, an exponentially scaled normalizing constant of the matrix Fisher distribution and its mathematical properties are introduced for robust numerical implementations. Next, two approximate matrix Fisher distributions are formulated for a highly concentrated case and an almost uniformly distributed case respectively. These approximate forms yield an explicit form of attitude estimation schemes for the considered cases, and it also illustrate the similarity between the Gaussian distribution and the matrix Fisher distribution in the highly concentrated cases.

Keywords:Flight control, Aerospace Abstract: Hybrid vertical take-off and landing vehicles (VTOL) with lift production from wings and distributed propulsive system present unique control challenges. Existing methods tend to stitch and switch different controllers specially designed for fixed-wing aircraft or multicopters. In this paper, we present a unified framework for designing controllers for such winged VTOL vehicles that are commonly found in recent flying car models. The proposed method is broken down into nonlinear control of both position, and attitude with forces and moments as inputs and real-time control allocation that integrates distributed propulsive actuation with conventional control surface deflection. We also present a strategy that avoids saturation of distributed propulsion control inputs. The effectiveness of the proposed framework is demonstrated through simulation and closed-loop flight experiment with our winged VTOL flying car prototype.

Keywords:Network analysis and control Abstract: In this paper, we study the global stability properties of a multi-agent model of natural resource consumption, which balances ecological and social network components in determining the consumption behavior of a group of agents. Recently, it was shown that if the social network component of the model is leaderless, a condition that ensures that no single node has a greater social influence than any other node on the dynamics of the resource consumption, then the behavior of a group of agents can be treated in aggregate. This aggregation facilitates the application of this model to large scale networks, however it is as yet poorly understood. This paper shows that any network structure can be made leaderless by the social preferences of the agents. It is also shown that if the social network is leaderless, a mild bound on agents' environmental concern is sufficient for global asymptotic stability to a positive consumption value; indicating that appropriately configured networks can consume without depleting the resource. The behavior of these leaderless resource consumption networks is discussed via simulation.

Keywords:Network analysis and control, Stability of nonlinear systems, Algebraic/geometric methods Abstract: Synchronization in the networks of coupled oscillators is a widely studied topic in different areas. It is well-known that synchronization occurs if the connectivity of the network dominates heterogeneity of the oscillators. Despite extensive study on this topic, the quest for sharp closed-form synchronization tests is still in vain. In this paper, we present an algorithm for finding the Taylor expansion of the inverse Kuramoto map. We show that this Taylor series can be used to obtain a hierarchy of increasingly accurate approximate tests with low computational complexity. These approximate tests are then used to estimate the threshold of synchronization as well as the position of the synchronization manifold of the network.

Keywords:Network analysis and control, Randomized algorithms, Distributed control Abstract: We propose gossip algorithms that can preserve the sum of network values (and therefore the average), and in the meantime fully protect node privacy even against eavesdroppers possessing the entire information flow and network knowledge. At each time step, a node is selected to interact with one of its neighbors via deterministic or random gossiping. Such node generates a random number as its new state, and sends the subtraction between its current state and that random number to the neighbor. Then the neighbor updates its state by adding the received value to its current state. We have shown in the first part of the paper that this type of privacy-preserving gossiping algorithms can be used as a simple encryption step in distributed optimization and computation algorithms. In this second part, we establish some concrete privacy-preservation performance analysis characterized by proven impossibilities for the reconstruction of the node initial values.

Keywords:Network analysis and control, Networked control systems, Large-scale systems Abstract: This paper provides a model to investigate the evolution of opinions in social networks comprising of individ- uals and other influential entities, which herein are referred to as information sources. Each individual holds an opinion represented by a scalar that evolves over time. The information sources are stubborn, in the sense that their opinions are time-invariant. Individuals receive the opinions of information sources that are closer to their belief, confirmation bias is explicitly incorporated into the model. The proposed dynamics of the social network is adopted from DeGroot-Friedkin model, where an individual’s opinion update mechanism is a convex combination of her innate opinion, her neighbors’ opinions at the previous time step, and the opinions passed along by information sources which she follows. In our specific model, the social network relies on trust and hence static, while the information sources are highly dynamic since they are weighted as a function of the distance between an individual state and the state of information source to account for confirmation bias. The conditions for convergence of the aforementioned dynamics to a unique equilibrium point are characterized. The estimation and exact computation of the steady-state values under non-linear and linear state-dependent weight functions are provided. Finally, the impact of the distance between polarized opinions of information sources in the public opinion evolution is numerically analyzed in the context of the well- known Krackhardt’s advice network.

Keywords:Networked control systems, Control of networks, Network analysis and control Abstract: This paper presents a collection of properties on composite networks in terms of the properties on their respective factor networks. We explore a large class of composite networks using the notion of a generalized graph product. We provide the spectral properties as well as the trajectory of linear networked dynamics systems driven by the composite network's adjacency matrix. This work extends our previous research on controllability of the networked system via Cartesian product to a broader family of graph products.

Keywords:Networked control systems, Network analysis and control, Agents-based systems Abstract: We investigate a variant of the Hegselmann-Krause model of opinion dynamics that relaxes the assumption that every agent has knowledge of every other agent’s opinion at all points in time. This is done by incorporating a physical connectivity graph that accounts for the external factors that may prevent interaction between certain pairs of agents. As opposed to the original Hegselmann-Krause dynamics (which terminate in finite time), we show that for any underlying graph that is connected but not complete, there exists an initial condition under which the dynamics never terminate. As a result, we show that for any continuous probability density function having the state space as its support, the expected termination time of the modified dynamics is infinity. We also study the rate of convergence to the steady state and derive bounds on the maximum convergence time in terms of the properties of the physical connectivity graph.

Keywords:Output regulation, Systems biology, Robust control Abstract: This tutorial paper deals with the Internal Model Principle (IMP) from different perspectives. The goal is to start from the principle as introduced and commonly used in the control theory and then enlarge the vision to other fields where "internal models" play a role. The biology and neuroscience fields are specifically targeted in the paper. The paper ends by presenting an "abstract" theory of IMP applicable to a large class of systems.

Keywords:Linear systems, Output regulation, Robust control Abstract: We briefly recall early literature anticipating the IMP in human cognition, followed by examples of the IMP in the frequency domain of classical control. Then we sketch how the state space version of linear multivariable control can be generalized to an elementary setting of plain sets and functions.

Keywords:Output regulation, Nonlinear output feedback, Robust control Abstract: The talk will deal with an introduction to the problem with a control theory perspective, by overviewing the principles for systems modeled by ordinary differential equations and the main challenges that justify the actual research directions.

Keywords:Biological systems, Robust control, Output regulation Abstract: The talk will shift the focus to the field of bioengineering by showing how the concept of internal model is inherently present in many biological organisms able to adapt their behaviours to changing external stimuli.

Keywords:Adaptive systems, Biologically-inspired methods, Output regulation Abstract: The human brain and the nervous system of many animal species are thought to include internal models of the sensorimotor plant and of the environment. This talk will review the experimental evidence for these neural computations, and discuss their relation to the framework of control theory.

Keywords:Output regulation, Robust control, Adaptive systems Abstract: In this paper we review the problem of output regulation for nonlinear systems. We discuss how the robustness properties and the simple structure of the linear regulator are linear artefacts which do not extend in more general nonlinear cases. We talk about the intertwining that is necessarily present between the internal model and the stabilising parts of a nonlinear regulator, in which the role of the exosystem mixes up with those of the residual plant's dynamics. We discuss a general guideline to deal with such structural challenges, by looking at adaptation and universal approximators as a promising way to provide systematic design procedures for approximate regulators in a general nonlinear setting.

Keywords:Output regulation, Robust control Abstract: In this paper we propose a general framework in which the robustness properties and requirements of output regulation schemes can be formally described. We introduce a topological definition of robustness relative to arbitrary steady state properties, extending the usual notion of robustness relative to the existence of a steady state in which the regulation error vanishes. We review some of the main control approaches for linear and nonlinear systems, by re-framing their robustness properties within the proposed setting. We show that the celebrated robustness property of the linear regulator, namely the ``internal model principle'' stated by Francis, Wonham and Davison in the 70's, can be generalized to nonlinear systems in a robustness property relative to the Fourier expansion of the regulation error. We then focus on nonlinear regulation, where we show that only practical regulation can be achieved robustly, while asymptotic regulation is achieved in a quite fragile way. The paper concludes with a conjecture stating that, in a general nonlinear context, asymptotic regulation cannot be achieved in a robust way with a finite dimensional regulator.

Keywords:Distributed control, Agents-based systems, Decentralized control Abstract: This paper considers a decentralized control scheme for Voronoi-based deployment of discrete-time multi-agent dynamical systems within multi-dimensional static convex polytopic environments. The deployment objective is to drive the multi-agent system to a static configuration in which coverage of the environment is optimized. To this end, local control laws steer each agent towards a Chebyshev center of its associated time-varying polytopic Voronoi-neighborhood. By introducing a novel time-varying interaction graph, mechanisms enforcing consensus on intra-neighbor distances among subsets of agents are uncovered. Subsequently the interaction graph is exploited to provide both proofs of convergence as well as structural characterizations of static configurations.

Keywords:Cooperative control, Estimation, Kalman filtering Abstract: In this paper, we address the problem of synchronized convergence of multiple Unmanned Vehicles (UVs) onto a single moving and maneuvering target in a GPS-denied environment with each agent having fractionated information and sensing constraints. The UVs (or agents) are considered to be distributed over a topographical region with limited sensing range and field-of-view (FOV) as compared to the expanse of the region under consideration. These constraints are addressed using cooperative localization technique augmented with Proportional Navigation (PN) guidance law. Using nonlinear observability analysis, it is shown that the combined algorithm proposed in this paper keeps the states of target and UVs observable as long as the observability criteria are not violated. Further, simulations are performed to show that the theory is consistent and is able to perform simultaneous convergence.

Keywords:Stochastic systems, Cooperative control, Distributed control Abstract: This work is concerned with consensus control of nonlinear multi-agent systems with multiplicative noises and time-varying measurement delays. For the general timevarying delays without knowing its differentiability, a Lyapunov function and an integral version of Halanay inequality are applied to obtain the sufficient condition for mean square and almost sure consensus. For the case with the differentiable timevarying delays, a Lyapunov functional is established to get the explicit sufficient consensus conditions. Based on the sufficient conditions, the consentability conditions related to the system parameters are also introduced for the existence of consensus protocols.

Keywords:Identification, Networked control systems, Control applications Abstract: We study the problem of sparse interaction topology identification using sample covariance matrix of the states of the network. We postulate that the statistics are generated by a stochastically-forced undirected consensus network with unknown topology in which some of the nodes may have access to their own states. We first propose a method for topology identification using a regularized Gaussian maximum likelihood framework where the l1-regularizer is introduced as a means for inducing sparse network topology. We also develop a method based on growing a Chow-Liu tree that is well-suited for identifying the underlying structure of large-scale systems. We apply this technique to resting-state functional MRI (FMRI) data as well as synthetic datasets to illustrate the effectiveness of the proposed approach.

Keywords:Cooperative control Abstract: A control scheme for the coverage of a convex region by a team of Mobile Aerial Agents (MAAs) under positioning uncertainty is presented in this article. Each MAA is outfitted with a downwards facing camera, the field of view of which differs among agents, resulting in a sensed area which depends on the MAA's altitude and the view angle of its camera. Additionally, the MAAs' projections on the ground and altitudes are assumed to be known with varying uncertainty. In order to take into account the MAAs' positioning uncertainty as well as their varying sensed areas, an Additively Weighted Guaranteed Voronoi (AWGV) partitioning of the region is utilized. Based on this partitioning scheme, a gradient--based algorithm is derived in order to guarantee monotonic increase of an area coverage metric, despite the positioning uncertainty, while also constraining the MAAs' altitudes. The proposed scheme is evaluated through simulation studies.

Keywords:Delay systems, Linear systems, Agents-based systems Abstract: This paper characterizes fully how time delay affects the rate of convergence of a class of linear time-delayed systems. Contrary to the prevailing intuition that links time delay with system sluggishness, we show that for specific ranges of time delay, faster response can be achieved in the presence of delay. Specifically, we determine exactly for what values of delay the rate of convergence of our system of interest increases with delay. We also prove that the ultimate bound on the maximum achievable rate of convergence via time delay is e (Eulers number) times the delay free rate. We demonstrate our results by studying the convergence rate of the Laplacian static average consensus algorithm in the presence of time delay.

Keywords:Delay systems, Stability of linear systems Abstract: The construction of Lyapunov matrices for integral delay systems with constant and exponential kernel are presented. It is reduced to the solutions of a matrix delay free system subject to boundary conditions. The results are validated by testing known necessary stability conditions in terms of the Lyapunov matrix.

Keywords:Delay systems Abstract: In this paper, we propose a method for solving the distributed optimization problem in which the objective function is the sum of separable convex functions with linear constraints. We modify the distributed Method of Multiplier algorithm based on cite{r23} by looking it as a potential Proportional Integral(PI) controller. This enables us to obtain the algorithm in which the convergence speed is greatly improved due to the different proportionality constants of PI compensator. The relation between these proportionality constants is determined by the positive real property of the algorithm when viewed as a dynamical system.

Keywords:Delay systems, Stability of nonlinear systems, Uncertain systems Abstract: We show that a Lyapunov-Krasovskii functional whose dissipation rate involves solely the current instantaneous value of the state norm is enough to guarantee integral input-to-state stability (iISS). This result generalizes existing sufficient conditions for iISS, where the dissipation rate involves the whole Lyapunov-Krasovskii functional itself, and simplifies their applicability. Moreover, it provides a more natural bridge with the classical condition for global asymptotic stability of input-free systems. The proof strategy we employ relies on a novel characterization of global asymptotic stability, which may be of interest on its own.

Keywords:Delay systems, Estimation, Uncertain systems Abstract: The interval estimation design is studied for a second-order delay differential equation with position delayed measurements, uncertain input and initial conditions. The proposed method contains two consecutive interval observers. The first one estimates the interval of admissible values for the position without delay for each instant of time using new delay-dependent conditions on positivity. Then derived interval estimates of the position are used to design the second observer estimating an interval of admissible values for the velocity of the considered dynamical system. The results are illustrated by numerical experiments for an example.

Keywords:Delay systems, Robust control, Stability of linear systems Abstract: We study the delay margin problem in the context of recent works by T. Qi, J. Zhu, and J. Chen, where a sufficient condition for the maximal delay margin is formulated in terms of an interpolation problem obtained after introducing a rational approximation. Instead we omit the approximation step and solve the same problem directly using techniques from function theory and analytic interpolation. Furthermore, we introduce a constant shift in the domain of the interpolation problem. In this way we are able to improve on their lower bound for the maximum delay margin.

Keywords:Linear systems, Lyapunov methods, Networked control systems Abstract: In networked control systems, the communication links and physical system components are coupled and hence vulnerable to a variety of attacks. Certain class of attacks on the communication network has a tendency to change the traffic flow causing delays and packet losses to increase, thus affecting the stability of the physical system. Therefore in this paper, a novel observer based flow control and detection scheme is proposed to capture the abnormality in traffic flow through the bottleneck node of the communication network by generating the attack detection residual. A linear matrix inequality (LMI) based controller design is proposed that ensures system stability by detecting attacks on the network as well as on the physical system. Since the dynamics of the physical system depend upon the network induced delay and packet losses, it is stabilized by adjusting the controller gains based on network state provided certain conditions are met. Simulation results are included to demonstrate the applicability of the proposed schemes against a class of attacks represented by attack models.

Keywords:Linear systems, Fault detection Abstract: This paper extends the concept of scalar cepstrum coefficients from single-input single-output linear time invariant dynamical systems to multiple-input multiple-output models, making use of the Smith-McMillan form of the transfer function. These coefficients are interpreted in terms of poles and transmission zeros of the underlying dynamical system. We present a method to compute the MIMO cepstrum based on input/output signal data for systems with square transfer function matrices (i.e. systems with as many inputs as outputs). This allows us to do a model-free analysis. Two examples to illustrate these results are included: a simple MIMO system with 3 inputs and 3 outputs, of which the poles and zeros are known exactly, that allows us to directly verify the equivalences derived in the paper, and a case study on realistic data. This case study analyses data coming from a (model of) a non-isothermal continuous stirred tank reactor, which experiences linear fouling. We analyse normal and faulty operating behaviour, both with and without a controller present. We show that the cepstrum detects faulty behaviour, even when hidden by controller compensation. The code for the numerical analysis is available online.

Keywords:Linear systems, Optimization algorithms Abstract: In this paper, an algorithm is proposed for the multi-objective optimal design of controllers with fixed structure, but tunable parameters, for linear systems. Differently from other tools available in the literature, the proposed method allows one to determine an exact solution to a multi-objective minimization problem without eliminating variables. Several applications of the proposed method, which span from the computation of a Pareto optimal solution for a cooperative differential game to the fast stabilization of the closed-loop system, are reported to corroborate the theoretical results.

Keywords:Linear systems Abstract: This work studies the null controllability of an actuated system of coupled parabolic PDEs. In particular, we consider an important subclass of such problems where the couplings are of first and zero-order and the underlying control system is underactuated. We pose our control problem using a recent framework which divides the problem into interconnected parts: we refer to the first part as the analytic control problem, where we use slightly non-classical techniques to prove null controllability by means of internal controls appearing on every equation; we refer to the second part as the algebraic control problem, where we use an algebraic method to "invert" a linear partial differential operator that describes our system; this allows us to recover null controllability by means of internal controls which appear on only a few of the equations. We establish a null controllability result for the original problem by solving these control problems concurrently.

Keywords:Linear systems, Uncertain systems, Optimization Abstract: This paper addresses the problem of achieving high-performance dynamic control allocation for uncertain plants by exploiting a data-driven design of the annihilator for the underlying plant. Previous work revealed that an output invisible control allocator can be decomposed as the cascade interconnection of a steady-state optimizer and an annihilator, where the latter unit modulates the allocator outputs in such a way to render such signals undetectable from the plant output. Clearly, the critical role and challenging requirements imposed on the annihilator make it the source of the lack of robustness of control allocation schemes in the presence of uncertainty; nonetheless this critical aspect can be (almost) completely circumvented by tuning the annihilator to the actual plant parameters, namely by envisioning a data-driven control allocation scheme. Relations are also highlighted between the present results and the concepts of moments and orthogonal moments of a plant at frequencies of interest, whose use and estimation have recently been the subject of increasing interest.

Keywords:Linear systems, Mean field games, Stochastic optimal control Abstract: Many interacting systems contain latent (i.e. exogenous) processes that affect their dynamics, yet which cannot themselves be directly observed. This paper studies a class of (non-cooperative) stochastic games with major and minor agents interacting in a system that is modulated by a latent Markov chain. Moreover, the agents' cost functionals are permitted to couple with the latent process. A novel convex analysis is developed to (i) solve the mean field game (MFG) limit of the problem, (ii) demonstrate that the best response strategies generate an epsilon-Nash equilibrium for the finite player game, and (iii) obtain explicit characterisations of the best response strategies.

Keywords:Robust adaptive control, Estimation, Nonlinear systems identification Abstract: This paper deals with the problem of adaptive estimation, i.e. the simultaneous estimation of the state and parameters, for a class of uncertain nonlinear systems. A nonlinear adaptive sliding-mode observer is proposed based on a nonlinear parameter estimation algorithm. The nonlinear parameter estimation algorithm provides a rate of convergence faster than exponential while the sliding-mode observer ensures ultimate boundness for the state estimation error attenuating the effects of the external disturbances. Linear matrix inequalities (LMIs) are provided for the synthesis of the adaptive observer and some simulation results show the feasibility of the proposed approach.

Keywords:Robust adaptive control, Time-varying systems, Identification for control Abstract: A performance-based approach is developed for adaptive robust control of linear systems with uncertain parameters. The dual control objective involves the disturbance attenuation and worst case identification of the unknown parameters. The proposed synthesis procedure relies on sufficient conditions, given in terms of suitable solutions of perturbed differential Riccati equations to exist. Although being reminiscent from the standard H-infinity synthesis, the resulting Riccati equations are to be updated on-line with estimated values of the unknown plant parameters. Capabilities of the proposed synthesis are illustrated by simulations made for a scalar linear system with unknown parameters.

Keywords:Robust adaptive control, LMIs, Control applications Abstract: There exist several optimal control strategies to harvest wave energy with a point absorber. However they are generally based on the assumption that the power takeoff (PTO) system has no dynamics or its dynamics is well-known. In practical WEC control implementation, this is generally not the case. The objective of this paper is to design a robust optimal control strategy that can take into account the uncertain PTO dynamics. Our choice is a robust adaptive PI control law. The proposed controller is validated and compared through simulation on irregular sea states.

Keywords:Adaptive control, Direct adaptive control, Robust adaptive control Abstract: Unlike traditional canonical nonlinear systems, the nonlinear system in noncanonical form does not have an explicit relative degree structure and cannot be transformed into a canonical form via a parameter-independent diffeomorphism. In this sense, controlling noncanonical nonlinear system is very difficult and challenging. To address this problem, in this paper, we study the adaptive control of noncanonical nonlinear systems with unknown input dead zone. A new Lyapunov-based control scheme and a new gradient control scheme are developed successively with the techniques of feedback linearization, adaptive dead-zone inverse compensation and system parametrization, to address the relative-degree-one case and relative-degree-two case of the considered noncanonical nonlinear system, respectively. The closed-loop signal boundedness and the asymptotic output tracking are ensured with the proposed adaptive schemes, and the effectiveness of the obtained results will be illustrated through simulation studies.

Keywords:Adaptive systems, Robust adaptive control, Nonlinear output feedback Abstract: Global adaptive control via output feedback is studied for a class of nonlinear systems with unknown parameters in the state and output equations. In contrast to the existing results, both the value and sign of the unknown parameter in the system output are not required to be known a priori. Moreover, the controlled plant is assumed to be nonlinearly dependent of the output and the unknown parameters but linearly in the unmeasured states, with a lower-triangular structure. Using the idea of K-filter, we first construct a nonlinear observer with a dynamic-gain for the uncertain system with measurement uncertainty. We then develop, by virtue of the universal control philosophy with a Nussbaum function, a universal adaptive control scheme that achieves global state regulation and boundedness of the closed-loop system.

Keywords:Adaptive control, Optimal control, Robust adaptive control Abstract: This paper presents a robust optimal neuro-adaptive controller for nonlinear systems with unstructured uncertainties. This work is also the first step towards employing control barrier functions (CBFs) for such systems to create safety constraints in the presence of disturbances. The proposed controller consists of three parts: feedforward term, adaptive term, and optimal term. The unknown dynamics of the system are estimated by a joint neural network and concurrent learning adaptation mechanism (NNCL) to inform the adaptive term. The optimal term uses an online quadratic program (QP) formulated to generate the optimal signal while providing system stability via a control Lyapunov function (CLF). The CBFs and control bounds (CBs) constraints are incorporated into the QP structure to create safety conditions on the system and bound the control effort. %when a disturbance is encountered. A robust term robustifies the proposed controller to disturbances and uncancelled uncertainty. The end result is a QP-RCLBF-NNCL controller for which uniformly ultimately boundedness of all system signals is proven using Lyapunov synthesis. The proposed controller is validated on an inverted pendulum. Simulation results show that the controller achieves good tracking performance and model identification. Two safety tests are performed to show that the proposed controller is able to bound the control signal and velocity by their predefined values when a disturbance acts on the system.

Keywords:Fault detection, Fault diagnosis, Uncertain systems Abstract: In this paper, a fast-convergent fault detection and isolation architecture is proposed for linear MIMO continuous-time systems. By exploiting a system decomposition technique and making use of kernel-based deadbeat estimators, the state variables can be estimated in a non-asymptotic way. Estimation residuals are then defined to detect the occurrence of a fault and identify the occurring fault function after fault detection. In the noisy scenario, thresholds are defined for the residual to distinguish the effect of the noise from that of the fault. Numerical examples are included to characterize the effectiveness of the proposed FDI architecture.

Keywords:Fault detection, Fault accomodation, Variable-structure/sliding-mode control Abstract: This paper deals with the design of a distributed super-twisting sliding mode observer-based scheme to isolate and reconstruct faults affecting both generator nodes and load nodes in power networks. It is assumed that voltage phase angles are measured at each node using Phasor Measurement Units (PMUs). Based on this information, an interconnection of super-twisting sliding mode observers is proposed both to estimate frequency deviation in each generator node and to perform robust fault reconstruction. The proposed scheme requires only local information about the system and its neighborhood, and thus exhibits a distributed structure. The key-novelty of the proposed distributed scheme is its ability to reconstruct simultaneous faults acting on the generator nodes and load nodes. A fault mitigation strategy is also proposed at each generator node utilizing the fault estimates. Numerical simulations validate the proposed distributed scheme.

Keywords:Fault detection, Identification, Kalman filtering Abstract: This paper considers inverse filtering problems for linear Gaussian state-space systems. We consider three problems of increasing generality in which the aim is to reconstruct the measurements and/or certain unknown sensor parameters, such as the observation likelihood, given posteriors (i.e., the sample path of mean and covariance). The paper is motivated by applications where one wishes to calibrate a Bayesian estimator based on remote observations of the posterior estimates, e.g., determine how accurate an adversary's sensors are. We propose inverse filtering algorithms and evaluate their robustness with respect to noise (e.g., measurement or quantization errors) in numerical simulations.

Keywords:Fault detection, Observers for Linear systems, LMIs Abstract: Quadratic boundedness is a notion of stability that is adopted to investigate the design of observers for dynamic systems subject to bounded disturbances. We will show how to exploit such observers for the purpose of fault detection. Toward this end, first of all we present the naive application of quadratic boundedness to construct state observers for linear time-invariant systems with state augmentation, i.e., where additional variables may be introduced to account for the occurrence of a fault. Then a Luenberger observer is designed to estimate the augmented state variable of the system in such a way to detect the fault by using a convenient threshold selection. Finally, such an approach is extended to piecewise affine systems by presenting a hybrid Luenberger observer and its related design based on quadratic boundedness. The design of all the observers for both linear time-invariant and piecewise affine systems can be done by using linear matrix inequalities. Simulation results are provided to show the effectiveness of the proposed approach.

Keywords:Fault detection, Fault diagnosis, Building and facility automation Abstract: Indoor Air Quality monitoring is an essential ingredient of intelligent buildings. The release of various airborne contaminants into the buildings, compromises the health and safety of occupants. Therefore, early contaminant detection is of paramount importance for the timely activation of proper contingency plans in order to minimize the impact of contaminants on occupants health. The objective of this work is to enhance the performance of a distributed contaminant detection methodology, in terms of the minimum detectable contaminant release rates, by considering the joint problem of partitioning selection and observer gain design. Towards this direction, a detectability analysis is performed to derive appropriate conditions for the minimum guaranteed detectable contaminant release rate for specific partitioning configuration and observer gains. The derived detectability conditions are then exploited to formulate and solve an optimization problem for jointly selecting the partitioning configuration and observer gains that yield the best contaminant detection performance.

Keywords:Fault detection, Estimation, Uncertain systems Abstract: In this paper, a novel Fault Detection (FD) architecture is developed for uncertain linear systems subject to actuator fault occurrences. The key idea is to take advantage of a moving horizon state estimation (MHE) strategy for improving the FD capabilities of a filter unit designed by formulating an optimization problem subject to H_infinity requirements. Specifically, this so-called pre-filter is synthesized by using Generalized KYP and Projection Lemma arguments under frequency domain conditions, while the robust MHE is derived by taking care of any source of uncertainties and by solving a min-max semidefinite programming problem. As one of its main merits, all the prescribed steps of the resulting fault detection architecture are recast as Linear Matrix Inequalities.

Keywords:Markov processes, Robust control, Linear parameter-varying systems Abstract: We address stability analysis and control synthesis for time-inhomogeneous Markov jump linear systems with partial observations of the Markov chain where the Markov parameter transition probabilities are non-stationary. We assume that the transition probabilities vary in a finite set and consider the case where a finite sequence of future transition probabilities is known. We use a detector-based approach to formally guarantee stability and expected l_{2} performance where the Markov chain state or scheduling parameter is indirectly measured through a detector. Our main results include a new Bounded Real Lemma for stability analysis and an output feedback H-infinity control synthesis algorithm expressed as a finite set of matrix inequalities that can be efficiently solved.

Keywords:Markov processes, Robust control, Optimization Abstract: Partially observable Markov decision processes (POMDPs) are models for sequential decision-making under state transition uncertainty, and sensing uncertainty of the underlying state. Model uncertainty is an important concern when the models, for which an action policy was optimized, change in time, e.g., degrading sensors that result in a drift in the observation function. Replanning a policy whenever a model drifts (if feasible) is both a time consuming and computationally expensive process. At the other extreme, ignoring the drift and following the original policy can lead to high-risk actions with high costs. We present an efficient approach that post-processes a policy computed using initial models to select actions robust to changes in the observation function. The key idea is to maintain a belief region rather than a belief point about the state of the system, and perform online robust action selection w.r.t. the current belief region. Specifically, we formulate a convex optimization problem to select the action that maximizes the worst case reward function for a convexified belief region. Simulation results demonstrate the ability of our approach to avoid high-risk actions when the system is in uncertain states.

Keywords:Modeling, Markov processes, Pattern recognition and classification Abstract: This paper presents a new evidential reasoning approach for autonomously modeling the state of an evolving wildfire. The objective is to update the current geospatial representation of a wildfire through the inclusion of the available evidence regarding a wildfire's presence at a given location. This evidential support is calculated from data provided by imperfect temperature and machine vision sensors using belief functions based in the Dempster-Shafer theory of probable reasoning. The derivation and mathematical validity of these belief functions is shown through rigorous analysis and a simplified example is considered that exhibits the benefits of this evidential reasoning approach. Based on the methods and models explored in this work, concepts for autonomous path-planning procedures are discussed for further studies.

Keywords:Discrete event systems, Automata, Markov processes Abstract: Privacy is a crucial concern in many practical systems. We consider a new notion of privacy based on beliefs of the system states, which is closely related to opacity in discrete event systems. To guarantee the privacy requirement, we propose to abstract the belief space whose dynamics is shown to be mixed monotone where efficient abstraction algorithm exists. Based on the abstraction, we propose two different approaches to preserve privacy with an illustrative example.

Keywords:Markov processes, Stochastic systems, Uncertain systems Abstract: In this paper, mean square stability and H2-control for Markov jump linear system (MJLS) with multiplicative noises are studied based on the context of partial information of the jumping parameter. We suppose the existence of a suitable detector which provides measurements of the Markov chain. The detector-based approach allows us to treat some existing scenarios in the MJLS literature with partial mode information, specifically: the case with complete observations, no information and cluster observations. Furthermore, the particular structure of the detector considered here support us to treat a new case where the detector should be missing mode information. The proposed results are given in terms of linear matrix inequalities. As a by product, H 2 -control design is applied to the dynamics of a vertical take-off and landing (VTOL) aircraft.

Keywords:Markov processes, Emerging control applications, LMIs Abstract: Privacy is an increasing concern in cyber-physical systems that operates over a shared network. In this paper, we propose a method for privacy verification of cyber- physical systems modeled by Markov decision processes (MDPs) and partially-observable Markov decision processes (POMDPs) based on barrier certificates. To this end, we consider an opacity-based notion of privacy, which is characterized by the beliefs in system states. We show that the belief update equations can be represented as discrete-time switched systems, for which we propose a set of conditions for privacy verification in terms of barrier certificates. We further demonstrate that, for MDPs and for POMDPs, privacy verification can be computationally implemented by solving a set of semi-definite programs and sum-of-squares programs, respectively. The method is illustrated by an application to privacy verification of an inventory management system.

Keywords:Nonlinear output feedback, Observers for nonlinear systems, Stability of nonlinear systems Abstract: Observer-based feedback control is the most popular paradigm for designing output feedback stabilizers. For a class of nonlinear systems, an observer can be constructed by rendering estimation error dynamics linear in unmeasured state variables. However, measurement disturbance violates the structure of the error dynamics and brings in undesirable terms in which the estimation error and the plant state are often coupled and multiplied by the measurement disturbance. This is why local analysis and semi-global design have been performed in many cases. This paper introduces new flexibility into the iISS small-gain framework to accommodate such terms. It is demonstrated how the flexible framework enables global analysis of observer-based output feedback control systems to achieve convergence and boundedness in the presence of measurement disturbance effectively.

Keywords:Nonlinear output feedback, Delay systems, Lyapunov methods Abstract: We design backstepping control to stabilize a piston moving freely in a cylinder filled with inviscid gas, under the actuation of gas injected at both extremities. The piston problem has been widely studied in engineering processes such as combustion engines, but boundary control of such a system is highly nontrivial. The gas dynamics are modeled by two sets of coupled first-order hyperbolic partial differential equations (PDEs), and each domain is separated by the piston's position, dynamics of which are represented by a second order ordinary differential equation (ODE). The control objective is to stabilize both the gas states (pressure and velocity) and the piston to a given setpoint. We design the state feedback controller based on a delay compensation technique using the backstepping method. With Lyapunov analysis on the moving boundary problem, we show local stability of the system in H^{1} norm. The performance of the controller is studied by numerical simulations, which illustrate the efficient stabilization of the piston position and velocity.

Keywords:Nonlinear output feedback, Hybrid systems, Stability of nonlinear systems Abstract: Existing results on periodic event-triggered control mainly focus on linear systems, and their extension to nonlinear systems are largely open. This paper investigates the observer-based control design for incrementally conic nonlinear systems with periodic event-trigger mechanisms in both the input and output channels. The closed-loop system is modeled using an impulsive system approach, and sufficient conditions based on linear matrix inequalities are presented to guarantee the asymptotically practical stability of the closed-loop system. A single-link robot arm example is given to illustrate the theoretical results.

Keywords:Nonlinear output feedback, Lyapunov methods, Stability of nonlinear systems Abstract: This note is devoted to the stabilization of a particular class of nonlinear cyclo-passive systems, namely, gradient-like systems. In order to accomplish the control task, we explore alternate representations of those systems with the aim of identifying (new) storage functions. Then, those storage functions are used to design a passivity-based controller that addresses the regulation problem without the necessity of solving partial differential equations.

Keywords:Output regulation, Nonlinear output feedback, Lyapunov methods Abstract: The paper deals with the problem of output regulation for a class of nonlinear multivariable systems possessing a normal form. With respect to the most of the literature on the subject we deal with the design of the regulator in the cases in which, besides the regulation error, others measurements not necessarily zero in steady state are available. Motivated by a linear analysis that is overviewed in the initial part of the paper, we propose a control structure in which the extra measurements are filtered by a post-processor specifically designed to block their steady state value. The method proposed in the paper lends itself to address relevant cases of nonlinear systems that are nonminimum-phase between the control input and the regulation error and for which extra measurements are necessary, or simply desirable, to succeed in robust output feedback stabilisation.

Keywords:Lyapunov methods, Nonlinear output feedback, Observers for nonlinear systems Abstract: A nonlinear output feedback control method is presented, which achieves asymptotic limit cycle oscillation (LCO) regulation in an aircraft wing section using synthetic jet actuators. To eliminate the standard requirement that LCO pitching and plunging rates are available for feedback, a finite-time sliding mode observer is utilized to estimate the rates using only measurements of LCO displacements. To achieve the result, a detailed mathematical model of the LCO dynamics is utilized, which includes nonlinear stiffness effects, unmodeled external disturbances, and dynamic model uncertainty, in addition to the parametric actuator uncertainty. A rigorous analysis is used to prove finite-time convergence of the estimation error, and a Lyapunov-based stability analysis is used to prove asymptotic regulation control of the LCO. Numerical simulation results are also provided which show the performance of the proposed sliding mode observer-based control design in comparison with our recently developed bank of filters-based output feedback LCO control method.

Keywords:Switched systems, Robust control, Optimization Abstract: The main goal of this paper is to develop a computationally tractable framework for data driven control of switched linear MIMO systems. Specifically, given a model structure and experimental data collected at different operating points, we seek to directly design a controller that stabilizes all plants compatible with this information, without an explicit plant identification. The main result of the paper shows that this problem can be recast into a polynomial optimization form and efficiently solved, leading to a robust controller with guaranteed l-infinity worse-case performance for any switching amongst all plants that could have generated the observed experimental data. The effectiveness of the proposed technique is illustrated with a numerical example.

Keywords:Switched systems, Markov processes, LMIs Abstract: In this work we investigate the design of stabilizing dynamic output feedback controllers for Markov jump linear systems considering a context of partial information on the Markov chain. We assume that the mode of operation of the system is not available, but only an estimation provided by a detector in the spirit of hidden Markov models. We present new nonlinear matrix inequalities conditions for the design of stabilizing dynamic controllers that depend only on the estimation, and by means of some interesting properties of this new condition, we are able to provide a type of ad hoc separation procedure involving linear matrix inequalities in which the controller is obtained via a two-stage algorithm. First a stabilizing state feedback gain depending only on the estimation is calculated and used as an input in the second step for obtaining the remaining controller parameters. The final stabilizing controller is composed by both the state feedback gain of the first stage and the dynamic system calculated in the last stage. We present a numerical example in the context of systems subject to failures in order to illustrate our results.

Keywords:Switched systems, Lyapunov methods, Stability of nonlinear systems Abstract: We use nonsmooth Lyapunov functions to establish stability for a class of differential inclusions where the set-valued map on the right-hand-side comprises the convex hull of a finite number of vector fields. Starting with a finite family of continuously differentiable positive definite functions, we study conditions under which a function obtained by max-min combinations over this family of functions is a Lyapunov function for the system under consideration. For the case of linear systems, using the S-Procedure, our conditions result in bilinear matrix inequalities. The proposed construction also provides nonconvex Lyapunov functions, which are shown to be useful for systems with state-dependent switching that do not admit a convex Lyapunov function.

Keywords:Switched systems, Hybrid systems, Learning Abstract: This paper addresses two fundamental problems in the context of jump linear systems (JLS). The first problem is concerned with characterizing the minimal state space dimension solely from input--output pairs and without any knowledge of the number of mode switches. The second problem is concerned with characterizing the number of discrete modes of the JLS. For the first problem, we develop a linear system theory based approach and construct an appropriate Hankel--like matrix. The rank of this matrix gives us the state space dimension. For the second problem we show that minimal number of modes corresponds to the minimal rank of a positive semi--definite matrix obtained via a non--convex formulation.

Keywords:Switched systems, Stability of hybrid systems, Simulation Abstract: We propose an algorithm to restrict the switching sequences of a constrained switched system in order to guarantee its stability, while at the same time attempting to keep the largest possible set of allowed switching sequences.

Our work is motivated by applications to (co-)simulation where numerical stability is a hard constraint, but should be attained by restricting as little as possible the allowed behaviours of the simulators.

We apply our results to certify the stability of an adaptive co-simulation orchestration algorithm, which selects the optimal switching signal at run-time, as a function of (varying) performance and accuracy requirements.

Keywords:Switched systems, Quantized systems, Control over communications Abstract: This paper introduces a notion of topological entropy for switched systems, formulated using the minimal number of initial states needed to approximate all initial states within a finite precision. We show that it can be equivalently defined using the maximal number of initial states separable within a finite precision, and introduce switching-related quantities such as the active time of each mode, which prove to be useful in calculating the topological entropy of switched linear systems. For general switched linear systems, we show that the topological entropy is independent of the set of initial states, and establish upper and lower bounds using the active-time weighted averages of the norms and traces of system matrices in individual modes, respectively. For switched linear systems with scalar-valued state or simultaneously diagonalizable matrices, we derive formulae for the topological entropy using active-time-weighted averages of eigenvalues, which can be extended to the case with simultaneously triangularizable matrices to obtain an upper bound. In these three cases with special matrix structure, we also provide more general but more conservative upper bounds for the topological entropy.

Keywords:Energy systems, Power systems Abstract: Conventional control strategies for ac power electronic inverters are based on the availability of very stable voltage and frequency references from synchronous generators with large inertia (i.e., the generators can be approximately treated as ideal infinite buses). Such strategies are no longer adequate for low or zero-inertia electricity generating systems like microgrids, which rely upon a high penetration of renewable energy sources. This has led to new inverter control strategies for microgrids, with the goal of fulfilling load power demand while guaranteeing stability of a microgrid.

In this paper we initiate the analysis of a nonlinear current control scheme for regulating microgrids that consists of a linear proportional and resonant controller in a feedback connection with a nonlinear phase-locked loop. Numerical simulations and laboratory experiments support heuristic arguments suggesting that this scheme can generate a sinusoidal voltage at a frequency which adapts itself to the impedance angle of the load, thus providing an intrinsic frequency droop for primary control in a microgrid. Moreover, multiple inverters can synchronise to a common frequency and the scheme can be augmented with additional control loops to provide voltage regulation, current magnitude droop and secondary control. In this paper we rigorously establish the existence of sinusoidal orbits for this current control scheme, for the special case of a single-phase inverter connected to an RL load. This confirms that the system can indeed generate a purely sinusoidal output voltage (i.e., contains no harmonics) as observed in simulations.

Keywords:Energy systems, Modeling, Stability of nonlinear systems Abstract: This paper introduces a fundamental energy-based modeling framework for complex electric energy systems. This approach captures dynamic interactions within such systems in terms of general conservation laws. Instead of effort and flow port variables, each component is characterized using diffemorphically mapped instantaneous real and reactive power quantities. In this paper, this mapping is proven for the first time. This new modeling approach is used to derive novel efficiency and realizability conditions for complex electric energy systems interpretable in engineering terms.

Keywords:Modeling, Energy systems, Automotive systems Abstract: The Doyle-Fuller-Newman (DFN) model is generally considered the modeling standard to assess the worthiness of reduced-order electrochemical models. An aspect of such a macroscale model which has often been overlooked is that they are approximate representations of pore-scale transport dynamics and their predictive ability is hence susceptible to certain operating conditions. In this paper, we identify battery operating conditions that lead to loss of accuracy and root mean square error as high as 83.9 mV in the voltage prediction of the DFN model, and interpret our observations using a phase diagram analysis. Under the same scenarios, we simulate the performance of a full-homogenized macroscale (FHM) model developed by applying multiple-scale expansions to the Poisson- Nernst-Planck (PNP) transport equations. The performance of both models is assessed against experiments conducted on 18650 cylindrical lithium-ion cells. Results infer that the DFN model fails to predict battery voltage accurately towards the end of discharge at temperatures higher than 40C. The FHM model accurately predicts measured battery terminal voltage with less than 22 mV RMS error for the evaluated conditions.

Keywords:Energy systems, Smart grid Abstract: This paper develops and compares algorithms to compute inner approximations of the Minkowski sum of convex polytopes. As an application, the paper considers the computation of the feasibility set of aggregations of distributed energy resources (DERs), such as solar photovoltaic inverters, controllable loads, and storage devices. To fully account for the heterogeneity in the DERs while ensuring an acceptable approximation accuracy, we leverage a union-based computation that advocates a homothet-based polytope decomposition. However, union-based approached can in general lead to high-dimensionality concerns; to alleviate this issue, this paper shows how to define candidate sets to reduce the computational complexity. Accuracy and trade-offs are analyzed through numerical simulations for illustrative examples.

Keywords:Energy systems, Automotive control, LMIs Abstract: Estimating the battery State-of-Charge (SoC) is often done using nonlinear extensions of the Kalman filter. These filters do not explicitly address convergence of the estimation error and robustness with respect to model uncertainty, and make nonrealistic assumptions on the noise. Therefore, these filters require extensive tuning of the covariance matrices, which is a non-intuitive and tedious task. In this paper, a robust Luenberger estimator is proposed that explicitly addresses the requirements on estimation-error convergence, robustness and noise attenuation and shows their inherent trade-off. Different observers are synthesised using polytopic embeddings of the nonlinear battery model and using linear matrix inequalities that provide bounds on the l_{2,inf}-, l_{inf,inf}- or the l_{2,2}-gains between input and output (to accommodate for model uncertainty and sensor noise). This guarantees a robustly converging SoC observer and makes its design more intuitive. The proposed observers are validated and compared with an Extended Kalman Filter (EKF) using experimental data. The results show that the performance of two out of three proposed observers is similar to the EKF, while the implementation is simpler and tuning is more intuitive and more straightforward.

Keywords:Energy systems, Distributed control, Optimization Abstract: In this paper, we study AC microgrid dynamics under a completely decentralized primary control, and a secondary frequency control the implementation of which is distributed over a communication network with communication links that are time-varying and can be (i) bidirectional, or (ii) unidirectional. For a certain class of controllers, the closed-loop system dynamics solves a certain multi-agent optimization problem by performing two steps: (i) gradient-descent, and (ii) distributed averaging. The proposed framework allows to explore many of the existing distributed algorithms developed for solving general multi-agent optimization problems over time-varying communication networks. In particular, we use the subgradient-push algorithm to design a distributed frequency controller, and we present the convergence analysis for the closed-loop system. We also dwell on this framework and propose a distributed frequency controller that does not require agents (power generators) to know their out-degree, which is a necessary assumption for the convergence of the subgradient-push algorithm.

Keywords:Optimization algorithms, Communication networks, Agents-based systems Abstract: In this paper, a gradient-free algorithm is proposed for a set constrained distributed optimization problem in a multi-agent system under a directed communication network. For each agent, a pseudo-gradient is designed locally and utilized instead of the true gradient information to guide the decision variables update. Compared with most gradient-free optimization methods where a doubly-stochastic weighting matrix is usually employed, this algorithm uses a row-stochastic matrix plus a column-stochastic matrix, and is able to achieve exact asymptotic convergence to the optimal solution.

Keywords:Optimization algorithms, Simulation, Stochastic systems Abstract: The Stochastic optimization (SO) problem consists of optimizing an objective function in the presence of noise. Most of the solution techniques in SO estimate gradients from noise corrupted observations of the objective and adjust parameters of the objective along the direction of the estimated gradients to obtain locally optimal solutions. Two prominent algorithms in SO namely Random Direction Kiefer-Wolfowitz (RDKW) and Simultaneous Perturbation Stochastic Approxi- mation (SPSA) obtain noisy gradient estimates by randomly perturbing all the parameters simultaneously. This forces the search direction to be random in these algorithms and presents one with additional noise on top of the noise incurred from the samples of the objective. For better convergence properties, the idea of using deterministic perturbations instead of randomized perturbations for gradient estimation has also been studied. Two specific constructions of the deterministic perturbation se- quence using lexicographical ordering and Hadamard matrices have been explored and encouraging results have been reported previously in the literature. In this paper, we characterize the class of deterministic perturbation sequences that can be utilized in the RDKW algorithm. This class expands the set of known deterministic perturbation sequences available in the literature. Using our characterization, we propose construction of a deterministic perturbation sequence that has the least cycle length among all such sequences. Through simulations we illustrate the performance gain of the proposed determin- istic perturbation sequence in the RDKW algorithm over the Hadamard as well as the random perturbation counterparts. We also establish the convergence of the RDKW algorithm for this generalized class of deterministic perturbations.

Keywords:Optimization algorithms, Agents-based systems, Networked control systems Abstract: This paper considers problems related to suppressing epidemic spread over networks given limited curing resources. The spreading dynamic is captured by a susceptible-infected-susceptible model. The epidemic threshold and recovery speed are determined by the contact network structure and the heterogeneous infection and curing rates. We develop a distributed algorithm that can be used for allocating curing resources to meet three potential objectives: 1) minimize total curing cost while preventing an epidemic; 2) maximize recovery speed given sufficient curing resources; or 3) given insufficient curing resources, limit the size of an endemic state. The distributed algorithm is of the Jacobi type, and converges geometrically. We provide an upper bound on the convergence rate that depends on the structure and infection rates of the underlying network. Numerical simulations illustrate the efficiency and scalability of our distributed algorithm.

Keywords:Optimization algorithms, Optimization, Agents-based systems Abstract: In this paper, we study the problem of searching for a moving object with multiple agents where each agent can access only a subset of a discrete search space at any time. We develop necessary conditions for an optimal search plan, extending prior results in search theory. Using these necessary conditions, we develop a forward-backward algorithm based on coordinate descent techniques to obtain solutions. For the case where agent's probabilities of detection depend only on the cell being searched, each iteration can be reduced to solution of a network optimization problem. To avoid local minima, we derive a convex relaxation of the dynamic search problem and show this can be solved optimally using coordinate descent techniques. The solutions of the relaxed problem are used to provide random starting conditions for the iterative algorithm. We also address the problem where the probabilities of detection depend on agents, time periods and locations. We reduce the problem to a submodular maximization problem over a matroid and give a greedy algorithm with performance guarantees. We illustrate the performance of our algorithms with experiments and compare the results with alternative algorithms based on combinatorial techniques.

Keywords:Optimization algorithms, Optimization, Linear systems Abstract: We study performance of accelerated first-order optimization algorithms in the presence of additive white stochastic disturbances. For strongly convex quadratic problems, we explicitly evaluate the steady-state variance of the optimization variable in terms of the eigenvalues of the Hessian of the objective function. We demonstrate that, as the condition number increases, variance amplification of both Nesterov’s accelerated method and the heavy-ball method by Polyak is significantly larger than that of the standard gradient descent. In the context of distributed computation over networks, we examine the role of network topology and spatial dimension on the performance of these first-order algorithms. For d- dimensional tori, we establish explicit asymptotic dependence for the variance amplification on the network size and the corresponding condition number. Our results demonstrate detrimental influence of acceleration on amplification of stochastic disturbances and suggest that metrics other than convergence rate have to be considered when evaluating performance of optimization algorithms.

Keywords:Stochastic optimal control, Machine learning, Adaptive control Abstract: In this paper, we present an online reinforcement learning algorithm, called Renewal Monte Carlo (RMC), for infinite horizon Markov decision processes with a designated start state. RMC is a Monte Carlo algorithm and retains the advantages of Monte Carlo methods including low bias, simplicity and ease of implementation while, at the same time, circumvents their key drawbacks of high variance and delayed (end of episode) updates. The key ideas behind RMC are as follows. First, under any reasonable policy, the reward process is ergodic. So, by renewal theory, the performance of a policy is equal to the ratio of expected discounted reward to the expected discounted time over a regenerative cycle. Second, by carefully examining the expression for performance gradient, we propose a stochastic approximation algorithm that only requires estimates of the expected discounted reward and discounted time over a regenerative cycle and their gradients. We propose two unbiased estimators for evaluating performance gradients---a likelihood ratio based estimator and a simultaneous perturbation based estimator---and show that for both estimators, RMC converges to a locally optimal policy. We also generalize the RMC algorithm to post-decision state models. We conclude by presenting numerical experiments on a randomly generated MDP and event driven communication.

Keywords:Stochastic optimal control, Robust control, Stochastic systems Abstract: The paper focuses on the continuity properties of stochastic control problems with respect to initial probability measures. The continuity results are used to study the robustness of optimal control policies applied to systems with incorrect prior models. It is shown that for multi-stage optimal cost problems, weak convergence or setwise convergence is not sufficient for continuity and robustness in general, but that the optimal cost is continuous in the priors under the convergence in total variation under mild conditions. We also propose some sufficient conditions for the continuity of the optimal cost under weak convergence of priors. Using these continuity results we find bounds on the mismatch error that occurs due to the application of a control policy which is designed for an incorrectly estimated prior model in terms of a distance measure between true model and the incorrect one. Implications of these results in empirical learning for control will be presented, where almost surely weak convergence of i.i.d. empirical measures occurs but stronger notions of convergence, such as total variation convergence, in general, do not. These lead to practically important results on empirical learning in stochastic control since often, in engineering applications, system models are learned through training data.

Keywords:Stochastic optimal control, Finance, Markov processes Abstract: This paper studies the portfolio optimization problem when the investor's utility is general and the return and volatility of the risky asset are fast mean-reverting, which are important to capture the fast-time scale in the modeling of stock price volatility. Motivated by the heuristic derivation in [J.-P. Fouque, R. Sircar and T. Zariphopoulou, emph{Mathematical Finance}, 2016], we propose a zeroth order strategy, and show its asymptotic optimality within a specific (smaller) family of admissible strategies under proper assumptions. This optimality result is achieved by establishing a first order approximation of the problem value associated to this proposed strategy using singular perturbation method, and estimating the risk-tolerance functions. The results are natural extensions of our previous work on portfolio optimization in a slowly varying stochastic environment [J.-P. Fouque and R. Hu, emph{SIAM Journal on Control and Optimization}, 2017], and together they form a whole picture of analyzing portfolio optimization in both fast and slow environments.

Keywords:Stochastic systems, Game theory, Power systems Abstract: The classic Vickrey-Clarke-Groves (VCG) mechanism ensures incentive compatibility, i.e., that truth-telling of all agents is a dominant strategy, for a static one-shot game. However, in a dynamic environment that unfolds over time, the agents' intertemporal payoffs depend on the expected future controls and payments, and a direct extension of the VCG mechanism is not sufficient to guarantee incentive compatibility. In fact, it does not appear to be feasible to construct mechanisms that ensure the dominance of dynamic truth-telling for agents comprised of general stochastic dynamic systems. The contribution of this paper is to show that such a dynamic stochastic extension does exist for the special case of Linear-Quadratic-Gaussian (LQG) agents with a careful construction of a sequence of layered payments over time.

For a set of LQG agents, we propose a modified layered version of the VCG mechanism for payments that decouples the intertemporal effect of current bids on future payoffs, and prove that truth-telling of dynamic states forms a dominant strategy if system parameters are known and agents are rational.

An important example of a problem needing such optimal dynamic coordination of stochastic agents arises in power systems where an Independent System Operator (ISO) has to ensure balance of generation and consumption at all time instants, while ensuring social optimality (maximization of the sum of the utilities of all agents). Addressing strategic behavior is critical as the price-taking assumption on market participants may not hold in an electricity market. Agents, can lie or otherwise game the bidding system. The challenge is to determine a bidding scheme between all agents and the ISO that maximizes social welfare, while taking into account the stochastic dynamic models of agents, since renewable energy resources such as solar/wind are stochastic and dynamic in nature, as are consumptions by loads which are influenced by factors such as local temperatures and thermal inertias of facilities.

Keywords:Stochastic systems, Stochastic optimal control, Statistical learning Abstract: We study the multi-player stochastic multiarmed bandit (MAB) problem in an abruptly changing environment. We consider a collision model in which a player receives reward at an arm if it is the only player to select the arm. We design two novel algorithms, namely, Round-Robin Sliding-Window Upper Confidence Bound# (RR-SW-UCB#), and the Sliding-Window Distributed Learning with Prioritization (SW-DLP). We rigorously analyze these algorithms and show that the expected cumulative group regret for these algorithms is upper bounded by sublinear functions of time, i.e., the time average of the regret asymptotically converges to zero. We complement our analytic results with numerical illustrations.

Keywords:Hybrid systems, Stochastic systems, Linear systems Abstract: In this paper control design for a class of linear systems based on stochastic hybrid framework is studied. The system is subject to external disturbances that affect the plant. The contribution of disturbance on dynamics of the system is modeled using stochastic differential equations. The control law is calculated based on state feedback and is applied to the system in random discrete time intervals. However, the control law can contain noise and uncertainty due to faulty actuators, noise in the system, etc. A question of interest is how to design the control law to have finite statistical moments of the system and reach to desired performance specifications (e.g., a specific mean and variance of the system state). Here, we derive exact solutions of the first two moments of the system, and use them to derive the stability conditions. We further design a control law that steers the system to a desired mean and variance. Next, we demonstrate our results on a general system. We show that under some specific conditions, randomness in the times that control law is applied can even reduce the variability contributed from disturbance. Finally, we discuss the trade-off between stability and achievable mean and variance, i.e., we can steer the system to any mean value as far as we do not violate the stability conditions.

Keywords:Finance, Estimation, Machine learning Abstract: We study an optimization-based approach to con- struct a mean-reverting portfolio of assets. Our objectives are threefold: (1) design a portfolio that is well-represented by an Ornstein-Uhlenbeck process with parameters estimated by maximum likelihood, (2) select portfolios with desirable characteristics of high mean reversion and low variance, and (3) select a parsimonious portfolio, i.e. find a small subset of a larger universe of assets that can be used for long and short positions. We present the full problem formulation, a specialized algorithm that exploits partial minimization, and numerical examples using both simulated and empirical price data.

Keywords:Finance, Stochastic systems, Stochastic optimal control Abstract: The celebrated Kelly betting strategy guarantees, with probability one, higher long-run logarithmic growth than any other causal investment strategy. However, on the way to its long-term supremacy, this strategy has a notable downfall: it typically displays high variation in the time-varying realization of the bettor's level of wealth. Hence, the following question has arisen: For a finite horizon involving N sequential bets, how might Kelly's scheme be modified so as to remain provably appealing in some sense and also less risky? One way to address this has been to employ fractional Kelly strategies. These strategies are arguably ad-hoc in that they involve scaling down the bet size without a significant theory providing rationale as to how this should be done. The results to follow in this paper can be interpreted as providing a systematic way of carrying out this scaling down process. To this end, we work with the so-called Conservative Expected Value, recently introduced in the literature, as an alternative for the classical expectation. As a first test case for this new paradigm, this paper considers the important special case where all N bets have even-money payoffs, are independent and follow the same Bernoulli distribution.

Keywords:Stochastic optimal control, Finance, Power generation Abstract: We consider stochastic optimal switching problems with reaction delays and propose an approximation technique that decreases the computational complexity. In a numerical example the approximation routine gives a considerable computational performance enhancement when compared to a conventional algorithm.

Keywords:Stochastic systems, Finance, Large-scale systems Abstract: We consider random vector fixed point (FP) equations in large dimensional spaces, and study their almost sure solutions. An underlying directed random graph defines the connections between various components of the FP equations. Existence of an edge between nodes i,j implies the i-th FP equation depends on the j-th component. We consider a special case where any component of the FP equation depends upon an appropriate aggregate of that of the random `neighbour' components. We obtain finite dimensional limit FP equations (in a much smaller dimensional space), whose solutions aid to approximate the solution of the random FP equations for almost all realizations, in the asymptotic limit (as the number of components become large). Our techniques are different from the traditional mean-field methods, which deal with stochastic FP equations in the space of distributions to describe the stationary distributions. In contrast our focus is on almost sure FP solutions. We apply the results to study systemic risk in a stylized large financial network captured by one big institution and many small ones, where our analysis reveal structural insights in a simple manner.

Keywords:Stochastic systems, Finance, Uncertain systems Abstract: In this paper, motivated by the celebrated work of Kelly, we consider the problem of portfolio weight selection to maximize expected logarithmic growth of a trader’s account. Going beyond existing literature, our focal point here is the rebalancing frequency which we include as an additional pa- rameter in the maximization. The problem is first set up in a control-theoretic framework, and then, the main question we address is as follows: In the absence of transaction costs, does high-frequency trading always lead to the best performance? Related to this question is our prior work on Kelly betting which examines the impact of making a wager and letting it ride. Our prior results indicate that it is often the case that there are no performance benefits associated with high-frequency trading. In the present paper, we generalize the analysis from the single-asset case to a portfolio with multiple risky assets. We show that if there is an asset satisfying a certain dominance condition, then an optimal portfolio consists of this asset alone; i.e., if the trader puts “all eggs in one basket,” performance becomes a constant function of rebalancing frequency. Said another way, the problem of rebalancing is rendered moot. The paper also includes simulations which address practical considerations associated with real stock prices vis-a-vis the dominance condition.

Keywords:Game theory, Network analysis and control, Agents-based systems Abstract: One of the key features of this paper is that the agents' opinion of a social network is assumed to be not only influenced by the other agents but also by two marketers in competition. One of our contributions is to propose a pragmatic game-theoretical formulation of the problem and to conduct the complete corresponding equilibrium analysis (existence, uniqueness, dynamic characterization, and determination). Our analysis provides practical insights to know how a marketer should exploit its knowledge about the social network to allocate its marketing or advertising budget among the agents (who are the consumers). By providing relevant definitions for the agent influence power (AIP) and the gain of targeting (GoT), the benefit of using a smart budget allocation policy instead of a uniform one is assessed and operating conditions under which it is potentially high are identified.

Keywords:Quantized systems, Control applications Abstract: Bilateral trading games are considered in which the buyer has access to more accurate information about the seller's valuation. The accuracy of the information, acquired by the buyer, is captured using quantization levels. We study how the level of accuracy and the rule for setting the final price in the bilateral trade game change the probability of striking a deal between the parties as well as the expected payoff of various parties. We also quantify the information level that maximizes the gain in the payoff for the smallest price of research assuming that acquiring accurate information is costly.

Keywords:Optimization, Optimization algorithms Abstract: We consider the problem of decentralized consensus optimization, where the sum of n convex functions are minimized over n distributed agents that form a connected network. In particular, we consider the case that the communicated local decision variables among nodes are quantized in order to alleviate the communication bottleneck in distributed optimization. We propose the Quantized Decentralized Gradient Descent (QDGD) algorithm, in which nodes update their local decision variables by combining the quantized information received from their neighbors with their local information. We prove that under standard strong convexity and smoothness assumptions for local cost functions, QDGD achieves a vanishing mean solution error. To the best of our knowledge, this is the first algorithm that achieves vanishing consensus error in the presence of quantization noise. Moreover, we provide simulation results that show tight agreement between our derived theoretical convergence rate and the experimental results.

Keywords:Networked control systems, Quantized systems, Hybrid systems Abstract: This paper studies the tracking control problem of nonlinear networked and quantized control systems. The desired trajectory is generated by the reference system. Due to the reference system and the network, the errors induced by the network are not attenuated and affect the convergence of the tracking error. Therefore, a unified hybrid model is developed. Using Lyapunov theory, sufficient conditions are derived to guarantee the convergence of the tracking error, which depends on the network-induced errors. In addition, the existence of the Lyapunov function is studied. Finally, a numerical example is used to illustrate the obtained results.

Keywords:Networked control systems, Quantized systems, Cooperative control Abstract: This paper proposes an encrypted control algorithm to the average consensus problem for agents whose communication topology is represented by a strongly connected digraph. Unlike many applications that use encryptions, encrypted control systems require encryptions and decryptions repeatedly at every sampling time. Thus, it is beneficial if the control algorithm allows us to balance the cipher strength and processing time. This property is acquired by constructing a finite-level uniform quantizer whose sensitivity changes with the evolution of the system, designing its associated control law, and then combining it with the Paillier cryptosystem. Numerical analysis of the quantized control law is also presented.

Keywords:Networked control systems, Quantized systems, Distributed control Abstract: This paper studies distributed quantized weight-balancing and average consensus over fixed digraphs. A digraph with non-negative weights associated to its edges is weight-balanced if, for each node, the sum of the weights of its outgoing edges is equal to that of its incoming edges. We propose and analyze the first distributed algorithm that solves the weight-balancing problem using only quantized (one-bit) information among nodes and simplex communications (compliant to the directed nature of the graph edges). Asymptotic convergence of the scheme is proved and a convergence rate analysis is provided. Building on this result, a novel distributed algorithm is proposed that solves the average consensus problem over digraphs, using, at each iteration, only two-bit simplex communications between adjacent nodes – one bit for the weight-balancing problem, the other for the average consensus. Convergence to the average of the real (i.e., unquantized) node’s initial values is proved, both almost surely and in mean square sense. Finally, numerical results validate our theoretical findings.

Keywords:Filtering, Quantized systems, Hybrid systems Abstract: This paper considers the problem of event-triggered filtering for Markovian jump systems with time delay and nonlinear perturbation. The purpose is to design a filter such that the filtering error system is stochastically stable with a prescribed mixed passivity and H_{infty} performance level. The existence condition for such filters is proposed, and the filter coefficients are found by solving a set of linear matrix inequalities. The usefulness of the filter design method is demonstrated by a numerical example.

Keywords:Large-scale systems, Decentralized control, Network analysis and control Abstract: We present two sensitivity function trade-offs that apply to a class of networks with a string topology. In particular we show that a lower bound on the H-infinity norm and a Bode sensitivity relation hold for an entire family of sensitivity functions associated with growing the network. The trade-offs we identify are a direct consequence of growing the network, and can be used to explain why poorly regulated low frequency behaviours emerge in long vehicle platoons even when using dynamic feedback.

Keywords:Hierarchical control, Predictive control for linear systems, Large-scale systems Abstract: Multi-rate hierarchical control approaches have gained increased attention in the optimal control of large scale systems due to their usually superior short- and long-term performance compared to distributed approaches and computational advantages compared to centralized controllers.

This paper presents a multi-rate hierarchical control scheme for the constrained control of an ensemble system, i.e. a group of individual (similar but heterogeneous) systems that follow a common goal. The approach is based on the definition of a small-scale reference system, which is common for all the subsystems. It allows to define a small-scale ensemble model, to be controlled in a scalable way by the centralized high level of the hierarchy. At the low level, a local shrinking horizon MPC controller is used for each subsystem. Feasibility results are provided and convergence properties are discussed. Finally, the properties of the present approach are illustrated in a case study.

Keywords:Large-scale systems, Decentralized control, Linear systems Abstract: Retrofit control is a promising approach for distributed design of decentralized sub-controllers for large-scale network systems, while most existing distributed control methods design sub-controllers in a centralized fashion. The key idea of retrofit control is to regard the network system as an interconnected system among a subsystem of interest and the others and to attach a controller that rectifies the effect between the interconnection signals. A parameterization of all retrofit controllers has been already given for the case where interconnection signal can be fed back. Our aim in this paper is to extend the result to the case where interconnection signal is unavailable. We consider state-feedback retrofit controllers without interconnection signals and derive a parameterization of all state-feedback retrofit controllers. We end with a numerical example demonstrating the effectiveness of retrofit control through a benchmark model representing the bulk power system in the eastern half of Japan.

Keywords:Large-scale systems, Network analysis and control, Control of networks Abstract: In this paper we consider the problem of controllability and energy consumption for large scale networks. Instead of controlling separately all the nodes of the network we control an output which is defined as some measurement (for instance the average) of the nodes which are not directly controlled. We thus exploit the concept of Output Controllability and the Output Controllability Gramian to analyze the properties of the system. In this context, we show that it is possible to obtain a reduced-order model which makes the Gramian compution and control design much easier. Simulations show that the reduced model is consistent with the original one and for low ratios of controlled nodes, more robust and performing with respect to the original.

Keywords:Large-scale systems, Control of networks, Optimal control Abstract: We propose a graphon regulation methodology to solve linear quadratic regulator (LQR) problems for complex networks of dynamical systems following the formulation initiated in [1]. Conditions for the exact and approximate controllability of graphon dynamical systems are investigated. Approximation schemes are then developed to obtain finite dimensional LQR control laws which are utilized on large-scale network systems and for which the convergence properties are established. Finally, an example of the application of graphon- LQR control to networks of dynamical systems is given in which the Riccati equation of the limit graphon system is solved explicitly.

Keywords:Linear parameter-varying systems, Large-scale systems, LMIs Abstract: The paper proposes a systematic framework for efficient decomposition of Linear Parameter Varying (LPV) systems. Our aim is to reveal the topological structure of the system, to facilitate various analysis and synthesis methods. For this purpose, first we extend the notion of Gramian based interaction measure for parameter dependent systems. However, the metric is based on the solution of an iterative optimization, subject to Linear Matrix Inequality (LMI) constraints. Therefore, in order to ease the computation burden, we apply a modal decomposition to the system. A simple structured Gramian computation is introduced, with fast conic programming. The proposed methodology is illustrated by a numerical example.

Keywords:Large-scale systems, Smart grid, Energy systems Abstract: Common household devices, such as solar panels and refrigerators, offer a considerable potential for frequency regulation, given their aggregate power generation and consumption. In this paper we present a simple approach to control the power contribution of a population of solar panels and thermostatically controlled loads, via a proportional control, in accordance with the current primary control practice. This control is suitable for a decentralized implementation. In addition, we consider the effect of renewables on the electricity network transfer function. We have tested the framework on a generation loss incident with different amount of solar power. Simulations display the capability of the control scheme and underline a chance of load shedding with a growing population of solar panels.

Keywords:Lyapunov methods, Control applications Abstract: The stabilization problem for a class of under-actuated systems is solved. This is achieved via a novel back-stepping based method that we call under-actuated back-stepping. The method is developed for linear under-actuated systems first and then extended to nonlinear systems via an example. Numerical simulations are given to demonstrate the effectiveness of the proposed under-actuated back-stepping method.

Keywords:Numerical algorithms, Optimal control, Automotive control Abstract: We consider a class of nonlinear equations that are related to the numerical solution of the Hamilton-Jacobi- Bellman equation for dynamic programming. Equations of this class can be solved with a simple fixed-point iteration, however this method may have slow convergence. We present two main contributions for increasing the efficiency of the solution: a simple preconditioning, inspired by the Jacobi method, and a selective node update procedure that reduces the number of required elementary operations.

Keywords:Estimation, Kalman filtering, Autonomous vehicles Abstract: This paper considers the challenge of preventing outlier measurements from affecting the accuracy and reliability of state estimation.Specifically, the paper extends the Risk-Averse Performance-Specified (RAPS) algorithm to nonlinear systems and applies it the Global Navigation Satellite Systems (GNSS) aiding an Inertial Navigation System (INS).The paper includes an application example, using data from a challenging environment, that allows a comparative study with the standard Neyman-Pearson (NP) test based extended Kalman Filter (EKF).In the experiment different aspects of measurements (e.g. risk metric, GDOP, no. of measurements) are used to highlight the tradeoffs between the important task of removing the effect of risky measurements even though this removal decreases the spatial diversity of the remaining measurement set.

Keywords:Time-varying systems, Linear parameter-varying systems, Emerging control applications Abstract: We propose a control system to regulate a periodic plant subject to significant load disturbances and measurement noise and a highly uncertain plant gain, but with negligible dynamics between control input and output. This is a common control problem in online advertising. The controller is periodic involving a periodic feed-forward adjustment of the reference setpoint and a periodic proportional-integral (PI) feedback controller. We derive the solution of the closed-loop system and prove that it is globally asymptotically stable. The proposed controller is compared with a control system based on the above feed-forward component and a standard linear and time-invariant PI controller.

Keywords:Markov processes, Robotics, Autonomous robots Abstract: This paper studies the problem of maximizing the return time entropy generated by a Markov chain subject to a given graph structure and a prescribed stationary distribution. The return time entropy is defined to be the weighted sum of the entropy of the first return time for the states in the Markov chains. The objective function in our optimization problem is a function series and does not have a closed form in general. First, we show that this problem is well-posed, i.e., the objective function is continuous over a compact set and there exists at least one optimal solution. Then, we analyze two special cases when the objective functions have closed-form expressions. Third, we obtain an upper bound for the return time entropy and solve analytically for the case when the given graph is a complete graph. Fourth, we approximate the problem by truncating the objective function and propose a gradient projection based method to solve it. We also illustrate the results through numerical simulations. The results derived in this paper are relevant to the design of stochastic surveillance strategies in robotic surveillance problems.

Keywords:Variable-structure/sliding-mode control, Uncertain systems, Constrained control Abstract: This paper proposes a discrete-time sliding mode control (DSMC) strategy for linear (possibly multi-input) systems with additive bounded disturbances, which guarantees the satisfaction of input and state constraints. The control law is generated by solving a finite-horizon optimal control problem at each sampling instant, aimed at obtaining a control variable that is as close as possible to a reference DSMC law, but at the same time enforces constraint satisfaction for all admissible disturbance values. Contrary to previously-proposed control approaches merging DSMC and model predictive control, our proposal guarantees the satisfaction of all standard properties of DSMC, and in particular the finite-time convergence of the state into a boundary layer of the sliding manifold.

Keywords:Variable-structure/sliding-mode control Abstract: In this paper, barrier function-based adaptive discontinuous and continuous integral sliding mode controls are proposed. The main advantage of the proposed algorithms is that they ensure that the solutions of the systems belong to a prescribed vicinity of the desired variables starting from the initial time moment despite of disturbance with unknown upper bound or disturbance with unknown upper bound of its derivative. The proposed algorithms do not require the knowledge of the upper bound of disturbance or its derivative, and, moreover, the control gains are not overestimated.

Keywords:Variable-structure/sliding-mode control Abstract: A continuous robustification methodology for the generation of self-oscillations using continuous switched integral sliding modes is presented. The robustification is achieved in finite time, assuring the frequency and amplitude of the oscillations remain despite the presence of Lipschitz matched uncertainties/perturbations. The sliding modes gains are designed to assure the convergence before the first switching under the assumption that the uncertainties/perturbations are continuous at the switching time. To illustrate the efficacy of the proposed approach, the designed methodology is applied to a Furuta Pendulum.

Keywords:Variable-structure/sliding-mode control, Robust control, Sampled-data control Abstract: The robust discrete-time sliding mode control problem is addressed. A novel approach to estimate the matched disturbance is presented. This approach is based on the approximation of a discrete-time function actual value by using various previous steps of itself. The matched disturbance previous step is calculated from the system model and then, using the mentioned approach, its actual value is estimated with an error of exponential order w.r.t. the sampling time and the used number of previous steps. Simulations show the effectiveness of the proposed approach to estimate a discrete time function and to robustly stabilize a dynamic system.

Keywords:Variable-structure/sliding-mode control, Power systems, Identification Abstract: In this paper, the outputs of a nonlinear system are divided into two groups: outputs of sensors which are protected, and outputs of sensors which are prone to get attacked. A higher-order sliding-mode observer is used to estimate the states of system and plant attacks. Equal to the number of outputs under protection, the input plant attacks can be reconstructed asymptotically, whilst the rest of the attacks can be identified by a Sparse recovery method. Finally, simulation results from a real electric power system illustrate the efficacy of the proposed observer.

Keywords:Variable-structure/sliding-mode control, Robotics, Machine learning Abstract: This paper deals with the design of an intelligent self-configuring control scheme for robot manipulators. The scheme features two control structures: one of centralized type, implementing the inverse dynamics approach, the other of decentralized type. In both control structures, the controller is based on Integral Sliding Mode (ISM), so that matched disturbances and uncertain terms, due to unmodeled dynamics or couplings effects, are suitably compensated. The use of the ISM control also enables the exploitation of its capability of acting as a ''perturbation estimator'' which, in the considered case, allows us to design a Deep Reinforcement Learning (DRL) based decision making mechanism. It implements a switching rule, based on an appropriate reward function, in order to choose one of the two control structures present in the scheme, depending on the requested robot performances. The proposed scheme can accommodate a variety of velocity and acceleration requirements, in contrast with the genuine decentralized or centralized control structures taken individually. The assessment of our proposal has been carried out relying on a model of the industrial robot manipulator COMAU SMART3-S2, identified on the basis of real data and with realistic sensor noise.

Keywords:Emerging control applications, Game theory, Networked control systems Abstract: A Stackelberg game framework is presented to choose the detector tuning for a general detector class under stealthy sensor attacks. In this framework, the defender acts as a leader and chooses a detector tuning, while the attacker will follow with a stealthy attack adjusted to this tuning. The tuning chosen is optimal with respect to the cost induced by the false alarms and the attack impact. We can show that under some practical assumptions the Stackelberg game always has a solution and we state two different sufficient conditions for the uniqueness of the solution. Interestingly, these conditions show that the attack impact does not have to be a convex function. An illustrative attack scenario of a false-data injection attack shows how one can use the Stackelberg game to find the optimal detector tuning.

Keywords:Emerging control applications, Autonomous systems, Autonomous vehicles Abstract: Unmanned aerial vehicles (UAVs) play essential roles in many areas including search and rescue, monitoring, and exploration. As such, fast and accurate trajectory tracking is crucial for UAVs especially in emergency situations or cluttered environment. This paper proposes a novel learning algorithm that improves UAVs' tracking performance through learning without human intervention. This learning algorithm, while possessing self-learning capacity, falls into the model-based learning methodology and therefore inherits the advantages of control techniques. This algorithm is particularly pursued and developed for scenarios that the reference trajectory is either too aggressive to follow or not compatible with system dynamics. Numerical study is conducted to validate the effectiveness and efficiency of the proposed learning algorithm and demonstrate the enhanced tracking and learning performance.

Keywords:Emerging control applications, Stochastic systems Abstract: This paper presents a stochastic model for block arrival times based on the difficulty retargeting rule used in Bitcoin, as well as other proof-of-work blockchains. Unlike some previous work, this paper explicitly models the difficulty target as a random variable which is a function of the previous block arrival times and affecting the block times in the next retargeting period. An explicit marginal distribution is derived for the time between successive blocks (the blocktime), while allowing for randomly changing difficulty. This paper also aims to serve as an introduction to Bitcoin and proof-of-work blockchains for the controls community, focusing on the difficulty retargeting procedure used in Bitcoin.

Ulsan National Institute of Science and Technology

Keywords:Emerging control applications, Variable-structure/sliding-mode control, Observers for nonlinear systems Abstract: In this paper, we propose an observer-based super-twisting sliding mode control with fuzzy variable gains (OSTFVG) for general second-order nonlinear systems. First, the super-twisting observer with fuzzy variable gains is designed for state estimation, for which we show finite-time convergence of the estimation error to zero under the bounded disturbance. Then, together with the proposed observer, the sliding mode control with fuzzy variable gains is designed to ensure precise tracking control performance and to alleviate the chattering phenomenon. We apply the OSTFVG to the overactuated quadrotor modeled by the second-order nonlinear system within the quaternion framework, which resolves underactuation and singularity problems appeared in standard quadrotors. In simulation results of attitude and position control, the fuzzy mechanism implemented in the OSTFVG guarantees faster convergence of the quadrotor to the desired position and more precision tracking performance compared to the standard observer-based super-twisting sliding mode control.

Keywords:Emerging control applications, Fault tolerant systems, Machine learning Abstract: This paper formulates general computation as a feedback-control problem, which allows the agent to autonomously overcome some limitations of standard procedural language programming: resilience to errors and early program termination. Our formulation considers computation to be trajectory generation in the program's variable space. The computing then becomes a sequential decision making problem, solved with reinforcement learning (RL), and analyzed with Lyapunov stability theory to assess the agent's resilience and progression to the goal. We do this through a case study on a quintessential computer science problem, array sorting. Evaluations show that our RL sorting agent makes steady progress to an asymptotically stable goal, is resilient to faulty components, and performs less array manipulations than traditional Quicksort and Bubble sort.

Keywords:Optimization, Biomedical, Emerging control applications Abstract: Hybrid neuroprosthesis (HN) systems combine the use of a powered exoskeleton with functional electrical stimulation of muscles to restore mobility in persons with paraplegia. At the same time, HN systems suffer from increased complexity due to redundant actuators that require coordination to function effectively. Muscle synergy-inspired control that coordinates these actuators can reduce system complexity. The calculation of these synergies requires the solution of a constrained optimization problem. As a way to reduce complexity during dynamic optimizations, we have developed a novel technique based on active subspaces to reduce the dimensionality of the redundant control system. Given an initial system state, a set of random control trajectories were generated, and the gradient of the cost function was obtained through the derivation of an adjoint function. The active subspaces were then obtained by performing eigenvalue decomposition on the outer product of the gradient of the cost function, and choosing the appropriate eigenvectors based on the magnitude of their corresponding eigenvalues. By leveraging the algorithm's parallel nature as well as simplifications that can be utilized in adjoint calculation, we show that by using this algorithm, synergies can be calculated more quickly than performing dynamic optimization. Once the active subspace is found, it is used in a gradient-projection optimization scheme to control the redundant actuators.

Keywords:Smart grid, Robust control, Predictive control for linear systems Abstract: In this paper, a computational low-demanding Model Predictive Control (MPC) strategy is proposed to deal with the transient stability control problem in Smart Grid systems. The proposed MPC controller is based on a dual model set-theoretic paradigm capable of robustly coping with model uncertainties and sensor measurement noise. Most of the required computations are moved into an offline phase leaving into the online phase a simple and computationally affordable convex optimization problem. A notable property of the proposed scheme is the capability of ensuring that transient stability is robustly achieved in a finite, and a priori known, time interval, regardless of any disturbance realization. The conducted simulation example shows the effectiveness of the proposed solution.

Keywords:Smart grid, Hierarchical control, Decentralized control Abstract: This paper presents a two-layer distributed energy resource (DER) coordination architecture that allows for separate ownership of data, operates with data subjected to a large buffering delay, and employs a new measure of power quality. The two-layer architecture comprises a centralized model predictive controller (MPC) and several decentralized MPCs each operating independently with no direct communication between them and with infrequent communication with the centralized controller. The goal is to minimize a combination of total energy cost and a measure of power quality while obeying cyber-physical constraints. The global controller utilizes a fast optimal power flow (OPF) solver and extensive parallelization to scale the solution to large networks. Each local controller attempts to maximize arbitrage profit while following the load profile and constraints dictated by the global controller. Extensive simulations are performed for two distribution networks under a wide variety of possible storage and solar penetrations enabled by the controller speed. The simulations show that (i) the two-layer architecture can achieve tenfold improvement in power quality relative to no coordination, while capturing nearly all of the available arbitrage profit for a moderate amount of storage penetration, and (ii) both power quality and arbitrage profits are optimized when the solar and storage are distributed more widely over the network, hence it is more effective to install storage closer to the consumer.

Keywords:Smart grid, Optimization algorithms, Energy systems Abstract: Recent works show that power-proportional data centers can save energy cost by dynamically adjusting active servers based on real time workload. The data center activates servers when the workload increases and transfers servers to sleep mode during periods of low load. In this paper, we investigate the right-sizing problem with heterogeneous data centers including various operational cost and switching cost to find the optimal number of active servers in a online setting. We propose an online regularization algorithm which always achieves a better competitive ratio compared to the greedy algorithm in cite{lin2012online}. We further extend the model by introducing the switching cost offset and propose another online regularization algorithm with performance guarantee. Simulations based on real world traces show that our algorithms both outperform the greedy algorithm.

Keywords:Smart grid, Agents-based systems, Game theory Abstract: This paper presents a novel receding horizon framework for the power scheduling of ﬂexible electric loads performing heterogeneous periodic tasks. The loads are characterized as price-responsive agents and their interactions are modelled through an inﬁnite-time horizon aggregative game. A distributed control strategy based on iterative better-response updates is proposed to coordinate the loads, proving its convergence and global optimality with Lyapunov stability tools. Robustness with respect to variations in the number and tasks of players is also ensured. Finally, the performance of the control scheme is evaluated in simulation,coordinating the daily battery charging of a large ﬂeet of electric vehicles.

Keywords:Distributed control, Smart grid, Networked control systems Abstract: In this letter we propose a new distributed control scheme, achieving current sharing and average voltage regulation in Direct Current (DC) microgrids. The considered DC microgrid is composed of several Distributed Generation Units (DGUs) interconnected through resistive-inductive power lines. Each DGU includes a generic energy source that supplies a local current load through a DC-DC buck converter. The proposed distributed control scheme achieves current sharing and average voltage regulation, independently of the initial condition of the controlled microgrid. Moreover, the proposed solution requires only measurements of the generated currents, and is independent of the microgrid parameters and the topology of the used communication network, facilitating Plug- and-Play capabilities. Global convergence to a desired steady state is proven and simulations indicate a good performance.

Keywords:Smart grid, Power systems, Identification Abstract: The low-voltage (LV) distribution network has been largely excluded from detailed analytical consideration and as a consequence it is now the least understood and most unpredictable element of the electricity grid. Many advanced network control and optimisation methods require feeder parameters to be known in advance, and thus accurate low-voltage power network models are an important prerequisite. Smart meters, being the only reliable source of information in such networks, improve the affordability of low voltage automation infrastructure and allow for accurate measurements at almost every node. We propose a fully smart meter data driven method for line impedance calculations by iteratively solving a non-convex problem for each line. The performance of our algorithms is demonstrated for different measurement accuracy scenarios through simulations.

Keywords:Statistical learning, Identification Abstract: Classification of particles produced by a nucleus-nucleus collision is still vastly a non-automatic procedure which requires expert scientists to be performed. This paper presents a nonparametric learning approach for the automatic classification of particles produced by the collision of a heavy ion beam on a target, by focusing on the identification of isotopes of the most energic light charged particles (LCP). In particular, it is shown that the measurement of the particle collision can be traced back to the impulse response of a linear dynamical system and, by employing recent kernel-based approaches, a nonparametric model is found that effectively trades off bias and variance of the model estimate. Then, the smoothened signals can be employed to classify the different types of particles. Experimental results show that the proposed method outperforms the state of the art approaches. All the experiments are carried out with the large detector array CHIMERA (Charge Heavy Ions Mass and Energy Resolving Array) in Catania, Italy

Keywords:Machine learning, Predictive control for nonlinear systems Abstract: Learning-based methods have been successful in solving complex control tasks without significant prior knowledge about the system. However, these methods typically do not provide any safety guarantees, which prevents their use in safety-critical, real-world applications. In this paper, we present a learning-based model predictive control scheme that can provide provable high-probability safety guarantees. To this end, we exploit regularity assumptions on the dynamics in terms of a Gaussian process prior to construct provably accurate confidence intervals on predicted trajectories. Unlike previous approaches, we do not assume that model uncertainties are independent. Based on these predictions, we guarantee that trajectories satisfy safety constraints. Moreover, we use a terminal set constraint to recursively guarantee the existence of safe control actions at every iteration. In our experiments, we show that the resulting algorithm can be used to safely and efficiently explore and learn about dynamic systems.

Keywords:Networked control systems, Learning, Control over communications Abstract: Recent control trends are increasingly relying on communication networks and wireless channels to close the loop in Internet-of-Things applications. Traditionally these approaches are modeled-based, i.e., given a network or channel model they analyze stability and design appropriate controller structures. However such modeling is a fundamental challenge as channels are typically unknown a priori and only available through data samples. In this work we aim to characterize the amount of channel modeling that is required to determine the stability of networked control tasks. Our most significant finding is a direct relation between the sample complexity and the system stability margin, i.e., the underlying packet success rate of the channel and the spectral radius of the dynamics of the control system.

Keywords:Machine learning, Networked control systems Abstract: An efficient representation of observed data has many benefits in various domains of engineering and science. Representing static data sets, such as images, is a living branch in machine learning and eases downstream tasks, such as classification, regression, or decision making. However, the representation of dynamical systems has received less attention. In this work, we develop a method to represent a dynamical system efficiently as a combination of a state and a local model, which fulfills a criterion inspired by the minimum description length (MDL) principle. The MDL principle is used in machine learning and statistics to quantify the trade-off between the ability to explain seen data and the model complexity. Networked control systems are a prominent example, where such a representation is beneficial. When many agents share a network, information exchange is costly and should thus happen only when necessary. We empirically show the efficiency of the proposed encoding for several dynamical systems and demonstrate reduced communication for event-triggered state estimation problems.

Keywords:Uncertain systems, Machine learning, Robust control Abstract: Data-driven approaches in control allow for identification of highly complex dynamical systems with minimal prior knowledge. However, properly incorporating model uncertainty in the design of a stabilizing control law remains challenging. Therefore, this article proposes a control Lyapunov function framework which semiglobally asymptotically stabilizes a partially unknown fully actuated control affine system with high probability. We propose an uncertainty-based control Lyapunov function which utilizes the model fidelity estimate of a Gaussian process model to drive the system in areas near training data with low uncertainty. We show that this behavior maximizes the probability that the system is stabilized in the presence of power constraints using equivalence to dynamic programming. A simulation on a nonlinear system is provided.

Keywords:Feedback linearization, Nonlinear systems identification, Statistical learning Abstract: We propose textit{random field system identification and inversion control (RF-SIIC)} as a method for simultaneous probabilistic identification and control of time-discretised control-affine systems. Identification is achieved by conditioning random field priors on observations of configurations and noisy estimates of configuration derivatives. In contrast to previous work that has utilised random fields for identification, we leverage the structural knowledge afforded by Lagrangian mechanics and learn the drift and control input matrix functions of the control-affine system separately. We employ feedback-linearisation with the aim to reduce, in expectation, the uncertain nonlinear control problem to one that is easy to regulate in a desired manner. Our method combines the flexibility of nonparametric Bayesian learning with epistemological guarantees on the expected closed-loop trajectory. We illustrate the viability of our approach in the context of a discretised fully-actuated mechanical system. Our simulations suggest that our approach can adapt rapidly to a priori uncertain dynamics sufficiently well to succeed in feedback-linearising and controlling the plant as desired.

Keywords:Automotive control, Adaptive control Abstract: We present a new adaption rule for the filtered x least mean squares (FxLMS) algorithm and its application as a disturbance compensator for the quarter car. Therefore we combine an adaption rule, which is based on the normalized, leaky-nu FxLMS algorithm, with a novel method for the initialization of the filter coefficients. This leads to fast convergence, which is important in the case of sudden changes in the primary path’s delay time. Thereafter, the new algorithm is applied as a disturbance compensator for road irregularities. The goal is to improve driving comfort and safety by exploiting the knowledge of the road surface (i.e. disturbance). Assuming that it is known a certain time in advance, we show the improved performance of the developed algorithm and compare it to the standard FxLMS algorithm and to a static disturbance compensator.

Keywords:Automotive control, Optimization, Optimal control Abstract: Eco-driving aims at minimizing the energy consumption of a vehicle by adjusting the vehicle’s velocity. This can be formulated as an optimal control problem and this paper provides a detailed view on the global optimal solution to this problem. A method to reformulate and discretize the problem avoiding the introduction of additional nonconvex terms is presented. Furthermore, physically realistic conditions are given that guarantee the existence of the global optimal solution to the eco-driving problem. Subsequently, a sequential quadratic programming algorithm is provided that allows finding the global optimal solution. Finally, two numerical examples are used to illustrate how solutions of the eco-driving problem can be obtained.

Keywords:Automotive control, Stochastic systems, LMIs Abstract: Due to varying in-cylinder conditions, cyclic combustion variation leads to fluctuating and deteriorated diesel engine performance. In this paper, we study both the deterministic and the stochastic cyclic variation of a closed-loop controlled combustion process with a cycle-to-cycle fuel injection controller using in-cylinder pressure information. A controller design method is proposed that yields a stabilizing controller with fast dynamical performance, while minimizing the unavoidable amplification of the stochastic cyclic variation. Following the design method with different design parameters, multiple controllers are designed and experimentally tested using a single-cylinder engine test setup. The reference tracking results illustrate the trade-off between reducing the deterministic and avoiding amplification of the stochastic cyclic combustion variation.

Keywords:Automotive control, Stability of nonlinear systems, Robust control Abstract: This letter presents a new notion of {it input-to-state safe control barrier functions} (ISSf-CBFs), which ensure safety of nonlinear dynamical systems under input disturbances. Similar to how safety conditions are specified in terms of forward invariance of a set, {it input-to-state safety} (ISSf) conditions are specified in terms of forward invariance of a slightly larger set. In this context, invariance of the larger set implies that the states stay either inside or very close to the smaller safe set; and this closeness is bounded by the magnitude of the disturbances. The main contribution of the letter is the methodology used for obtaining a valid ISSf-CBF, given a control barrier function (CBF). The associated universal control law will also be provided. Towards the end, we will study unified quadratic programs (QPs) that combine control Lyapunov functions (CLFs) and ISSf-CBFs in order to obtain a single control law that ensures both safety and stability in systems with input disturbances.

Keywords:Automotive control, Optimal control, Autonomous vehicles Abstract: The fuel consumption of heavy-duty vehicles in urban driving is strongly dependent on the acceleration and braking of the vehicles. In intersections with traffic lights, large amount of fuel can be saved by adapting the velocity to the phases of the lights. In this paper, a heavy-duty vehicle obtains information about the future signals of traffic lights within a specific horizon. In order to minimize the fuel consumption, the driving scenario is formulated as an optimal control problem. The optimal control is found by applying a model predictive controller, solving at each iteration a quadratic program. In such problem formulation, the constraints imposed by the traffic lights are formulated using a linear approximation of time. Since the fuel-optimal velocity can deviate strongly from how vehicles normally drive, constraints on the allowed velocity are imposed. Simulations are performed in order to investigate how the horizon length of the information from the traffic lights influences the fuel consumption. Compared to a benchmark vehicle without knowledge of future light signals, the proposed controller using a control horizon of 1000 m saves 26 % of energy with similar trip time. Increasing the control horizon further does not improve the results.

Swiss Federal Institute of Technology Zurich (ETH Zürich)

Keywords:Optimal control, Automotive control, PID control Abstract: The powertrain of the Formula 1 car is composed of an electrically turbocharged internal combustion engine and an electric motor used for boosting and regenerative braking. The energy management system that controls this hybrid electric power unit strongly influences the achievable lap time, as well as the fuel and battery consumption. Therefore, it is important to design robust feedback control algorithms that can run on the ECU in compliance with the sporting regulations, and are able to follow lap time optimal strategies while properly reacting to external disturbances. In this paper, we design feedback control algorithms inspired by equivalent consumption minimization strategies (ECMS) that adapt the optimal control policy implemented on the car in real-time. This way, we are able to track energy management strategies computed offline in a lap time optimal way using three PID controllers. We validate the presented control structure with numerical simulations and compare it to a previously designed model predictive control scheme.

Keywords:Control of networks, Distributed control, Optimal control Abstract: The control of complex networks has generated considerable interest in a variety of fields from traffic management to neural systems. A commonly used metric to compare two particular control strategies that accomplish the same task is the control energy, the time-integral of the sum of squares of all control inputs. The minimum control energy problem determines the control input that lower bounds all other control inputs with respect to their control energies. Here, we focus on the infinite lattice graph with linear dynamics and analytically derive the expression for the minimum control energy in terms of the modified Bessel function. We then demonstrate that the control energy of the infinite lattice graph accurately predicts the control energy of finite lattice graphs.

Keywords:Control of networks, Output regulation, Robotics Abstract: This paper deals with the problem of achieving consensus of multiple Euler-Lagrange (EL) systems. Following the energy shaping methodology, we propose a novel decentralized controller that is capable of solving the leaderless and the leader-follower consensus problems in finite-time in networks of fully-actuated EL-systems without employing velocity measurements. As in the energy shaping methodology, the controller is another EL-system and the plant-controller interconnection is the gradient of a suitable defined potential function. The controller's potential energy and dissipation functions are entitled with some homogeneous properties in order to perform finite-convergence

Keywords:Distributed control, Networked control systems, Cooperative control Abstract: Two well-established complementary distributed linear quadratic regulator (LQR) methods applied to networks of identical agents are extended to the non-identical dynamics case. The first uses a top-down approach where the centralized optimal LQR controller is approximated by a distributed control scheme whose stability is guaranteed by the stability margins of LQR control. The second consists of a bottom-up approach in which optimal interactions between self-stabilizing agents are defined so as to minimize an upper bound of the global LQR criterion. In this paper, local state-feedback controllers are designed by solving model-matching type problems and mapping all the agents in the network to a target system specified a priori. Existence conditions for such schemes are established for various families of systems. The single-input and then the multi-input case relying on the controllability indices of the plants are first considered followed by an LMI approach combined with LMI regions for pole clustering. Then, the two original top-down and bottom-up methods are adapted to our framework and the stability problem for networks of non-identical dynamical agents is solved. The applicability of our approach for distributed network control is illustrated via a simple example.

Keywords:Control of networks, Networked control systems, Agents-based systems Abstract: This paper studies the approach of taking network topology as a control variable for the analysis of second-order multi-agent systems. We particularly consider the setting where the local control inputs of individual agents are governed by their relative positions only. Based on the known results in the theory of stability of switched linear systems, we propose a time- dependent topology-switching algorithm that enables the agents to asymptotically achieve consensus. The main advantages of the proposed method, with respect to the prior work, are two- fold: we allow the control protocol to work without velocity measurements; and we do not constrain the magnitudes of coupling weights. Simulation results are provided to verify the effectiveness of the algorithm.

Keywords:Control of networks, Network analysis and control Abstract: Leader-follower controllability of signed multi-agent networks is investigated in this paper, where the agents interact via neighbor-based Laplacian feedback and the interactions between agents admit positive and negative weights capturing cooperative and competitive interactions. To enable full control of the leader-follower signed network, graph-inspired topological characterizations of the controllability of signed networks are investigated. Specifically, sufficient conditions on the controllability of signed path and cycle networks are developed based on the investigation of the interaction between network topology and agent dynamics. Constructive examples are provided to illustrate how the developed controllability result on signed path and cycle networks can be potentially extended to general signed networks.

University of Applied Sciences of Western Switzerland

Keywords:Control of networks, Network analysis and control, Power systems Abstract: New classes of performance measures have been recently introduced to quantify the transient response to ex- ternal disturbances of coupled dynamical systems on complex networks. These performance measures are time-integrated quadratic forms in the system’s coordinates or their time derivative. So far, investigations of these performance measures have been restricted to Dirac-delta impulse disturbances, in which case they can be alternatively interpreted as giving the long time output variances for stochastic white noise power de- mand/generation fluctuations. Strictly speaking, the approach is therefore restricted to power fluctuating on time scales shorter than the shortest time scales in the swing equations. To account for power productions from new renewable energy sources, we extend these earlier works to the relevant case of colored noise power fluctuations, with a finite correlation time tau > 0. We calculate a closed-form expression for generic quadratic performance measures. Applied to specific cases, this leads to a spectral representation of performance measures as a sum over the non-zero modes of the network Laplacian. Our results emphasize the competition between inertia, damping and the Laplacian modes, whose balance is determined to a large extent by the noise correlation time scale tau.

Keywords:Network analysis and control, Networked control systems, Cooperative control Abstract: This tutorial paper aims to explore the role of graph theory for studying networked and multi-agent systems. The session will cover basic concepts from graph theory along with surveying its role in problems related to cooperative control and distributed decision-making. Finally, we will also introduce some advanced topics from graph theory in the hope of encouraging further discussion and explore new research opportunities in system and control theory.

Keywords:Network analysis and control, Algebraic/geometric methods, Cooperative control Abstract: The first part of the tutorial acquaints the reader with tools and terminology in graph theory that have proven useful in the control theory of multi-agent networked systems. Topics presented include basic of graph theory, matrices associated with graphs (adjacency, incidence, and Laplacian), fundamental subspaces associated with graphs, spectral graph theory, graph symmetries, and combinatorics of patterned matrices.

Keywords:Network analysis and control, Algebraic/geometric methods, Control of networks Abstract: In this part of the presentation, we examine how the combinatorics of patterned matrices shed light on structural questions of networked systems. Topics discussed include the relation between structural controllability, graph matching, cacti structure, cycle covers, as well as stability analysis of patterned systems and k-decompositions.

Keywords:Network analysis and control, Control of networks Abstract: Consensus on networks has been one of the most well-studied models in multiagent networks, particularly as it provides a rather direct bridge between graph theoretic concepts and system theory. In this part of the presentation, we discuss consensus, as well as the role of graph symmetries in controllability analysis. This is then followed by examining the role of cycles in H2 performance of consensus-type networked systems.

Keywords:Control of networks, Learning, Optimization Abstract: In this part of the tutorial we discuss graph theoretic topics that we believe will play a more prominent role at the interaction of systems/control theory on one hand and graph theory/networks on the other. Topics presented include hyergraphs, graphons, extremal graph theory, graph products, and learning and optimization on networks.

Keywords:Agents-based systems, Markov processes, Network analysis and control Abstract: This paper analyzes a stochastic model for opinion dynamics in social networks. The change of opinion of each agent in the network is modeled by a finite-state Markov chain whose transition rate matrix is affected by the current opinion of the neighboring agents. A positive scalar parameter is introduced to describe the strength of the reciprocal influence, that is possibly modulated through filtering algorithms by the social network platform. Then, the complete network is described by a high dimensional Markov model, which, however, soon becomes untractable as the number of agents grows. A main result of the paper is to show that, under some assumptions, this model can be marginalized so as to obtain a differential equation of lower dimension describing the evolution of the individual probability distributions. Moreover, formulas for the steady state probability distribution for both finite and infinite values of the influence parameter are obtained. Some interesting case studies of networks composed by homogeneous subgroups with conflicting opinions, possibly connected through broker agents, are discussed.

Keywords:Cooperative control, Autonomous systems, Agents-based systems Abstract: In this paper, we consider the problem of localizing a team of unicycle agents with collaborative ranging, onboard compass measurements, and access to a subset of agent positions. Unlike previous work, we study the general multi-agent localization problem where we would like to also simultaneously estimate compass errors and an environmental disturbance experienced by all agents. The motivating example is localizing a team of autonomous underwater vehicles (AUVs), where GPS is not available to all agents, acoustic range-only measurements are common, and compass bias as well as environmental disturbances must be overcome. Significant work has been done in cooperative localization, however the idea of localization under the described conditions has not received much attention. We approach this problem by first looking at the nonlinear observability matrix, then analyzing it to determine conditions for observability of the multi-agent system. We then reduce the observability matrix to a metric that we exploit for planning observability maximizing agent trajectories under sensor bias and environmental disturbance. We then close with simulations.

Keywords:Cooperative control, Automotive control, Control system architecture Abstract: In this paper we propose a new distributed multiparty consensus for multi agent systems with a leader follower framework. The agents in multi-party consensus are separeted in different parties, but with in a party the agents synchronize with each other, but different parties have different orientation. So far the allignment is formulated by using complex numbers [1] [2]. Instead of complex valued Laplacian for a connected graph, we propose a matrix sharing technique to obtain different orientation between parties. The weight matrix will contain the scaling and orientation information among the parties. A sufficient condition is developed to obtain multi-party consensus. By using fixed time control technique a multi-party consensus controller is realized. Simulation studies demonstrate the effectiveness of the proposed approach.

Keywords:Distributed control, Cooperative control, Adaptive control Abstract: The leaderless consensus problem of uncertain multi-agent systems is much challenging under general directed graphs due to the combination of uncertainties and the nonsymmetric Laplacian matrix. Motivated by the classical model reference adaptive control, in this paper, we propose a simple and efficient scheme, called the model reference adaptive consensus (MRACon), by arranging each agent a reference to track. Under this scheme, the consensus problem is divided into two parts, namely, the tracking to the output of the reference models for the uncertain agent dynamics and the consensus of the reference models themselves. The proposed algorithms can be implemented using the relative measurements in the absence of communication. Furthermore, the results have been extended to the cases of switching directed graphs, unknown control directions, and general linear uncertain multi-agent systems..

Keywords:Distributed control, Cooperative control, Large-scale systems Abstract: This paper contributes to the studies in control of multiagent networks as systems. This class of multiagent networks consists of floating agents (i.e., agents that exchange local information) and driver agents (i.e., agents that not only exchange local information but also take input and output roles), where control algorithms are applied to the actuators of the driver agents based on the measurements collected from their sensors for the purpose of influencing the overall behavior of the resulting system. Specifically, we consider time-critical applications in the control of multiagent networks as systems. To this end, a finite-time control approach is proposed based on a recent time transformation method. The key feature of this method is that it guarantees execution of control algorithms over a prescribed time interval [0,T), where T is a user-defined convergence time, based on analysis performed over a stretched, infinite-time interval [0, ∞). Utilizing this method for finite-time control of multiagent networks as systems, we discuss user-defined finite-time convergence of the resulting system regardless of the initial conditions of agents and show a separation principle of the proposed time-critical algorithm. A numerical example is also presented to demonstrate the proposed system-theoretical results.

Keywords:Network analysis and control, Large-scale systems, Stochastic systems Abstract: In this paper we deal with the problem of unveiling the community structure of a system in which the network of connections among components evolves in time. First, we propose a general and flexible model for temporal networks, based on the activity-driven network paradigm, which is capable of modeling both the temporal evolution of the system and the presence of a hierarchical, overlapping, and heterogeneous community structure. Then, based on this model and using the paradigm of statistically validated networks, we develop our community detection algorithm. The application of this novel method enables us not only to identify the set of communities in the system, but also to uncover the components' roles in the various communities, giving deeper insights into the system than its mere community partition. Finally, our approach is successfully validated on a synthetic benchmark.

Keywords:Delay systems, Stability of linear systems, Distributed parameter systems Abstract: We present the construction of a Lyapunov matrix for a multiple distributed time-delay system with piecewise-function kernel. The construction of this matrix is reduced to the computation of the solutions of a delay free system of matrix equations. The Lyapunov matrix also allows us to perform a stability analysis in the time-domain. This analysis consists in the positivity test of a matrix composed of Lyapunov matrices. Two illustrative examples show the results of the approach.

Keywords:Distributed parameter systems, Variable-structure/sliding-mode control, Delay systems Abstract: The paper studies the problem of minimax control design for linear evolution equations in Hilbert spaces with measurement noise and additive exogenous disturbances. The key result of the paper is an algorithm, generating a control in an output-feedback form, which steers the state of the system as close as possible to a given sliding hyperplane, asymptotically as time goes to infinity. The control is designed in the state space of the minimax filter, and guarantees that the state of the filter will be exactly on the sliding surface, and the state of the plant will belong to an ellipsoid centered at the filter's state vector for large enough time. The optimality of the designed feedback and estimation error is proven. The feedback is represented by means of the unique solution of an algebraic Riccati equation. The theory is then applied to design a minimax control for linear hereditary systems subject to noise and disturbances. This is achieved by projecting the hereditary system onto a finite dimensional subspace of the corresponding state space by means of a finite-volume approximation method, designing feedback in the state space of the resulting finite dimensional system. The solution of the operator Riccati equation is obtained using a (modified) Kleinman-Newton method. The efficacy of the proposed algorithm is illustrated by a numerical example for a time-delay linear systems with constant point delays.

Keywords:Delay systems, Markov processes, Robust control Abstract: This paper addresses the regulation problem for discrete-time linear systems with unknown random state delay. The system under consideration can be subject to norm-bounded uncertainties in all parameter matrices. By the lifting method, the delay system is converted to an augmented delay-free Markovian jump system whose Markov chain is not observed. The Markovian system is reformulated as a deterministic system associated with an indicator function. A robust recursive regulator is then deduced by the robust regularized least-squares approach. The provided solution is given in terms of algebraic Riccati equations presented through a square matrix framework. A numerical comparison with methods available in the literature is performed to illustrate the effectiveness of the proposed approach.

Keywords:Delay systems, Sampled-data control, Stability of nonlinear systems Abstract: In this paper, the reduction method is extended to time-delay systems affected by two mismatched input delays. To this end, the intrinsic feedback structure of the retarded dynamics is exploited to deduce a reduced dynamics which is free of delays. Moreover, among other possibilities, an Immersion and Invariance feedback over the reduced dynamics is designed for achieving stabilization of the original dynamics. A chained sampled-data dynamics is used to show the effectiveness of the proposed control strategy through simulations.

Keywords:Delay systems, Linear systems, Adaptive control Abstract: In this paper, we propose a delay independent control scheme that regulates to zero the state and the control input of a linear input delayed system whose open loop poles are at the origin. Two main features of our control scheme are its non-distributed nature in the sense that only the current state is used in the feedback, and its delay independence in the sense that no knowledge of the delay is required. The main ingredients of our control scheme and the regulation proof include a design of the delay independent truncated predictor feedback law with a time-varying feedback parameter, a Lyapunov function based adaptation of the time-varying parameter, a mechanism for switching between two update laws of the time-varying parameter, and the partial differential equation based analysis for delayed systems.

Keywords:Delay systems, Time-varying systems, Stability of linear systems Abstract: We provide new sequential predictors for a large class of linear time-varying systems that contain constant delays in the vector fields and also constant delays in the inputs. We allow the input delays to be arbitrarily large. We prove global exponential stability of the origin for an augmented system that includes the original system in closed loop with our sequential predictors based feedback control. This improves on prior sequential predictor results for systems with input delays that did not allow delays in the vector fields. We illustrate our new theorem in an example from identification theory.

Keywords:Linear systems, LMIs, Uncertain systems Abstract: This paper deals with the design of a system, defined as the interconnection of identical LTI subsystems, whose frequency-response is under modulus constraints. Based on the notions of LFT and dissipativity, we propose a method able to compute a solution by solving a linear minimisation problem under LMI constraints. This extends the usual approach by especially generalising the spectral factorisation technique from systems with state-space model to identical dissipative systems interconnection.

Keywords:Linear systems, Uncertain systems Abstract: For finite-dimensional continuous-time single-input and single-output linear time-invariant systems, we introduce the concept of extended zero dynamics and generalize the concept of minimum phase, which accommodates the presence of disturbance inputs. By representing a SISO LTI system with a finite relative degree in its extended zero dynamics canonical form, we obtain its extended zero dynamics, which is simply its zero dynamics (according to [1]) driven by the noiseless output of the system and the disturbance input. We then say a system is minimum phase if its extended zero dynamics is absent or satisfies that, for any bounded admissible initial condition, any bounded noiseless output, and any bounded admissible disturbance input waveform, the zero dynamics state trajectory is bounded. The system is minimum phase (according to this extended notion) if its zero dynamics is asymptotically stable. It is proved that the converse holds under the additional condition that the system be stabilizable from the control input. For a system to be minimum phase, it is necessary that the transfer function from the control input to the output has all zeros with negative real parts. The converse holds when the system is both controllable (from the control input) and observable. It is further shown that the generalized minimum phase property is necessary for model reference control that achieves 1) perfect tracking of any bounded reference trajectories with bounded derivatives up to certain order without any disturbances and 2) the existence of bounded state trajectory for any admissible bounded initial condition, any admissible bounded disturbance input waveform, and any bounded reference trajectory with bounded derivatives up to a certain order.

Keywords:Switched systems, Linear systems, Fault tolerant systems Abstract: We propose a state-dependent switching L2 gain for analyzing the fluctuations in transient response after an unpredictable switch between two linear time-invariant systems. Its value depends on the state of a pre-switch system at a switching time. Thus, it enables us to theoretically discuss the effects of the situation at a switching time on the fluctuations in transient responses after the switch. For example, its value distribution in the state space of a pre-switch system can be used for evaluating the dangerous extent of the situation at an occurrence time of a control device failure.

Keywords:Linear systems, Optimal control, LMIs Abstract: This paper presents static and dynamic parallel feedforward controller synthesis methods that render a linear time-invariant system minimum phase by augmenting its output. The system output is perturbed the least amount possible by minimizing the gain of the parallel feedforward controller while ensuring the augmented system is minimum phase. This is done by minimizing the maximum singular value of a static parallel feedforward controller or the weighted H-Infinity norm of a dynamic parallel feedforward controller. Static and dynamic parallel feedforward controllers are synthesized using direct and indirect methods that involve bilinear matrix inequality constraints and are solved iteratively using linear matrix inequalities. The direct method enforces a minimum gain constraint directly on the augmented system, while the indirect method solves for an asymptotically stabilizing negative feedback controller that is inverted to obtain the parallel feedforward controller. Numerical examples are provided to demonstrate the effectiveness of the proposed controller synthesis methods.

Keywords:Linear systems, Time-varying systems, Uncertain systems Abstract: In this paper, we propose a novel method, using the frameworks of differential inequalities and essentially nonnegative matrices, to construct hyper-rectangular over-approximations of reachable sets for a general class of linear uncertain systems whose nominal parameters and bounds on uncertainties are time-varying. The motivation of this paper is the need for relatively accurate yet computationally inexpensive over-approximation method that is practical in various control methods especially abstraction-based control synthesis. We demonstrate the proposed method in an illustrative example and two control examples related to abstraction-based control synthesis. In these examples, the proposed method shows excellent results in terms of representing reachable sets with reasonable accuracy and allowing the implementation of time-varying control input signals.

Keywords:Adaptive control, Linear systems Abstract: In this paper, a novel multiple-model based model reference adaptive control (MRAC) scheme is designed for discrete-time multivariable systems with uncertain actuation delays. Such an adaptive control scheme is capable of handling the structure uncertainties caused by uncertain actuation delays. A set of system structure uncertainty patterns is formed, and corresponding to each pattern, a reference model system is chosen. Multiple direct adaptive controllers are designed for the system under different structure uncertainties, based on different reference model systems. A control switching mechanism is designed with multiple modified performance indexes based on normalized estimation errors, which is desirable for selecting the most appropriate controller. The results shows an important step forward in employing the minimal amount of necessary prior knowledge to design a stable control scheme for a linear multivariable system.

Keywords:Uncertain systems, Constrained control, Optimal control Abstract: This paper presents a novel reference governor scheme capable of ensuring constraint satisfaction for discrete-time linear systems subject to parametric uncertainties. Given a pre-stabilized system, the proposed method generates a sequence of recursively feasible references that guarantee constraint enforcement by exploiting invariance properties. At each time step, it is shown that the next reference can be computed in closed-form by solving a set of simple second order inequalities. Parametric uncertainties are then addressed by either computing a quadratic common Lyapunov function or using suitable bounds on the parameter-dependent Lyapunov function. The efficiency of the method is illustrated by means of numerical examples.

Keywords:Biotechnology, Process Control, Uncertain systems Abstract: The problem of state estimation for microalgae growth processes in batch cultures based on an extended Droop model is addressed. Sufficient conditions for local strong observability are derived within an unknown input framework considering a biased optical density (OD) measurement and a (non-biased) substrate measurement. To account for discrete-time measurements with different sampling rates a continuous-discrete extended Kalman Filter is designed and tested as well as within numerical simulations as also with experimental data for Haematococcus pluvialis.

Keywords:Uncertain systems, Autonomous vehicles, Modeling Abstract: For robots to effectively navigate in the presence of humans, they must safely leverage the human's perceived unwillingness to collide. Drawing on Viability Theory, we propose a novel approach to robustly anticipate human collision-avoiding behavior. We assume that rational humans try to optimally control their motion to avoid collision, but they are also prone to error, which makes their behavior suboptimal. We offer a robust control model which varies the level of optimality expected over time, assuming that humans may act very unpredictably for a brief period of time, but their actions approach optimal collision-avoiding behavior as time progresses. We show how the proposed model can be used to produce a set of initial states for which a rational human will avoid collision. Further, we produce a robust policy which characterizes the set of control inputs expected by the human at any state. We illustrate our approach using two representative scenarios.

Keywords:Uncertain systems, Predictive control for nonlinear systems Abstract: This paper presents a computationally efficient method for performance verification and tuning of model-based controllers in constrained nonlinear systems subject to probabilistic uncertainties with arbitrary distributions. The proposed method is based on an extension of generalized polynomial chaos, an asymptotically convergent spectral method for uncertainty propagation, to directly handle arbitrary uncertainty distributions. The proposed arbitrary polynomial chaos (aPC) method only requires knowledge of the statistical moments of the distribution, and is capable of estimating the aPC expansion coefficients using a minimal number of closed-loop simulations. Advantages of the proposed aPC method are demonstrated on a benchmark continuous reactor problem controlled by a scenario-based nonlinear model predictive controller.

Keywords:Uncertain systems, Flight control, Autonomous systems Abstract: This paper presents a novel application of mu-synthesis design for nonlinear control of fixed-wing UAVs with unstructured, time-varying uncertainties during flight. The nominal/uncertain plant approach is utilized, with additive uncertainty weighting functions incorporating the information for the respective unknown parameters with time-varying structure. The proposed controller design framework is tested and validated through simulation for a circulation control based UAV, which has inherent time-varying aerodynamic characteristics due to lift enhancement. The proposed methodology is not limited to aerodynamic uncertainties only; it can be generalized for navigation and control of UAVs with changing mass, inertia properties and airfoil characteristics with an appropriate modification of the upper/lower bounds used for the derivation of the additive uncertainty weighting functions.

Keywords:Predictive control for linear systems, Optimal control, Uncertain systems Abstract: This paper proposes an Adaptive Learning Model Predictive Control strategy for uncertain constrained linear systems performing iterative tasks. The additive uncertainty is modeled as the sum of a bounded process noise and an unknown constant offset. As new data becomes available, the proposed algorithm iteratively adapts the believed domain of the unknown offset after each iteration. An MPC strategy robust to all feasible offsets is employed in order to guarantee recursive feasibility. We show that the adaptation of the feasible offset domain reduces conservatism of the proposed strategy compared to classical robust MPC strategies. As a result, the controller performance improves. Performance is measured in terms of following trajectories with lower associated costs at each iteration. Numerical simulations highlight the main advantages of the proposed approach.

Keywords:Networked control systems, Fault detection, LMIs Abstract: This paper considers fault detection and isolation in a distributed setting with agents under consensus dynamics. The distributed fault detection and isolation problem is introduced along with system models to represent nominal and faulty conditions. It is shown that the proportional-integral observer (PIO) effectively estimates the fault signal in an agent and that it can be used for residual generation and fault isolation. The conditions under which fault isolation is achievable are derived as a function of the distributed topology of the agents in the network. An LMI is derived that can be used to conveniently obtain the residual generator gains. The distributed PIO design approach is illustrated with an example.

Keywords:Fault diagnosis, Fault accomodation, Adaptive systems Abstract: This paper presents an adaptive sensor fault diagnosis and accommodation scheme for multiple sensor bias faults for a class of input-output nonlinear systems subject to modeling uncertainty and measurement noise. The proposed scheme consists of a nonlinear estimation model that includes an adaptive component which is initiated upon the detection of a fault, in order to approximate the magnitude of the bias faults. A detectability condition characterizing the class of detectable sensor bias faults is derived and the robustness and stability properties of the adaptive scheme are presented. The estimation of the magnitude of the sensor bias faults allows the identification of the faulty sensors and it is also used for fault accommodation purposes. The effectiveness of the proposed scheme is demonstrated through a simulation example.

Keywords:Fault diagnosis, Fault detection, Stochastic optimal control Abstract: The paper deals with the problem of active fault diagnosis with deferred decisions for a discrete time stochastic system described using multiple-model framework. The emphasis is placed on reliability of decisions over an infinite time horizon and the admissible lag of a deferred decision is known in advance. The design of the active fault detector with deferred decisions is formulated as a functional optimization problem that is solved hierarchically due to the deferring of decisions. At the top level, the infinite time horizon problem is split into an initial finite time horizon and a terminal infinite time horizon problems that are interconnected at their boundary. The infinite time horizon problem is solved first by using a reformulation to perfect state information problem and subsequent use of approximate dynamic programming. The proposed active fault detector with deferred decisions is illustrated using a numerical example.

Keywords:Fault tolerant systems, Uncertain systems, Automotive systems Abstract: The main contribution of this paper is an integrated design of robust fault estimation (FE) and fault accommodation (FA), applied to uncertain linear time invariant (LTI) systems. In this design, the robust H-infinity proportional-integral (PI) observer allows a precise estimation of actuator fault by dealing with system disturbances and uncertainties, while the feed-back controller compensates the actuator fault, and therefore assuring the closed-loop stability. Thanks to the application of majoration and Young inequalities, the observer-controller decoupling problem is solved and both above objectives are combined into only one linear matrix inequalities (LMI) allowing a simultaneous solution for both observer and controller. Finally, an example of vehicle suspension system is illustrated to highlight the performance of the proposed method.

Keywords:Fault tolerant systems, Energy systems, Optimization Abstract: In this paper, we present a novel active fault-adaptive control (FAC) methodology for wind turbines, which minimizes the economic cost of turbines by achieving two broad objectives: power maximization and fatigue reduction possibly under the effect of bias faults in converters. The proposed FAC system is composed of two modules: a fault diagnosis subsystem and controller redesign subsystem. The latter module is synthesized using a model-predictive control (MPC) scheme in which the constraints set of the decision variables is not naturally convex. A major contribution of the paper is the reformulation of the non-convex optimization problem into a convex problem through some new decision variables. The fault diagnosis algorithm is built upon an unknown-input-residual generator and a specifically designed filter which extracts the complete information of the fault. This fault information is subsequently used to update in real-time the constraints of the MPC thereby ensuring automatic adaptation of the control law to the new operating mode. The effectiveness of the developed scheme is demonstrated on a 2MW wind turbine system.

Keywords:Network analysis and control, Fault detection, Algebraic/geometric methods Abstract: In this paper we propose a necessary and sufficient graphical condition for fault detection in structured affine systems where only the sparsity structure of system and fault matrices are known. The fault detection for such systems enables one to distinguish between the outputs of a nominal model and a faulty model within T time-steps. The resulting graphical condition involves checking for the existence of certain walks between pairs of vertices. Subsequently, we provide a simple algorithm to check for this condition and illustrate it via an example.

Keywords:Kalman filtering, Filtering, Estimation Abstract: In this paper, we discover that the trace of the division of the optimal output estimation error covariance over the noise covariance attained by the Kalman-Bucy filter can be explicitly expressed in terms of the plant dynamics and noise statistics in a frequency-domain integral characterization. Towards this end, we examine the algebraic Riccati equation associated with Kalman-Bucy filtering using analytic function theory and relate it to the Bode integral. Our approach features an alternative, frequency-domain framework for analyzing algebraic Riccati equations and reduces to various existing related results.

Keywords:Kalman filtering, Filtering, Estimation Abstract: It is well known that the Kalman filter is globally optimal for linear time-invariant systems excited with white Gaussian noise along the process and measurement channels. However, its application to practical situations is often suboptimal because the noise covariance matrices typically are not accurately known. This paper presents a new covariance matching Kalman filter (CMKF) algorithm which estimates the measurement (R) or the process (Q) noise covariance matrix in addition to the state. The convergence of the filter for estimating Q or R matrices respectively is proved for discrete stochastic linear time-invariant systems under relatively mild conditions of observability.

Keywords:Kalman filtering, Networked control systems, Sensor networks Abstract: In this paper, we investigate a distributed robust state estimation problem for linear Gaussian systems measured by a sensor network, where the sensors can communicate only with their neighbors and each sensor runs a local filter to estimate the state of the process based on the measurements from its neighbors. We present a distributed risk-sensitive filtering algorithm, where the high-gain dynamic consensus filter is utilized to compute the fused measurement data and the fused covariance-inverse matrices, based on which, the local filter is updated in a Riccati-based linear recursive form. We show that the proposed distributed filtering algorithm is a risk-sensitive generalization of the distributed Kalman filter with dynamic consensus data fusion and the former reduces to the latter if the risk-sensitive parameter is chosen to be zero. For linear time-invariant systems, the asymptotic stability of local estimators in the proposed distributed risk-sensitive filtering algorithm is guaranteed if the value of the risk-sensitive parameter is chosen such that the centralized risk-sensitive filter is asymptotically stable. The robustness of the proposed risk-sensitive filtering algorithm to system uncertainty is verified by simulation results.

Keywords:Kalman filtering, Networked control systems, Estimation Abstract: In this paper, we consider Denial-of-service attacks against remote state estimation. A sensor measures the state of a discrete-time linear process, and sends data packets to a router via a fading channel. The router then forwards data packets to a remote estimator via another fading channel. Due to the capability limitation, a malicious attacker can generate noises to degenerate the performance of at most one fading channel at each time step. The aim of the attacker is to jeopardize the estimation quality of the remote estimator. We first formulate the problem as a Markov decision process (MDP), and then prove the existence of the optimal stationary and deterministic policy of the attacker. It is shown that the optimal policy has a switching-curve structure, which is beneficial for offline computation and online implementation. Simulation examples are provided to demonstrate the result.

Keywords:Kalman filtering, Estimation, Linear systems Abstract: Measurements made on a practical system can often be subject to outliers due to sensor errors, changes in ambient environment, data loss or malicious cyber attacks. The outliers can seriously reduce the accuracy of the Kalman filter (KF) when it is applied for state estimation. This paper proposes an innovation saturation mechanism to robustify the standard KF against outliers. The basic notion is to saturate an innovation when it is distorted by an outlier, thus preventing it from impairing the state estimation process. The mechanism presents an adaptive adjustment of the saturation bound. The design is performed for both continuous- and discrete-time systems, provably leading to bounded-error estimation given bounded outliers. Numerical simulation further shows the efficacy of the proposed design. Compared to many existing methods, the proposed design is computationally efficient and amenable to practical implementation, and also requires neither measurement redundancy nor extensive manual tuning.

Keywords:Kalman filtering, Estimation, Linear systems Abstract: This paper presents a new zonotopic constrained approach for the Kalman filter that takes advantage of the particular structure of the original optimization problem. This technique consists in projecting the state estimation by solving an optimization problem, to ensure that the estimated state belongs to a zonotope. Based on a classical gradient algorithm method, i.e. the iterative shrinkage-thresholding algorithm (ISTA), this paper proposes a reduced complexity approach suitable for the state estimation of systems subject to a large number of state constraints. The algorithm's speed is improved via a faster ISTA approach, called FISTA.

Keywords:Nonlinear systems identification, Identification for control, Identification Abstract: The modal decomposition based on the spectra of the Koopman operator has gained much attention in various areas such as data science and optimal control, and dynamic mode decomposition (DMD) has been known as a data-driven method for this purpose. However, there is a fundamental limitation in DMD and most of its variants; these methods are based on the premise that the target system is time-invariant at least within the data at hand. In this work, we aim to compute DMD on time-varying dynamical systems. To this end, we propose a probabilistic model that has factorially switching dynamic modes. In the proposed model, which is based on probabilistic DMD, observation at each time is expressed using a subset of dynamic modes, and the activation of the dynamic modes varies over time. We present an approximate inference method using expectation propagation and demonstrate the modeling capability of the proposed method with numerical examples of temporally-local events and transient phenomena.

Keywords:Predictive control for nonlinear systems, Fluid flow systems Abstract: The Koopman operator theory is an increasingly popular formalism of dynamical systems theory which enables analysis and prediction of the state space dynamics from measurement data. Building on the recent development of the Koopman model predictive control framework [14], we propose a methodology for closed-loop feedback control of nonlinear partial differential equations in a fully data-driven and model-free manner. In the first step, we compute a Koopman-linear representation of the system using a variation of the extended dynamic mode decomposition algorithm and then we apply the model predictive control to the constructed linear model. Our methodology is also capable of utilizing sparse measurements by incorporating delay-embedding of the available data into the identification and control processes. We illustrate the application of this methodology for the periodic Burgers' equation and the boundary control of a cavity flow governed by the Navier-Stokes equations in two spatial dimensions.

Keywords:Identification for control, Machine learning, Predictive control for nonlinear systems Abstract: Conserved quantities, i.e. constants of motion, are critical for characterizing many dynamical systems in science and engineering. These quantities are related to underlying symmetries and they provide fundamental knowledge about physical laws, describe the evolution of the system, and enable system reduction. In this work, we formulate a data-driven architecture for discovering conserved quantities based on Koopman theory. The Koopman operator has emerged as a principled linear embedding of nonlinear dynamics, and its eigenfunctions establish intrinsic coordinates along which the dynamics behave linearly. Interestingly, eigenfunctions of the Koopman operator associated with vanishing eigenvalues correspond to conserved quantities of the underlying system. In this paper, we show that these invariants may be identified with data-driven regression and power series expansions, based on the infinitesimal generator of the Koopman operator. We further establish a connection between the Koopman framework, conserved quantities, and the Lie-Poisson bracket. This data-driven method for discovering conserved quantities is demonstrated on the three-dimensional rigid body equations, where we simultaneously discover the total energy and angular momentum and use these intrinsic coordinates to develop a model predictive controller to track a given reference value.

Keywords:Algebraic/geometric methods, Linear systems, Reduced order modeling Abstract: In this paper, we point out and study a connection between the recently flourishing consideration of Koopman operators and classical systems theoretic concepts such as aggregation and observability decompositions of nonlinear systems. The exploration of this newly unveiled cross-connection promotes a cross-fertilization of different methodologies and ideas intrinsic to the two different frameworks, resulting in a deeper understanding of both domains. In particular, the insights established in the paper connect intuitive systems theoretic viewpoints with the framework of Koopman operators.

Keywords:Estimation, Stochastic systems, Optimization Abstract: Dynamical systems described by ordinary and stochastic differential equations can be analyzed through the eigen-decomposition of the Perron-Frobenius (PF) and Koopman transfer operators. While the Koopman operator may be approximated by data-driven techniques, e.g., Extended Dynamic Mode Decomposition (EDMD), the approximation of the PF operator uses a single-pass Monte Carlo approach in Ulam's method, which requires a sufficiently long time step. This paper proposes a finite-dimensional approximation technique for the PF operator that uses multi-pass Monte Carlo data to pose and solve a constrained EDMD-like least-squares problem to approximate the PF operator on a finite-dimensional basis. The basis functions used to project the PF operator are the characteristic functions of the state-space partitions. The results are analyzed theoretically and illustrated using deterministic and time-homogeneous stochastic systems.

Keywords:Feedback linearization, Optimal control, Stability of nonlinear systems Abstract: In this paper, we provide a systematic approach for the design of stabilizing feedback controllers for nonlinear control systems using the Koopman operator framework. The Koopman operator approach provides a linear representation for a nonlinear dynamical system and a bilinear representation for a nonlinear control system. The problem of feedback stabilization of a nonlinear control system is then transformed to the stabilization of a bilinear control system. We propose a control Lyapunov function (CLF)-based approach for the design of stabilizing feedback controllers for the bilinear system. The search for finding a CLF for the bilinear control system is formulated as a convex optimization problem. This leads to a schematic procedure for designing CLF-based stabilizing feedback controllers for the bilinear system and hence the original nonlinear system. Another advantage of the proposed controller design approach outlined in this paper is that it does not require explicit knowledge of system dynamics. In particular, the bilinear representation of a nonlinear control system in the Koopman eigenfunction space can be obtained from time-series data. Simulation results are presented to verify the main results on the design of stabilizing feedback controllers and the data-driven aspect of the proposed approach.

Keywords:Switched systems, Robust control, LMIs Abstract: We derive novel criteria for robust stability and output-feedback gain-scheduling controller synthesis for a class of switched systems that are affected by piecewise constant parameters with dwell-time constraints. Our findings are based on clock-dependent Lyapunov arguments and rely, in contrast to other approaches, on separation techniques from robust control involving dynamic multipliers. The obtained conditions are expressed as infinite-dimensional LMIs which can be solved by, e.g., using sum-of-squares relaxation methods. We illustrate our results by means of a numerical example.

Keywords:Switched systems, LMIs, Linear systems Abstract: The notion of path-complete p-dominance for switching linear systems (in short, path-dominance) is introduced as a way to generalize the notion of dominant/slow modes for LTI systems. Path-dominance is characterized by the contraction property of a set of quadratics cones in the state space. We show that path-dominant systems have a low-dimensional dominant behavior, and hence allow for a simplified analysis of their dynamics. An algorithm for deciding the path-dominance of a given system is presented.

Keywords:Switched systems, Stability of hybrid systems Abstract: In this paper, controllers are designed for stabilizing state-based switching bilinear systems. The controller is designed based on the special features of bilinear systems comparing with linear systems, and is carried out through three steps: first, deriving the state-based switching linear system corresponding to the switching bilinear system; then, state-feedback controllers are designed to asymptotically stabilize the corresponding switching linear system; finally, stabilizing controllers are obtained for the original system, the switching bilinear system. The stability of the controller is proved step by step through the decreasing of the overall Lyapunov function.

Keywords:Time-varying systems, Switched systems, Stability of nonlinear systems Abstract: In this paper, we apply a total variation approach to bridge the stability criteria for nonlinear time-varying systems and nonlinear switched systems. In particular, we derive a set of stability conditions applying to both nonlinear time-varying systems and nonlinear switched systems. We show that the derived stability conditions, when applied to nonlinear time-varying systems and nonlinear switched systems, recover the existing stability results in the literature. We also show that the derived stability conditions can be applied to qualitatively recover a unified stability criterion for slowly time-varying linear systems and switched linear systems proposed in our recent work.

Keywords:Adaptive control, Switched systems, Uncertain systems Abstract: This paper introduces a new switched adaptive control mechanism that can cope with parametric uncertainty while using discrete and saturated actuators. Control of air handling units (AHUs), where air and water supply have discrete and saturated characteristics, is the motivational drive behind this work. We show that the cheap actuation and low computational requirements of building automation installations can be met after recasting the AHU thermal dynamics as a switched linear system with discrete working modes. Adaptive laws with anti-windup compensation and a switching law based on dwell time are introduced to cope with the uncertainties and input constraints of the switched linear system. Tracking performance is shown analytically and demonstrated via a numerical test case.

Keywords:Lyapunov methods, Switched systems, Stability of nonlinear systems Abstract: Functional electrical stimulation (FES) can be combined with a motorized cycle to offer various rehabilitation options for individuals with neurological conditions. Typically, FES cycling controllers use cooperating muscles and an electric motor to track cadence. In this paper, in addition to cooperative cadence tracking, the motorized cycle tracks an admittance trajectory generated using torque feedback. This method allows the cycle to deviate from the desired cadence trajectory and admit to the rider-applied torque, ensuring safe human-machine interaction. Two sets of uncertain, nonlinear dynamics are presented, one for the human rider and one for the robot, linked by a common measurable interaction torque. After developing cadence and admittance controllers, a Lyapunov-like switched system stability analysis is provided to prove global exponential tracking of the cadence error system, and a passivity analysis is conducted to prove passivity of the cycle’s admittance controller with respect to the rider’s interaction torque.

Keywords:Energy systems, Machine learning, Neural networks Abstract: A novel multivariate deep causal network model (MDCN) is proposed in this paper, which combines the theory of conditional variance and deep neural networks to identify the cause-effect relationship between different interdependent time-series. The MCDN validation is conducted by a double step approach. The self validation is performed by information theory-based metrics, and the cross validation is achieved by a foresting application that combines the actual interdependent electricity, transportation, and weather datasets in the City of Tallahassee, Florida, USA.

Keywords:Energy systems, Identification, Optimization Abstract: Advanced battery management systems rely on dynamical models in order to provide safe and profitable battery operations. Such models need to be suitable for control and estimation purposes while, at the same time, as accurate as possible. This feature can be satisfied only if model parameters are accurately estimated. In this work we investigate the design of optimal experiments in order to minimize the uncertainty of the parameters of the Single Particle Model in the context of Lithium-ion battery. Simulation results show the effectiveness of the proposed methodology when compared with standard current profiles (e.g. constant current).

Keywords:Energy systems, Smart grid, Transportation networks Abstract: We study the decision problem faced by a Charging Network Operator (CNO) that owns a network of Electric Vehicle (EV) public charging stations and offers a menu of differentiated services to its users. Specifically, we design optimal pricing and routing schemes for the setting where users cannot directly choose which station they can charge their vehicle at. Instead, they choose their priority level and energy request amount from the menu, and then the CNO directly assigns them to a station nearby. In designing our optimal pricing-routing policies, we consider the heterogeneity of the stations’ locations, electricity prices, and capacity, as well as the heterogeneity of users' values of time and energy requests. We design prices that incentivize users to reveal their true preferences to the CNO, as well as optimal routing schemes to allocate them to charging stations, under the scenario where the CNO is a social welfare maximizing entity.

Keywords:Energy systems, Smart grid, Game theory Abstract: We consider the problem of selling renewable electricity in a two-stage market to a number of load serving entities (LSEs). Since the generation is random, the renewable generator promises to pay a penalty, which is linear in the shortfall, to each LSE. We derive allocation and pricing rules that induce all load serving entities to truthfully bid their willingness to pay per unit of electricity in dominant strategies.

Keywords:Energy systems, Stability of nonlinear systems, Uncertain systems Abstract: In this paper we propose a procedure for estimating the region in which a controller robustly stabilizes a system which is subject to affine parametric uncertainty by applying transverse contraction-based stability tools. The method consists of an optimization problem in which transverse contraction conditions are verified via sum-of-squares programs. The optimization approach can be used either to maximize the bounds on the allowable parameter uncertainty or to maximize the size of the region of contraction (ROC) given a fixed level of uncertainty. In a case study we apply the procedure to an Airborne Wind Energy system where the flight path of a power generating kite is controlled by a linear quadratic regulator based on a model which is prone to large parametric uncertainties. We consider periodic trajectories of the stabilized kite system and transform the dynamics into transversal coordinates for simplification of the controller design and reduction of the computational cost. The numerical results of the proposed optimization show that uncertainty in the steering gain parameter decreases the size of the ROC while uncertainty in wind speed or line length within the considered range of operating conditions does not affect the size of the robust ROC.

Keywords:Modeling, Energy systems, Large-scale systems Abstract: A significant portion of electricity consumed worldwide is used to power thermostatically controlled loads (TCLs) such as air conditioners, refrigerators, and water heaters. Because the short-term timing of operation of such systems is inconsequential as long as their long-run average power consumption is maintained, they are increasingly used in demand response (DR) programs to balance supply and demand on the power grid. Here, we use the phase model representation of TCLs to design and evaluate control policies for modulating the power consumption of aggregated loads with parameter heterogeneity and stochastic drift. In particular, we design a phase model based minimum energy control law that modulates the duty cycle of a TCL in order to reduce its energy consumption. We further demonstrate that the designed control policy can be used to effectively modulate the aggregate power of a heterogeneous TCL population while maintaining load diversity and minimizing power overshoots. More importantly, an acceptable quality of service for the utility customers is maintained. The developed control policy can be used to compensate for the intermittent generation by renewable energy sources (RESs) such as wind and solar by regulating the aggregated load of a TCL ensemble, and hence will facilitate the broader integration of RESs.

Keywords:Optimization algorithms, Linear systems, Distributed control Abstract: We consider the problem of optimal sensor selection in large-scale dynamical systems. To address the combinatorial aspect of this problem, we use a suitable convex surrogate for complexity. The resulting non-convex optimization problem fits nicely into a sparsity-promoting framework for the selection of sensors in order to gracefully degrade performance relative to the optimal Kalman filter that uses all available sensors. Furthermore, a standard change of variables can be used to cast this problem as a semidefinite program (SDP). For large-scale problems, we propose a customized proximal gradient method that scales better than standard SDP solvers. While structural features complicate the use of the proximal Newton method, we investigate alternative second-order extensions using the forward-backward quasi-Newton method.

Keywords:Optimization algorithms, Optimization, Large-scale systems Abstract: In this paper we consider a distributed convex optimization problem over time-varying networks. We propose a dual method that converges R-linearly to the optimal point given that the agents’ objective functions are strongly convex and have Lipschitz continuous gradients. The proposed method requires half the amount of variable exchanges per iteration than methods based on DIGing, and yields improved practical performance as empirically demonstrated.

Univ. of New South Wales at the AustralianDefenceForceAcad

Keywords:Flexible structures, Optimization, Linear systems Abstract: Negative imaginary (NI) systems theory has attracted considerable attention in the area of robust control of highly resonant flexible structures systems. These systems, often naturally, satisfy the NI property. In this paper, we present a control synthesis methodology for NI systems based on nonlinear optimization techniques. In the presented method, a parametrized library of strictly negative imaginary (SNI) controllers is created and used in a standard numerical non-linear optimization setup. The SNI controller library contains generic controllers that are widely used in the control highly resonant flexible structures such as positive position feedback (PPF) and integral resonant control (IRC). Sequential quadratic programming (SQP) techniques are used in the numerical optimization problem. The synthesized controller satisfies the SNI property as well as optimizing H_2 performance. As an application of these results, an example of controlling an Euler-Bernoulli beam with piezo-electric actuator and sensor is presented.

Keywords:Optimization algorithms, Lyapunov methods, Power systems Abstract: The recent large-scale penetration of renewable energy in power networks has also introduced with it a risk of random variability. This new source of power uncertainty can fluctuate so substantially that the traditional base-point forecast and control scheme may fail to work. To address this challenge, we study the so-called robust AC optimal power flow (AC-OPF) so as to provide robust control solutions that can immunize the power system against the intermittent renewables.

In this paper we generalize the continuous-time primal-dual gradient dynamics approach to solve the robust AC-OPF. One advantage of the proposed approach is that it does not require any convexity assumptions for the decision variables during the dynamical evolution. This paper first derives a stability analysis for the primal-dual dynamics associated with a generic robust optimization, and then applies the primal-dual dynamics to the robust AC-OPF problem. Simulation results are also provided to demonstrate the effectiveness of the proposed approach.

Keywords:Optimization algorithms, Stochastic systems, Hybrid systems Abstract: This paper presents a class of stochastic dynamical systems designed to solve non-convex optimization problems on smooth manifolds. In order to guarantee convergence with probability one to the set of global minimizers of the cost function, the proposed dynamics combine continuous-time flows, characterized by a differential equation, and discrete- time jumps, characterized by a stochastic difference inclusion. By using the framework of stochastic hybrid inclusions, we provide a detailed stability characterization of the dynamics, as well as a simple extension to address learning problems in games defined on manifolds. Our results are illustrated by a numerical example in the setting of a weighted non-cooperative potential game defined on the torus.

Keywords:Optimization algorithms, Network analysis and control, Machine learning Abstract: We propose a new class-optimal algorithm for the distributed computation of Wasserstein Barycenters over networks. Assuming that each node in a graph has a probability distribution, we prove that every node can reach the barycenter of all distributions held in the network by using local interactions compliant with the topology of the graph. We provide an estimate for the minimum number of communication rounds required for the proposed method to achieve arbitrary relative precision both in the optimality of the solution and the consensus among all agents for undirected fixed networks.

Keywords:LMIs, Distributed parameter systems Abstract: Boundary feedback control design for a system of n 1-D linear conservation laws is studied. Sufficient conditions in the form of Lyapunov-like functional inequalities are given to certify the existence of a bound on the L2 (spatial) norm of the state with respect to energy bounded measurement noise. Semidefinite programming techniques are adopted to devise a systematic design algorithm. The effectiveness of the approach is shown in a numerical example.

Keywords:LMIs, Observers for nonlinear systems, Numerical algorithms Abstract: This paper deals with nonlinear observer design for a class of nonlinear systems with nonlinear output measurements. The proposed methodology uses Linear Matrix Inequalities~(LMIs) to handle the problem of mathcal{W}^{1,2}-Convergence criterion. Some new assumptions and recent convenient Young's formulation are used to get less conservative LMI conditions compared to the literature. Indeed, the obtained LMIs contain additional decision variables, which render the conditions more general. In addition, the class of systems studied in this paper is more general than those available in the literature in the same context.

Keywords:Compartmental and Positive systems, LMIs Abstract: This paper proposes two iterative algorithms for solving static output feedback stabilization problem for LTI multi-input multi-output systems. Contrary to the existing literature, in this paper, no restrictive assumption has been made on the state-space description of the open-loop plant for which a static output feedback controller is to be designed to synthesize a stable internally positive system in closed-loop. Algorithm 1 involves the cone complementarity linearization technique to overcome the underlying difficulties of BMI problem, whereas the success of Algorithm 2 depends on a scalar search associated with a positive definite matrix obtained as the stabilizing solution of a Riccati equation. Numerical examples show that, in some cases where the existing algorithms fail, the proposed algorithms can find a static output feedback stabilizing controller ensuring the positive system properties.

Keywords:Delay systems, Stochastic systems, LMIs Abstract: Stochastic LTI system is considered with a delay term described by Stieltjes integral. This includes systems with discrete or distributed delays. Two Lyapunov-based methods for the asymptotic mean square stability are presented that lead to sufficient conditions in the form of linear matrix inequalities (LMIs). The first one employs neutral type model transformation and augmented Lyapunov functionals. Differently from the existing LMI stability conditions based on neutral type transformation, the proposed conditions do not require the stability of the corresponding integral equations. Moreover, it is shown that in the existing LMI stability conditions based on simple (non-augmented) Lyapunov functionals, the stability analysis of the integral equation can be omitted. The second method is based on a stochastic extension of simple Lyapunov functionals depending on the state derivative. Numerical examples give comparison of results via different methods.

Keywords:Constrained control, Uncertain systems, LMIs Abstract: This paper proposes an algorithm to find a robust control invariant (RCI) set of desired complexity and the associated linear, state-feedback control law. The candidate RCI set is restricted to be symmetric around the origin. The algorithm is applicable to rational parameter dependent systems with bounded additive disturbance. The system constraints are framed as simple affine inequalities whereas the invariance condition as a set of sufficient LMI conditions. The proposed iterative algorithm is guaranteed to be recursively feasible and converge to some stationary point.

Keywords:Distributed parameter systems, Lyapunov methods, LMIs Abstract: This article deals with the stability analysis of a drilling system which is modelled as a coupled ordinary differential equation / string equation. The string is damped at the two boundaries but leading to a stable open-loop system. The aim is to derive a linear matrix inequality ensuring the exponential stability with a guaranteed decay-rate of this interconnected system. A strictly proper dynamic controller based on boundary measurements is proposed to accelerate the system dynamics and its effects are investigated through the stability theorem and simulations. It results in an efficient finite dimension controller which subsequently improves the system performances.

Keywords:MEMs and Nano systems, Mechatronics, Control applications Abstract: We introduce an algorithm to identify the nonlinear dynamics of a class of smart micropositioning systems, which is modeled as a Hammerstein system, that is, a cascade of a generalized Prandtl-Ishlinskii (GPI) hysteresis nonlinearity with a linear dynamic system. The GPI hysteresis nonlinearity, the linear dynamic system, and the intermediate signal between them are assumed to be unknown. The first stage in the algorithm is to identify the linear dynamic plant from measurements of the input and output of the Hammerstein system. Then, the unknown intermediate signal is reconstructed using the output and the identified model of the linear system. Finally, the GPI nonlinearity is estimated using the input and the reconstructed intermediate signal.

Keywords:Quantum information and control, Lyapunov methods, Stochastic systems Abstract: This article provides a novel continuous-time state feedback control strategy to stabilize an eigenstate of the Hermitian measurement operator of a two-level quantum system. In open loop, such system converges stochastically to one of the eigenstates of the measurement operator. Previous work has proposed state feedback that destabilizes the undesired eigenstates and relies on a probabilistic analysis to prove convergence. In contrast, we here associate the state observer to an adaptive version of so-called Markovian feedback (essentially, proportional control) and we show that this leads to a global exponential convergence property with a strict Lyapunov function. Furthermore, besides the instantaneous measurement output, our controller only depends on the single coordinate along the measurement axis, which opens the way to replacing the full state observer by lower-complexity filters in the future.

Keywords:Quantum information and control, Observers for Linear systems, Estimation Abstract: We give an explicit construction for a quantum observer coherently replicating the dynamics of a cavity mode system, without any disturbance of the system’s dynamics. This gives the exact analogue of the Luenberger observer used in controller design in engineering.

CNRS, Laboratoire Des Signaux Et Systèmes, Supélec

Keywords:Quantum information and control, Lyapunov methods, Stochastic systems Abstract: In this paper, we study the stabilization problem of quantum spin-1/2 systems under continuous-time measurements. In the case without feedback, we show exponential stabilization around the excited and ground state by providing a lower bound of the convergence rate. Based on stochastic Lyapunov techniques, we propose a parametrized measurement-based feedback which ensures exponential convergence toward the excited state. Moreover, we give a lower bound of the convergence rate for this case. Then, we discuss the effect of each parameter appeared in the control law in the convergence rate. Finally, we illustrate the efficiency of such feedback law through simulations.

Keywords:Quantum information and control, Robust control, Control of networks Abstract: Quantum spin networks form a generic system to describe a range of quantum devices for quantum information processing and sensing applications. Understanding how to control them is essential to achieve devices with practical functionalities. Energy landscape shaping is a novel control paradigm to achieve selective transfer of excitations in a spin network with surprisingly strong robustness towards uncertainties in the Hamiltonians. Here we study the effect of decoherence, specifically generic pure dephasing, on the robustness of these controllers. Results indicate that while the effectiveness of the controllers is reduced by decoherence, certain controllers remain sufficiently effective, indicating potential to find highly effective controllers without exact knowledge of the decoherence processes.

Keywords:Quantum information and control, Model/Controller reduction, Reduced order modeling Abstract: We provide model reduction formulas for open quantum systems consisting of a target component which weakly interacts with a strongly dissipative environment. The time-scale separation between the uncoupled dynamics and the interaction allows to employ tools from center manifold theory and geometric singular perturbation theory to eliminate the variables associated to the environment (adiabatic elimination) with high-order accuracy. An important specificity is to preserve the quantum structure: reduced dynamics in (positive) Lindblad form and coordinate mappings in Kraus form. We provide formulas of the reduced dynamics. The main contributions of this paper are (i) to show how the decomposition of the environment into K components enables its efficient treatment, avoiding the quantum curse of dimension; and (ii) to extend the results to the case where the target component is subject to Hamiltonian evolution at the fast time-scale. We apply our theory to a microwave superconducting quantum resonator subject to material losses, and we show that our reduced-order model can explain the transmission spectrum observed in a recent pump probe experiment.

Univ of Illinois, Urbana-Champaign and Khalifa University

Keywords:Sampled-data control, Uncertain systems, Fault diagnosis Abstract: This paper proposes a multirate output-feedback controller for multi-input multi-output (MIMO) systems, possibly with non-minimum-phase zeros, using the L1 adaptive control structure. The analysis of stability and robustness of the sampled-data controller reveals that under certain conditions the performance of a continuous-time reference system is uniformly recovered as the sampling time tends to zero. The controller is designed for detection and mitigation of actuator attacks. By considering a multirate formulation, stealthy zero-dynamics attacks become detectable. The experimental results from the flight test of a small quadtotor are provided. The tests show that the multirate L1 controller can effectively detect the zero dynamics actuator attack and recover the stability of the quadrotor.

Keywords:Sampled-data control, Optimal control, Robust control Abstract: This paper is concerned with the problem of minimizing the L_2 norm of the response to the worst-timing impulse input in linear time-invariant (LTI) sampled-data systems. Such a measure is recently introduced by the authors as an alternative to the two existing definitions of H_2 norm for LTI sampled-data systems, and it is also called the third H_2 norm of the systems. Taking into account of the linear periodically time-varying (LPTV) nature of LTI sampled-data systems, the third H_2 norm was defined as the supremum of the L_2 norms of all the tau-dependent outputs for the impulse inputs occurring at the instant tau on the sampling interval [0,h). A discretization approach to the continuous-time generalized plant has been developed through the lifting technique together with a gridding approximation method, by which the analysis problem of the third H_2 norm can be approximately reduced to that of the discrete-time H_2 norm. This approach allowed us to compute an upper bound and a lower bound of the third H_2 norm in an asymptotically exact fashion as the gridding parameter N tends to infty. However, it is unclear whether the discretization approach is valid also in the associated controller synthesis problem since the gap between the upper and lower bounds given for a fixed (finite) parameter N is dependent on the discrete-time controller. In this sense, this paper aims at establishing a theoretical validity of the discretization approach in the optimal controller synthesis problem by deriving an important inequality independent of the discrete-time controller. This inequality verifies that designing an optimal controller based on the discretization approach and letting the gridding approximation parameter N sufficiently large lead to a method of the optimal controller synthesis for minimizing the third H_2 norm of LTI sampled-data systems in the convergence rate of 1/N.

Keywords:Sampled-data control, Constrained control, Optimal control Abstract: In the context of continuous-time control systems, we address the problem of guaranteeing that the constraints imposed along the trajectory are in fact satisfied for all times. The problem is relevant and non-trivial in situations in which a continuous-time internal representation of the system is used with a digital device, such as in sampled-data model-based control, in an optimal control solver, or in sampled-data model predictive control. In this paper, we establish a condition that when verified on a finite set of time instants (using limited computational power) can guarantee that the trajectory constraints are satisfied on an uncountable set of times. The case of constrained optimal control problems is further explored here. We develop an algorithm for the numerical solution of constrained nonlinear optimal control problems that combines a guaranteed constraint satisfaction strategy with an adaptive mesh refinement strategy.

Keywords:Sampled-data control, Decentralized control Abstract: This paper deals with the stability analysis of decentralized sampled-data Linear Time Invariant (LTI) control systems with asynchronous sensors and actuators. We consider the case where each controller in the decentralized setting has its own sampling and actuation frequency which translates to asynchrony between sensors and actuators. The errors induced due to sampling and asynchronicity are modelled using two different operator approaches, leading to simple L2-stability criteria for the overall decentralized control system. The simplicity of the obtained criteria is illustrated by an example and simulation results exhibit the effectiveness of the approach.

Keywords:Sampled-data control, Constrained control, LMIs Abstract: This work proposes a new approach to asses stability of sampled-data controlled linear systems under aperiodic sampling and subject to input saturation. From an impulsive representation of the system and considering a partition of the interval between two successive sampling instants, it is shown that the discrete-time dynamics of the closed-loop system can be described by a difference inclusion. A general Lyapunov-based result allowing to conclude about the local stability of the sampled-data system is derived. Thus, considering the particular case of quadratic functions, a constructive condition in terms of linear matrix inequalities (LMIs) is proposed to compute estimates of the region of attraction of the nonlinear closed-loop system.

Keywords:Sampled-data control, Linear systems, Robust control Abstract: This paper studies the problem of reconstructing continuous-time signals from discrete-time uniformly sampled data. This signal reconstruction problem has been studied by the authors in various contexts, and led to a new signal processing paradigm. The key idea there is to employ a physically realizable signal generator model, and design an (sub)optimal filter via H-infinity optimal sampled-data control theory. The present paper aims at extending this framework to a more general setting where observed data are acquired through an acquisition device (prefilter) that has compact support. In this way, the framework can capture the properties of processing signals with a localized acquisition filter. We give a general setup as well as approximate solution methods along with their convergence results. A simulation is presented to illustrate some properties of the result.

Keywords:Control of networks, Linear systems, Network analysis and control Abstract: In this paper, we study the target controllability problem of networked dynamical systems, in which we are tasked to steer a subset of network states towards a desired objective. More specifically, we derive necessary and sufficient conditions for the structural target controllability problem of linear time-invariant (LTI) systems with symmetric state matrices, such as undirected dynamical networks with unknown link weights. To achieve our goal, we first characterize the generic rank of symmetrically structured matrices, as well as the modes of any numerical realization. Subsequently, we provide a graph-theoretic necessary and sufficient condition for the structural controllability of undirected networks with multiple control nodes. Finally, we derive a graph-theoretic necessary and sufficient condition for structural target controllability of undirected networks. Remarkably, apart from the standard reachability condition, only local topological information is needed for the verification of structural target controllability.

Keywords:Observers for Linear systems, Estimation, Fault detection Abstract: An unknown input observer provides perfect asymptotic tracking of the state of a system affected by unknown inputs. Such an observer exists (possibly requiring a delay in estimation) if and only if the system satisfies a property known as strong detectability. In this paper, we consider the problem of selecting (at design-time) a minimum cost subset of sensors from a given set in order to make a given system strongly detectable. We show that this problem is NP-hard even when the system is stable. Furthermore, we show that it is not possible to approximate the minimum cost within a factor of log(n) in polynomial-time (unless P=NP). However, we show that if a given system (with a selected set of sensors) is already strongly detectable, finding the smallest set of additional sensors to install in order to obtain a zero-delay observer can be done in polynomial time. Finally, we consider the problem of attacking a set of deployed sensors in order to remove the property of strong detectability. We show that finding the smallest number of sensors to remove is NP-hard.

Keywords:Optimization, Algebraic/geometric methods, Optimization algorithms Abstract: We investigate the joint actuator-sensor design problem for stochastic linear control systems. Specifically, we address the problem of identifying a pair of sensor and actuator which gives rise to the minimum expected value of a quadratic cost. It is well known that for the linear-quadratic-Gaussian (LQG) control problem, the optimal feedback control law can be obtained via the celebrated separation principle. Moreover, if the system is stabilizable and detectable, then the infinite-horizon time-averaged cost exists. But such a cost depends on the placements of the sensor and the actuator. We formulate in the paper the optimization problem about minimizing the time-averaged cost over admissible pairs of actuator and sensor under the constraint that their Euclidean norms are fixed. The problem is non-convex and is in general difficult to solve. We obtain in the paper a gradient descent algorithm (over the set of admissible pairs) which minimizes the time-averaged cost. Moreover, we show that the algorithm can lead to a unique local (and hence global) minimum point under certain special conditions.

Keywords:Algebraic/geometric methods, Linear systems, Control system architecture Abstract: Consider a linear time-invariant dynamical system. The well-known linear quadratic regulator (LQR) provides feedback controller that stabilizes the system while minimizing a quadratic cost function in the state of the system and the magnitude of the control. The optimal actuator design problem then consists of choosing an actuator that minimizes the cost incurred by an LQR. While this procedure guarantees a low overall cost incurred, it only takes into account the magnitude of the control signals the regulator sends to the actuator. Physical actuators are, however, also limited in their ability to follow rapid change in control signals. We show in this paper how to design actuators so that the high-frequency content of the control signals is limited, while insuring stability and optimality of the resulting closed-loop system.

Keywords:Control of networks, Network analysis and control, Large-scale systems Abstract: In this paper, we consider the problem of optimal actuator placement for networked linear time-invariant (LTI) systems with underlying undirected topologies. We aim to leverage the undirected topology for the design of an actuator deployment strategy that guarantees symmetric structural controllability, i.e. generic controllability of the system subject to symmetric weights. Naturally, the objective is to make this design as cost effective and computationally efficient as possible. Therefore, we focus on two related (yet different) problems: (i) to determine the subset of state nodes that need to be actuated to ensure symmetric structural controllability at the lowest cost incurred by the actuators; and (ii) given a symmetrically structurally controllable system (whose input nodes may actuate on more than one state node), to determine a subset of its input nodes that still ensure symmetric structural controllability, at the lowest possible cost. We show that both problems can be solved in polynomial time by implicitly providing an efficient algorithm that determines their solutions. Several numerical experiments are provided to illustrate our main results.

Keywords:Estimation, Kalman filtering, Optimization algorithms Abstract: Given a linear dynamical system affected by noise, we consider the problem of optimally placing sensors (at design-time) subject to certain budget constraints to minimize the trace of the steady-state error covariance of the Kalman filter. Previous work has shown that this problem is NP-hard in general. In this paper, we impose additional structure by considering systems whose dynamics are given by a stochastic matrix corresponding to an underlying consensus network. In the case when there is a single input at one of the nodes in a tree network, we provide an optimal strategy (computed in polynomial-time) to place the sensors over the network. However, we show that when the network has multiple inputs, the optimal sensor placement problem becomes NP-hard.

Keywords:Adaptive systems, Biomedical, Human-in-the-loop control Abstract: A multiparameter and deterministic extremum seeking (ES) algorithm is applied to tune Proportional-Integral-Derivative (PID) controllers for functional neuromuscular electrical stimulation (NMES). The proposed scheme controls the patient's arm such that the desired movements of flexion/extension for its elbow can be generated. The PID tuning using ES eliminates initial off-line tests with patients since the control gains are automatically computed in order to minimize a cost function according to the tracking error between the elbow's angle and the reference trajectory. Experiments with eight stroke patients show advances in terms of reduced root-mean-square error (RMSE) and improved ultimate responses when compared to the initial evaluation cycle.

Keywords:Autonomous vehicles, Automotive control, Control applications Abstract: An automated trajectory planning approach is presented in this work to incorporate the logical decision--making phase of a Cooperative Collision Avoidance (CCA) system and to avoid design errors caused by traditional methods. The linear temporal logic, which is an expressive language of temporal logic, is used to write specifications and automatically synthesize a logical controller strategy for a vehicle. This results in a specification--correct control automaton. The trajectory is represented by a sequence of acceptable states respecting the specification. This automaton is implemented using a controller which generates reference signals to be followed by the vehicle. The performance of this approach is tested using the so--called elk test.

Keywords:Optimal control, Control applications, Optimization Abstract: In this letter, a formulation of Fermat's principle as an optimization problem over a finite number of stages is used to prove strong convexity and smoothness of the solutions to certain geometric optics problems. The class of problems considered in this letter consists in the determination of the trajectory followed by a ray between a light source and a final fixed point, separated by a finite number of layered homogeneous media, characterized by their refractive indices. To obtain the theoretical results, a dynamic programming argument is used in the analysis. Then, strong convexity and smoothness are exploited to get an error bound valid when an exact solution is replaced by an approximate solution. Numerical results are provided to validate the theoretical achievements.

Keywords:Power electronics, Energy systems, Control applications Abstract: The increasing penetration of renewables requires advanced control algorithms to enable accurate control of the grid side converter (GSC) of renewable systems. The control of GSC mainly depends on the fast and accurate estimation of grid voltage phase angle and frequency under adverse grid conditions. Various grid disturbances occur on electricity grids, however, those that require special attention are harmonics, interharmonics and DC offset. Typically, a Phase-locked Loop (PLL) is used to obtain the grid voltage information. When designing a GSC control algorithm the accurate and proper design as well as the computational complexity, are important elements for the accurate real-time control. For real-time PV systems, embedded microcontrollers have limited computational resources and thus their effective utilization is critical. This paper proposes an advanced less-complex disturbance rejection PLL (LCDRPLL) that offers improved performance with reduced complexity. The proposed PLL is equipped with advanced features such as immunity to grid voltage unbalance, presence of harmonics, interharmonics and DC offset. More importantly, its computational complexity is very low. Experimental and simulation results are provided to justify the performance and complexity of proposed LCDRPLL.

Keywords:Sensor networks, Communication networks, Linear parameter-varying systems Abstract: We consider the combined energy management and rate control problem in wireless sensor networks (WSNs) with energy harvesting (EH) capability. In our previous work, we have established that the energy management problem can be viewed as a queue control problem, where the objective is to control the energy queue to a reference level based on predictions of energy to be harvested. In this work, we consider the problem of controlling both the energy and the data queue. The energy queue is controlled by adjusting the capacity of the data queue, while the data queue is controlled by adjusting the advertised rate at the network users which are assumed to be compliant with and without delay. We assume linear models of the data and energy queues and controllers are derived respectively. We demonstrate that the rate control problem, in the presence of a well controlled energy queue, can be reduced to a queue control problem with varying link capacity and we discuss the design options emanating from such a consideration. The stability of the combined control policy is established analytically. Further, we consider an arbitrary network case and we address global stability problem in the case of time varying capacity as a result of the energy variations.

Keywords:Variable-structure/sliding-mode control, Distributed control, Power systems Abstract: This paper proposes a novel control scheme based on the joint use of decentralized Sliding Mode (SM) control and distributed averaging control for cooperative voltage regulation in Alternate Current (AC) microgrids. The considered model of the microgrid includes several Distributed Generation Units (DGUs) interconnected through resistive-inductive power lines. In each DGU a Voltage Sourced Converter (VSC) supplies an unknown current load. The proposed control strategy consists of two different control schemes. A decentralized SM control scheme constrains the state of the microgrid on a suitable manifold where the q-component of the voltage of each DGU is equal to zero. On this manifold, the d-component of the control input is generated by distributed controllers aimed at sharing the d-component of the generated current and preserving the average of the microgrid voltages. Global convergence to a desired steady state is proven and simulation results confirm the effectiveness of the proposed solution.

Keywords:Variable-structure/sliding-mode control Abstract: The twisting algorithm is a well-known control law ensuring second order sliding mode establishment when applied to an uncertain nonlinear system. However, the convergence domain has not been formally determined. Thanks to an original approach that is based on the fact that the twisting control law can be viewed as a controller with switching gain, the domain of convergence of a closed-loop system controlled by the twisting algorithm is obtained. Simulations show the efficiency of the obtained result.

Keywords:Variable-structure/sliding-mode control, Networked control systems Abstract: In this paper discrete time sliding mode control based methods for networked control systems in the presence of variable time delays and external perturbations are presented. The goal of robustly stabilizing the system is achieved by using a sliding variable of relative degree more than one. One of the two presented methods is based on the switching and the other one on the nonswitching reaching law. The validity of the two new approaches proposed in this paper is mathematically proved by providing and evaluating the width of the quasi sliding mode band. The effectiveness of the proposals is also assessed in simulation with satisfactory results.

Università Degli Studi Della Campania Luigi Vanvitelli

Keywords:Variable-structure/sliding-mode control, Adaptive control, Aerospace Abstract: The design of control strategies for bidirectional DC/DC converters is proposed. The motivation for this paper is the increased request from aeronautic applications of innovative and ``smart'' controllers able to manage automatically electrical energy distribution onboard. Two different control strategies are proposed, and also a higher level, supervisory control law is presented, to switch between the two low-level strategies in a safe way, i.e., ensuring the stability of the overall control law. The first low-level controller is based on the definition of a sliding manifold on which the system state evolution is confined by means of High-Gain or Variable Structure Control, while the second low-level controller exploits an adaptive approach to define a suitable reference current. The high-level switching strategy enables the commutation from one low-level controller to the other only if the Region of Attraction of the second controller has been reached, thus ensuring stability of the commutation. The strategies are designed for the case of Constant Power Loads (CPL), that are well known causes of instability. Detailed simulation results in MATALB/Simulink are provided, in different scenarios, showing the effectiveness of the proposed controllers.

Keywords:Variable-structure/sliding-mode control, Robust control, Lyapunov methods Abstract: A continuous sliding mode controller using super-twisting algorithm is presented for a class of double integrator systems with constant unknown control direction. The system is also considered to be perturbed by unknown non-vanishing Lipschitz disturbances. In contrast to existing continuous control solutions on this subject that at best can achieve exponential stability, the developed controller yields finite time convergence of the states to the origin of the system. Simulation results are provided to demonstrate the robustness of the controller to unknown control direction.

Keywords:Variable-structure/sliding-mode control, Robust control Abstract: The output tracking problem for a class of nonlinear systems presented in Nonlinear Block Controllable (NBC) form is addressed. Both matched and unmatched perturbations are considered. First, the Block Control iterative feedback linearization technique combined with a perturbation estimation are employed to design a sliding manifold. With the perturbation estimation, the effect of unmatched perturbation is mitigated. Then, a discrete-time sliding mode controller is synthesized such that the system state is driven toward a vicinity of the designed sliding manifold and stays there for all sampled time instants, avoiding chattering and reducing the matched perturbation effect. The effectiveness of the proposed methodology is confirmed by simulation.

Keywords:Variable-structure/sliding-mode control, Stability of linear systems, Time-varying systems Abstract: This paper presents a cascaded observer structure for linear time varying systems which yields ﬁnite-time exact state estimates despite an unknown input. The observer is based on a tangent space observer and a higher order sliding mode reconstruction scheme. Theoretical insights in the construction of the observer are given along with conditions for stability of the tangent space observer in the presence of unknown inputs. A numerical simulation example shows the applicability of the proposed approach.

Keywords:Sensor fusion, Estimation, Information theory and control Abstract: We investigate an adaptive sensor selection problem in which a stochastic process is monitored by multiple sensors. We design a sensor selection policy that assigns a set of sensors to collect measurements for which the sensor selection depends on previously collected measurements and auxiliary data, and is subject to a constraint on the number of sensors to be selected. We use the mutual information to assess the performance of the policy.

The goal of this paper is to find an approximate solution to the sensor selection problem and to assess the performance of the solution. For this purpose, we define greedy adaptive policies using greedy heuristics and derive a performance bound on greedy policies with respect to the performance of adaptive policies satisfying so-called diminishing property and optimality conditions. The main result shows that the performance of a greedy adaptive policy is at least 1/2 of that of the best policy satisfying these two conditions.

Keywords:Sensor fusion, Agents-based systems, Information theory and control Abstract: We propose a sequential and adaptive hypothesis test that operates in a completely distributed setting, relying on a sensor network where no single data-fusion center is present. The test is inspired by Chernoff's optimal solution, originally derived in a centralized setting. We compare the performance of our test with the optimal sequential test in sensor networks and provide sufficient conditions for which the proposed test achieves asymptotic optimality, minimizing the expected cost required to reach a decision plus the expected cost of making a wrong decision, when the observation cost per unit time tends to zero. Under these conditions, the proposed test is also shown to be asymptotically optimal with respect to the higher moments of the time required to reach a decision.

Keywords:Sensor fusion, Robotics, Mechatronics Abstract: For many articulated systems (i.e. systems composed of several mechanically connected objects), the assumption of full rigidity is only a mere approximation. The various flexibilities of the structure, if not accounted for, all hinder the positioning ability of the device, by generating biases in the estimations determined from rigid models. In this paper, we propose a sensor-based methodology for estimating the flexibilities of an open kinematic chain. To estimate the real position and orientation of the elements of the system, we reconcile data from Inertial Measurement Units (IMU) with the kinematics of the rigid system. We show that, under a model of punctual, spring-like deformations, this methodology allows one to observe all the deformations, if one IMU is installed downstream of each deformation in the chain. We design and test such an observer in simulation and on an exoskeleton, where it proved a suitable way of estimating the position of the flying foot. Experimental results, validated against a motion capture device, demonstrate the ability of this observer to fully capture the dynamics induced by these flexibilities.

Keywords:Sensor fusion, Optimal control, Optimization Abstract: The problem of path planning for mobile sensors with the task of target monitoring is considered. A receding horizon optimal control approach based on the information filter is presented, where the limited field of view of the sensor can be modeled by introducing binary variables. The resulting nonlinear mixed integer problem to be solved in each sample, with no apparent tractable solution, is shown to be equivalent to a problem that robustly can be solved to global optimality using off-the-shelf optimization tools.

Keywords:Sensor networks, Distributed control, Optimization algorithms Abstract: Many problems that are relevant to sensor networks such as active sensing and coverage planning have objectives that exhibit diminishing returns and specifically are submodular. When each agent selects an action local space of actions, sequential maximization techniques for submodular function maximization obtain solutions within half of optimal even though such problems are often NP-Hard. However, adapting methods for submodular function maximization to distributed computation on sensor networks is challenging as sequential execution of planning steps is time-consuming and inefficient. Further, prior works have found that planners suffer severely impaired worst-case performance whenever large numbers of agents plan in parallel. This work develops new tools for analysis of submodular maximization problems which we apply to design of randomized distributed planners that provide constant-factor suboptimality approaching that of standard sequential planners. These bounds apply when the objective satisfies a higher-order monotonicity condition and when cumulative interactions between agents are proportional to the optimal objective value. Problems including generalizations of sensor coverage satisfy these conditions when agents have spatially local sensing actions and limited sensor range. We present simulation results for two such cases.

Keywords:Sensor networks, Optimal control, Markov processes Abstract: We consider the use of a wireless body area network for remote patient health monitoring applications. Our proposed network consists of a controller and multiple sensors, whose signals provide information on the health state of a patient. We model this patient-sensor network as a partially observable Markov decision process. The sensor outputs are used by the controller to update the patient’s health-state belief probabilities and select a subset of sensors to be activated at the next decision epoch. We propose two operational algorithms that allow accurate monitoring of a patient’s health state while minimizing operational and misclassification costs: i) a greedy algorithm, which applies a one-step look-ahead approach, and ii) a dynamic programming-based algorithm which yields the optimal policy. We provide a numerical example which demonstrates the applicability of the suggested methods and provides insights.

Keywords:Energy systems, Identification, Smart grid Abstract: To perform any meaningful optimization task, power distribution operators need to know the topology and line impedances of their electric networks. Nevertheless, distribution grids currently lack a comprehensive metering infrastructure. Although smart inverters are widely used for control purposes, they have been recently advocated as the means for an active data acquisition paradigm: Reading the voltage deviations induced by intentionally perturbing inverter injections, the system operator can potentially recover the electric grid topology. Adopting inverter probing for feeder processing, a suite of graph-based topology identification algorithms is developed here. If the grid is probed at all leaf nodes but voltage data are metered at all nodes, the entire feeder topology can be successfully recovered. When voltage data are collected only at probing buses, the operator can find a reduced feeder featuring key properties and similarities to the actual feeder. To handle modeling inaccuracies and load non-stationarity, noisy probing data need to be preprocessed. If the suggested guidelines on the magnitude and duration of probing are followed, the recoverability guarantees carry over from the noiseless to the noisy setup with high probability.

Keywords:Smart grid, Uncertain systems, Fault detection Abstract: Phasor Measurement Units (PMUs) provide significant value towards ensuring autonomous cognition in the power grid by enabling the abnormal events to be fault-detected and so as to trigger proactive measures to avoid large catastrophic system states. For instance, a change in the baseline distribution of PMU signals can indicate imminent voltage collapse, false data injection, and other security threats. Fractal geometry inspired analysis of PMU signals (via the Hurst exponent) reveals that an imminent voltage collapse is preceded by a significant increase in the Hurst exponent. This pioneering finding calls for developing robust change point detection techniques for endowing the power grid with cognitive intelligence. Towards this end, in this paper, we propose a novel change point detection strategy that optimally anticipates the fractal geometry change point from the PMU signals subject to a pre-specified false alarm rate.

Keywords:Smart grid, Stability of nonlinear systems, Large-scale systems Abstract: We consider the problem of load side participation providing ancillary services to the power network within the primary frequency control timeframe. In particular, we consider on-off loads that switch when prescribed frequency thresholds are exceeded in order to assist existing primary frequency control mechanisms. However, such control policies are prone to chattering, which limits their practicality. To resolve this issue, we propose loads that follow a hysteretic on-off policy, and show that chattering behavior is not observed within such setting. Furthermore, we provide design conditions that ensure the existence of equilibria when such loads are implemented. However, as numerical simulations demonstrate, hysteretic loads may exhibit limit cycle behavior, which is undesirable. This is resolved by proposing a novel control scheme for hystertic loads. For the latter scheme, we provide asymptotic stability guarantees and show that no limit cycle or chattering will be exhibited. The practicality of our analytic results is demonstrated with numerical simulations on the Northeast Power Coordinating Council (NPCC) 140-bus system.

Keywords:Machine learning, Optimization, Smart grid Abstract: Designing a data sharing mechanism without sacrificing too much privacy can be considered as a game between data holders and malicious attackers. This paper describes a compressive adversarial privacy framework that captures the trade-off between the data privacy and utility. We characterize the optimal data releasing mechanism through convex optimization when assuming that both the data holder and attacker can only modify the data using linear transformations. We then build a more realistic data releasing mechanism that can rely on a nonlinear compression model while the attacker uses a neural network. We demonstrate in a series of empirical applications that this framework, consisting of compressive adversarial privacy, can preserve sensitive information.

Keywords:Smart grid, Control of networks, Algebraic/geometric methods Abstract: Cascading failures in power systems propagate non-locally, making the control and mitigation of outages extremely hard. In this work, we use the emerging concept of the tree partition of transmission networks to provide an analytical characterization of line failure localizability in transmission systems. Our results reveal that the ``bridges'' of the tree partition play a crucial role in understanding failure propagations. Specifically, when a non-bridge line is tripped, the impact of this failure only propagates within components of the tree partition defined by the bridges. In contrast, when a bridge line is tripped, the impact of this failure propagates globally across the network, affecting the power flow on all remaining transmission lines. This characterization suggests that it is possible to improve the system robustness by temporarily switching off certain transmission lines, so as to create more, smaller components in the tree partition; thus spatially localizing line failures and making the grid less vulnerable to large-scale outages. We illustrate this approach using the IEEE 118-bus test system and demonstrate that switching off a negligible portion of transmission lines allows the impact of line failures to be significantly more localized without substantial changes in line congestion.

Keywords:Learning, Smart grid, Robust control Abstract: It is critical to obtain stability certificate before deploying reinforcement learning in real-world mission-critical systems. This study justifies the intuition that smoothness (i.e., small changes in inputs lead to small changes in outputs) is an important property for stability-certified reinforcement learning from a control-theoretic perspective. The smoothness margin can be obtained by solving a feasibility problem based on semi-definite programming for both linear and nonlinear dynamical systems, and it does not need to access the exact parameters of the learned controllers. Numerical evaluation on nonlinear and decentralized frequency control for large-scale power grids demonstrates that the smoothness margin can certify stability during both exploration and deployment for (deep) neural-network policies, which substantially surpass nominal controllers in performance. The study opens up new opportunities for robust Lipschitz continuous policy learning.

Keywords:Stability of nonlinear systems, Numerical algorithms Abstract: Conditions for the existence and convergence to zero of numeric approximations with state-depend step of discretization to solutions of asymptotically stable homogeneous systems are obtained for the explicit and implicit Euler integration schemes. It is shown that for a sufficiently small discretization step the convergence of the approximating solutions to zero can be guaranteed globally in a finite or a fixed time, but in an infinite number of discretization iterations. It is proven that the absolute and relative errors of the respective discretizations are globally bounded functions. Efficiency of the proposed discretization algorithms is demonstrated by the simulation of the super-twisting system.

Keywords:Numerical algorithms, Stability of nonlinear systems, Optimization Abstract: We introduce continuous Lagrangian reachability (CLRT), a new algorithm for the computation of a tight, conservative and continuous-time reachtube for the solution flows of a nonlinear, time-variant dynamical system. CLRT employs finite strain theory to determine the deformation of the solution set from time ti to time ti+1. We have developed simple explicit analytic formulas for the optimal metric for this deformation; this is superior to prior work, which used semi-definite programming. CLRT also uses infinitesimal strain theory to derive an optimal time increment hi between ti and ti+1, nonlinear optimization to minimally bloat (i.e., using a minimal radius) the state set at time ti such that it includes all the states of the solution flow in the interval [t_i; t_{i+1}]. We use delta-reachability to ensure the correctness of the bloating. Our results on a series of benchmarks show that CLRT performs favorably compared to state-of-the-art tools such as CAPD in terms of the continuous reachtube volumes they compute.

Keywords:Numerical algorithms, Optimization, Robust control Abstract: This paper provides a description of a practically efficient minimal-representation algorithm for polytopes. The algorithm is based on a primal active-set method that heavily exploits warm-starts and low-rank updates of matrix factorizations in order to reduce the required computational work. By using a primal active-set method, several nonredundant inequalities can be identified for each solved linear program. Implementation details are provided both for the minimal-representation algorithm and for the underlying active-set method.

Keywords:Numerical algorithms, LMIs, Computational methods Abstract: Linear matrix inequalities (LMIs) play a fundamental role in robust and optimal control theory. However, their practical use remains limited, in part because their solution complexities of O(n^{6.5}) time and O(n^{4}) memory limit their applicability to systems containing no more than a few hundred state variables. This paper describes a Newton-PCG algorithm to efficiently solve large-and-sparse LMI feasibility problems, based on efficient log-det barriers for sparse matrices. Assuming that the data matrices share a sparsity pattern that admits a sparse Cholesky factorization, we prove that the algorithm converges in linear O(n) time and memory. The algorithm is highly efficient in practice: we solve LMI feasibility problems over power system models with as many as n=5738 state variables in 2 minutes on a standard workstation running MATLAB.

Keywords:Numerical algorithms, Uncertain systems Abstract: This paper over-approximates the reachable sets of a continuous-time uncertain system using the sensitivity of its trajectories with respect to initial conditions and uncertain parameters. We first prove the equivalence between an existing over-approximation result based on the sign-stability of the sensitivity matrices and a discrete-time approach relying on a mixed-monotonicity property. We then present a new over-approximation result which scales at worst linearly with the state dimension and is applicable to any continuous-time system with bounded sensitivity. Finally, we provide a simulation-based approach to estimate these bounds through sampling and falsification. The results are illustrated with numerical examples on traffic networks and satellite orbits.

Keywords:Observers for nonlinear systems, Mechatronics, Adaptive systems Abstract: In this paper we address the problem of sensorless control of the 1-DOF magnetic levitation system. Assuming that only the current and the voltage are measurable, we design an adaptive state observer using the technique of signal injection. Our main contribution is to propose a new filter to identify the virtual output generated by the signal injection. It is shown that this filter, designed using the dynamic regressor extension and mixing estimator, outperforms the classical one. Two additional features of the proposed observer are that (i) it does not require the knowledge of the electrical resistance, which is also estimated on-line and (ii) exponential convergence to a tunable residual set is guaranteed without excitation assumptions. The observer is then applied, in a certainty equivalent way, to a full state-feedback control law to obtain the sensorless controller, whose performance is assessed via experiments.

Keywords:Mechatronics, Output regulation, Modeling Abstract: This paper deals with position control of an actuator system consisting of a dielectric elastomer membrane biased with a combination of a linear and a bi-stable spring. The highly nonlinear response of dielectric elastomer material, in conjunction with the bi-stable biasing spring, makes the control of the overall system challenging. To systematically address the design of the control system, a novel approach is proposed based on port-Hamiltonian (PH) theory. First, based on a recently developed PH model of the dielectric elastomer material, a PH model of the overall actuator system is obtained. Subsequently, several control laws are designed by means of PH theory, i.e., interconnection and damping assignment passivity-based control (IDA-PBC), and IDA-PBC with integral of non-passive output for robust regulation. The developed control laws are finally compared with a conventional PID, showing improved dynamic performance in the overall actuation range.

The Netherlands Institute for Space Research (SRON)

Keywords:Modeling, Mechatronics, Grey-box modeling Abstract: We present modeling and analysis of the so-called butterfly hysteresis behavior, based on the use of the Preisach operator. The desired butterfly loop properties can be obtained under some mild conditions on the weighting function that defines the Preisach operator. The proposed framework is used to model the electric-field dependence of the strain in a piezoelectric material purposely designed to exhibit asymmetric butterfly loops with remnant deformation.

Keywords:Robotics, Stability of nonlinear systems, Mechatronics Abstract: The new approach to the problem of motion planning for underactuated mechanical systems is proposed. The novelty comes from new opportunities to handle singularities of the dynamics of the motion generator provided that the motion is rewritten using the nested representation and kinematic servo-connection between generalized coordinates of the system. The contribution is illustrated by the example of planning oscillations of the Furuta pendulum around the horizontal.

Université De Valenciennes Et Du Hainaut-Cambrésis

Keywords:Robotics, Mechatronics, Lyapunov methods Abstract: This paper presents a method for the control design of a two degrees of freedom (2-DoF) serial manipulator using descriptor Takagi-Sugeno modelling. The design goal is to achieve a guaranteed mathcal{H}_{infty} model reference tracking performance while significantly reducing the numerical complexity of the designed controller through a robust control scheme. Based on Lyapunov stability theory, the control design is formulated as an LMI (linear matrix inequality) optimization problem. Simulation results carried out with the SimMechanics environment clearly demonstrate the effectiveness of the proposed method.

Keywords:Mechatronics, Nonlinear output feedback, Observers for nonlinear systems Abstract: We propose a rate-dependent hysteresis model constructed with a Netushil operator for modeling hysteresis nonlinearities. This hysteresis operator is constructed with an ordinary differential equation and a positive perturbation constant. We show that the positive perturbation constant in Netushil operator {captures} the rate-dependency in hysteresis loops when a harmonic input is applied. Furthermore, a linear combination of Netushil operators are proposed to model current-to-displacement hysteresis loop of a magnetostrictive actuator over different operating conditions. We further consider the problem of output-feedback tracking control of a class of mechanical systems that include rate-dependent hysteresis nonlinearities. In particular, we take an iron pendulum in a magnetic field system as a case study. We show that, in this case, an extended high-gain observer-based feedback linearizing control can be employed to solve the problem. The proposed control system has a number of features; namely, (i) it can guarantee ultimate boundedness of the tracking error, where the ultimate bound can be made arbitrarily small, for any given initial conditions and for bounded unknown exogenous inputs and modeling parameters, and (ii) it provides the possibility of shaping the transient response of the closed-loop system as desired. Simulation results are provided to verify the effectiveness of these results.

Keywords:Autonomous systems, Control of networks, Network analysis and control Abstract: Networked systems are often controlled by selecting a subset of nodes to act as inputs, which then control the remaining network nodes via local interactions. In this paper, we investigate the problem of selecting input nodes in order to control structured linear descriptor systems, which contain free parameters that can take any value as well as fixed parameters that take a known, fixed value. This class of system generalizes standard models of networked systems, which typically assume that all parameters are either fixed or free. We develop a framework for joint selection to ensure controllability, stabilizability via output feedback, and performance, by mapping conditions for controllability and stabilizability to matroid constraints on the set of input nodes. We propose polynomial-time algorithms with provable optimality bounds when the performance metrics under consideration are submodular. Our results are illustrated through a numerical study.

Keywords:Boolean control networks and logic networks, Stability of nonlinear systems, Control of networks Abstract: Controllability is one of the most important properties of a Boolean control network (BCN). Essentially there are two kinds of controls: networked inputs and free logical inputs. This paper considers the controllability of BCN under mixed controls. The technique proposed is to convert a BCN with two kinds of controls into a set controllability problem. Using results obtained for set controllability, a necessary and sufficient condition for controllability of BCN with mixed inputs is obtained. An example is presented to depict the theoretical result.

Keywords:Compartmental and Positive systems, Network analysis and control Abstract: Spreading processes that propagate through local interactions have been studied in multiple fields (e.g. epidemiology, complex networks, social sciences, etc.) using the SIR (Susceptible-Infected-Recovered) and SIS (Susceptible-Infected-Susceptible) frameworks. The former assumes individuals acquire full immunity to the infection after recovery, while the latter assumes individuals acquire no immunity after recovery. However, in many spreading processes individuals may acquire only partial immunity to the infection or, in some cases, may also become more susceptible to reinfection after recovery. Here we study a model for reinfection called SIRI (Susceptible-Infected-Recovered-Infected). The SIRI model generalizes the SIS and SIR models and allows for study of systems in which the susceptibility of agents changes irreversibly after first exposure to the infection. We show that when the rate of reinfection is higher than the rate of primary infection, the SIRI model exhibits bistability with a small difference in the initial fraction of infected individuals determining whether the infection dies out or spreads through the population. We find this critical value and show that when the infection does not die out there is a resurgent epidemic in which the number of infected individuals decays initially and remains at a low level for an arbitrarily long period of time before rapidly increasing towards an endemic equilibrium in which the fraction of infected individuals is non-zero.

Keywords:Genetic regulatory systems, Stability of nonlinear systems, Control of networks Abstract: Multistable dynamical systems are ubiquitous in nature, especially in the context of regulatory networks controlling cell fate decisions, wherein stable steady states correspond to different cell phenotypes. In the past decade, it has become experimentally possible to "reprogram" the fate of a cell by suitable externally imposed input stimulations. In several of these reprogramming instances, the underlying regulatory network has a known structure and often it falls in the class of cooperative monotone dynamical systems. In this paper, we therefore leverage this structure to provide concrete guidance on the choice of inputs that reprogram a cooperative dynamical system to a desired target steady state. Our results are parameter-independent and therefore can serve as a practical guidance to cell-fate reprogramming experiments.

Keywords:Sensor networks, Fault detection, Kalman filtering Abstract: In this paper we consider the distributed consensus-based filtering problem for linear time-invariant systems over sensor networks subject to random link failures when the failure sequence is not known at the receiving side. We assume that the information exchanged, traveling along the channel, is corrupted by a noise and hence, it is no more possible to discriminate with certainty if a link failure has occurred. Therefore, in order to process the only significant information, we endow each sensor with detectors which decide on the presence of link failures. At each sensor the proposed approach consists of three steps: failure detection, local data aggregation and Kalman consensus filtering. A numerical example show the effectiveness of this method.

Keywords:Variational methods, Game theory, Communication networks Abstract: We consider an instance of a nonatomic routing game. We assume that the network is parallel, that is, constituted of only two nodes, an origin and a destination. We consider infinitesimal players that have a symmetric network cost, but are heterogeneous through their set of feasible strategies and their individual utilities. We show that if an atomic routing game instance is correctly defined to approximate the nonatomic instance, then an atomic Nash Equilibrium will approximate the nonatomic Wardrop Equilibrium. We give explicit bounds on the distance between the equilibria according to the parameters of the atomic instance. This approximation gives a method to compute the Wardrop equilibrium at an arbitrary precision.

Keywords:Autonomous vehicles, Automotive control, Automotive systems Abstract: This paper describes a method for real-time integrated motion planning and control of autonomous vehicles. Our method leverages feedback control, positive invariant sets, and equilibrium trajectories of the closed-loop system to guarantee collision-free closed-loop trajectory tracking. Our method jointly steers the vehicle to a target region and controls the velocity while satisfying constraints associated with the future motion of the obstacles with respect to the vehicle. We develop a receding-horizon implementation and verify the method in a simulated road scenario. The results show that our method generates safe dynamically feasible trajectories while accounting for obstacles in the environment and modeling errors. In addition, the computation times indicate that the method is sufficiently efficient for real-time implementation.

Keywords:Autonomous vehicles Abstract: This paper introduces a unified, scalable and replicable approach to make implementation of the autonomous system on a new vehicle faster while preserving its autonomous performance. The main idea of this approach is to create a standard hardware architecture, along with a Simulink or similar library and templates for autonomous driving for a unified approach to vehicle autonomy, making it easier to scale the solution and replicate it on other vehicle platforms. However, this scaling and replicating of the autonomous driving system between vehicles remains difficult especially for low-level controller design due to parametric difference between vehicles. This paper, hence, demonstrates a sequential controller design procedure with specific example of lateral control for a chosen vehicle. The same design process can be replicated to adapt controller parameters for other vehicles. The parameter space approach is applied here to ensure robust path following performance of a proportional-derivative (PD) steering controller, considering uncertainties of vehicle load, speed and tire cornering stiffness. To further reduce the tracking error and handle unmodeled dynamics and reject disturbances, a model regulator was added based on overall system analysis. To evaluate the control strategy, a validated high-fidelity model of an autonomous research vehicle is used within a hardware-in-the-loop (HIL) simulation environment. Soft sensors were also connected to the soft automated vehicle in the HIL environment to test high-level control and decision making mechanisms. The road used for the simulations is a replica of a designated real world short AV pilot route in the Ohio State University West campus. Traffic is generated with Simulation of Urban MObility (SUMO) software in order to analyze the problems due to the presence of other vehicles and evaluate performance more realistically in the HIL simulator.

Keywords:Autonomous vehicles, Simulation Abstract: Autonomous driving functions (ADF ) are evolving rapidly, but there is still no agreement on how to test them for safety and performance in real world. There is, however, a general consensus that simulation based assessment is needed, as sufficient road testing will not be feasible due to constraints of time and costs. For such an assessment, the scenarios included in the simulation should be representative for the intended real world use of the function under test. However, there is no guideline on how to choose the time horizon or to make sure that the scenarios are really representative of the intended use. Against this background, this paper aims to tackle the first question proposing an outcome oriented approach with determination of the simulation length needed to achieve a given level of confidence on the result. This allows obtaining comparable results for different simulation runs in different operating conditions while optimizing the total simulation time. As a by-product, the suggested method can also be used to asses the degree of novelty of additional scenarios.

Keywords:Automotive control, Predictive control for nonlinear systems, Automotive systems Abstract: Future vehicles are expected to be able to exploit increasingly the connected driving environment for efficient, comfortable, and safe driving. Given relatively slow dynamics associated with the state of charge and temperature response in electrified vehicles with large batteries, a long prediction/planning horizon is needed to achieve improved energy efficiency benefits. In this paper, we develop a two-layer Model Predictive Control (MPC) strategy for battery thermal and energy management of electric vehicle (EV), aiming at improving fuel economy through real-time prediction and optimization. In the first layer, the long-term traffic flow information and an approximate model reflective of the relatively slow battery temperature dynamics are leveraged to minimize energy consumption required for battery cooling while maintaining the battery temperature within the desired operating range. In the second layer, the scheduled battery thermal and state of charge (SOC) trajectories planned to achieve long-term battery energy-optimal thermal behavior are used as the reference over a short horizon to regulate the battery temperature. Additionally, an intelligent online constraint handling (IOCH) algorithm is developed to compensate for the mismatch between the actual and predicted driving conditions and reduce the chance for battery temperature constraint violation. The simulation results show that, depending on the driving cycle, the proposed two-layer MPC is able to save 2.8-7.9% of the battery energy compared to the traditional rule-based controller in connected and automated vehicle (CAV) operation scenario. Moreover, as compared to a single layer MPC with a long horizon, the two-layer structure of the proposed MPC solution reduces significantly the computing effort without compromising the performance.

Keywords:Autonomous vehicles, Automotive control, Control applications Abstract: We propose a map-aided vehicle localization method for GPS-denied environments. This approach exploits prior knowledge of the road grade map and vehicle on-board sensor measurements to accurately estimate the longitudinal position of the vehicle. Real-time localization is crucial to systems that utilize position-dependent information for planning and control. We validate the effectiveness of the localization method on a hierarchical control system. The higher level planner optimizes the vehicle velocity to minimize the energy consumption for a given route by employing traffic condition and road grade data. The lower level is a cruise control system that tracks the position-dependent optimal reference velocity. Performance of the proposed localization algorithm is evaluated using both simulations and experiments.

Keywords:Optimal control, Autonomous vehicles, Smart cities/houses Abstract: This paper is devoted to the development of an optimal acceleration/speed profile for autonomous vehicles in free flow mode approaching a traffic light without stopping. The design objective is to achieve both short travel time and low energy consumption as well as avoid idling at a red light. This is achieved by taking full advantage of the traffic light information based on infrastructure-to-vehicle communication. The direct adjoining approach is used to solve both free and fixed terminal time optimal control problems subject to state constraints. We show that we can derive a real-time online analytical solution, distinguishing our method from most existing approaches based on numerical calculations. Extensive simulations are executed to compare the performance of autonomous vehicles under the proposed speed profile and human driving vehicles. The results show quantitatively the advantages of the proposed algorithm in terms of energy consumption and travel time.

Keywords:Decentralized control, Cooperative control, Distributed control Abstract: Muti-agent consensus controllers typically use discrete communication and hence are restricted to fixed-rate or event-triggered communication. Fixed-rate communication suffers from inefficient use of communication and computational resources but is easy to implement, while event-triggered communication conserves resources but suffers from the ambiguity of all event-triggered systems--inability to distinguish failure from lack of new information. We propose a novel hybrid strategy of co-regulating communication with state disagreement amongst the agents obtaining the benefits of discrete fixed-rate and event-triggered consensus while mitigating the associated disadvantages. Our approach dynamically adjusts the communication rate in response to disagreement in the shared state variable, resulting in a discrete-time-varying, asynchronous network topology. We prove convergence properties of the proposed consensus algorithm, develop metrics to evaluate dynamic approaches, and demonstrate the results in simulation, which shows a reduction in communication resources, while maintaining the same convergence time.

Keywords:Decentralized control, Distributed parameter systems, Optimization algorithms Abstract: Continuum robot manipulators present challenges for controller design due to the complexity of their infinite-dimensional dynamics. This paper develops a practical dynamics-based approach to synthesizing state feedback controllers for a soft continuum robot arm composed of segments with local sensing, actuation, and control capabilities. Each segment communicates its states to its two adjacent neighboring segments, requiring a tridiagonal feedback matrix for decentralized controller implementation. A semi-discrete numerical approximation of the Euler-Bernoulli beam equation is used to represent the robot arm dynamics. Formulated in state space representation, this numerical approximation is used to define an H-infinity optimal control problem in terms of a Bilinear Matrix Inequality. We develop three iterative algorithms that solve this problem by computing the tridiagonal feedback matrix which minimizes the H-infinity norm of the map from disturbances to regulated outputs. We confirm through simulations that all three controllers successfully dampen the free vibrations of a cantilever beam that are induced by an initial sinusoidal displacement, and we compare the controllers' performance.

Keywords:Decentralized control, Large-scale systems, Robust control Abstract: In this letter, we propose concepts of persistence and persistent control for uncertain dynamical systems. Motivated from their application to local controller design for expanding huge-scale systems, a problem of persistent control is formulated. A controller is designed such that for any arbitrarily large uncertainty the overall control system is stable. In addition, the performance of the overall system, measured by some norm, can be deteriorated for the large uncertainty, but is persistently prevented from being collapsed. Then, the control problem is solved via controller parametrization, and the characterization of the persistent controllers is given. Finally, a numerical example with some design guideline of the controller is illustrated.

Keywords:Decentralized control, Robust control, Time-varying systems Abstract: This paper presents a decentralised interpolating control scheme for the robust constrained control of uncertain linear discrete-time interconnected systems with local state and control constraints. The control law of each distinct subsystem relies on the gentle interpolation between a local high-gain controller with a global low-gain controller. Both controllers benefit from the computation of separable robust invariant sets for local control design, which overcomes the computational burden of large-scale systems. Another advantage is that for each subsystem both low- and high-gain controllers can be efficiently determined off-line, while the inexpensive interpolation between them is performed on-line. For the interpolation, a new low-dimensional linear programming problem is solved at each time instant. Proofs of recursive feasibility and robust asymptotic stability of the proposed control are provided. A numerical example demonstrates the robustness of decentralised interpolating control against model uncertainty and disturbances. The proposed robust control is computationally inexpensive, and thus it is well suited for large-scale applications.

Keywords:Decentralized control, Stability of nonlinear systems, Energy systems Abstract: This paper investigates the application of passivity-based nonlinear control to the problem of primary voltage stabilization in medium-voltage DC microgrids (MVDC mGs) given by the interconnection of nonlinear distributed generation units (DGUs) and power lines. To this aim, we propose nonlinear local regulators which steer the voltage at the output terminal of each DGU to a reference value. Each controller can be explicitly synthesized relying on DGU parameters, voltage reference values of the neighboring DGUs and resistance of the neighboring power lines. The control design enables plug-and-play (PnP) operations: a plug-in or -out of a DGU requires only the update of regulators of neighboring DGUs without spoiling the stability of overall mG. Theoretical results are backed up by simulations in Simulink environment.

Keywords:Distributed control, Decentralized control, Optimization algorithms Abstract: This paper studies the convergence property of the projected consensus algorithm. Under the assumption that i) the intersection of all constraint sets is nonempty, ii) the directed graph representing the communication among agents is time-invariant, strongly connected and aperiodic, and iii) the sum of the weights on incoming edges to each vertex of the graph is one, we prove that the states of all agents converge to a common point in the intersection of all constraint sets. Our proof does not need the assumption that every vertex has a self-loop. The validity of the theoretical analysis is confirmed through numerical experiments performed for a system of linear equations with nonnegativity constraints.