Keywords:Stochastic optimal control, Stochastic systems, Autonomous robots Abstract: We consider nonlinear stochastic systems that arise in path planning and control of mobile robots. As is typical of almost all nonlinear stochastic systems, optimally solving the problem is intractable. Moreover, even if obtained it would require centralized control, while the path planning problem for mobile robots requires decentralized solutions. We provide a design approach which yields a tractable design that is quantifiably near-optimal. We exhibit a decoupling result under a small noise assumption consisting of the optimal open-loop design of nominal trajectory followed by decentralized feedback law to track this trajectory. As a corollary, we obtain a trajectory-optimized linear quadratic regulator design for stochastic nonlinear systems with Gaussian noise.

Keywords:Mean field games, Estimation;Finance Abstract: The stock market can be modeled as a large population non-cooperative game where (following standard financial models) each trader has stochastic linear dynamics with quadratic cost function. We consider the case where there exists one major trader with significant influence on market movements together with a large number of minor traders with individually asymptotically negligible effect on market. The traders are coupled in their dynamics and cost functions by the market’s average trading rate (a component of the system mean field). In this work the theory of partially observed mean field games is extended to cover indefinite LQG problems and then employed to obtain ε-Nash equilibria for the market, together with the best response trading strategy for each agent so as to (i) maximize its wealth, and then also (ii) track a fraction of market’s average trading rate, and (iii) avoid large execution prices and large trading accelerations. Illustrative simulations are presented.

Keywords:Stochastic optimal control, Filtering;Sensor fusion Abstract: We consider the problem of detecting which Gaussian model generates an observed time series data. We consider as possible generative models two linear systems driven by white Gaussian noise with Gaussian initial conditions. We also consider two collaborating observers. The observers observe a function of the state of the systems. Using these observations, the aim is to find which one of the two Gaussian models has generated the observations. For each observer we formulate a sequential hypothesis testing problem. Each observer computes its own likelihood ratio based on its own observations. Using the likelihood ratio, each observer performs sequential probability ratio test (SPRT) to arrive at its decision on the hypothesis. Taking into account the random and asymmetric stopping times of the two observers, we present a consensus algorithm which guarantees asymptotic convergence to the true hypothesis. The consensus algorithm involves exchange of information, i.e., the decision of the observers. Through simulations, the "value" of the information exchanged, probability of error and average time to consensus are computed.

Keywords:Hierarchical control, Stochastic systems Abstract: The Control-Coding Capacity (CC Capacity) is defined as the maximum amount of information in bits/second, which can be encoded into randomized control strategies, transmitted over the control system, and decoded at its outputs, with arbitrary asymptotic small probability of error. This paper shows that optimal randomized control strategies which achieve the CC Capacity impose a natural hierarchical decomposition into two simpler sub-optimization problems, one related to the control objectives and one related to the information transmission objectives. The hierarchical decomposition states that control signals and communication signals interact in a specific order, optimal strategies are decentralized, and the information transmission rate is zero, unless the power allocated to the overall system is above a certain threshold, which is the minimum cost to achieve the control objectives.

Keywords:Mean field games, Game theory, Stochastic systems Abstract: This paper considers mean field games in a multi-agent Markov decision process (MDP) framework. Each player has a continuum state and binary action. We analyze two stationary mean field games with discounted individual costs and long-run average individual costs, respectively. We show existence of a solution to the associated equation system, leading to threshold policies. Uniqueness is obtained under a product form cost and positive externalities.

Keywords:Stochastic optimal control, Mean field games Abstract: We study risk-sensitive optimal control of a stochastic differential equation of mean-field type, where the coefficients are allowed to depend on some functional of the law as well as the state and control processes. Moreover the risk-sensitive cost functional is also of mean-field type. We derive optimality equations in infinite dimensions connecting dual functions associated with Bellman functional to the adjoint process of the Pontryagin maximum principle. The case of linear-exponentiated quadratic cost and its connection with the risk-neutral solution is discussed.

Keywords:Adaptive control;Distributed parameter systems, Linear systems Abstract: We extend previous results on adaptive output-feedback stabilization of a 1-D linear hyperbolic PDE with uncertain system parameters, by solving a model reference adaptive control (MRAC) problem for a slightly generalized class of systems which allows for the measurement and actuation to be scaled by uncertain nonzero constants. The only required knowledge of the system is the total transport delay and the sign of the product of the actuation and measurement scaling constants. It is also shown that the adaptive stabilization problem is a subproblem of the MRAC problem. The theory is demonstrated in a simulation on a linearized Korteweg de Vries-like equation.

Keywords:Distributed parameter systems;Control applications, Stability of linear systems Abstract: In this paper the control by immersion and structural invariants is extended to the distributed control of infinite dimensional port-Hamiltonian systems defined on a 1D spatial domain. The main novelty lies in fact that the structural invariants are not used to shape the closed loop energy function but to modify the closed loop structure of the system by an appropriate choice of the controller structure. In particular it is shown that in the fully actuated case, this control strategy allows to transform an hyperbolic system composed of two conservation laws into a parabolic one. This work is illustrated on the example of the wave equation but can be easily generalised to a large class of systems encompassing vibrating strings and beam equations.

Keywords:Distributed parameter systems;Switched systems Abstract: In this research we are concerned with a switched system that switches very fast between two infinite-dimensional LTI subsystems, such that the overall system spends on average an equal amount of time in both possible subsystems. We ask if it is possible to approximate the switched system with an average system that is the limit of our switched system when the switching period tends to zero. We are mainly concerned with the situation when both subsystems are described by a contraction semigroup on a Hilbert space. We examine in particular the case when both subsystems are obtained from a basic subsystem via different output feedback operators.

Keywords:Optimal control;Fluid flow systems;Distributed parameter systems Abstract: We discuss the optimal control problem of enhancing heat transfer between two fluids via controlling the velocity of the cold fluid flow. In this paper, we consider that the fluid flow for cooling the hot fluid is a Stokes fluid flow induced by the boundary control inputs through the Navier slip boundary conditions. This approach is motivated by the study of optimal heat transfer by counter rotating walls. The objective is to minimize the average temperature of the hot fluid by optimal control of the cold flow velocity. This essentially leads to a bilinear control problem. We present a rigorous proof of the existence of an optimal control and derive the first-order necessary conditions for optimality by using a variational inequality.

Keywords:Distributed parameter systems, Optimization, Kalman filtering Abstract: This paper is concerned with state estimation for systems governed by partial differential equations. Kalman filters are popular state estimators since they are optimal in minimizing the estimation error variance for given measurements. The focus of this paper is to achieve further minimization of the error variance by also optimizing over the sensor design. The optimal sensor design problem is thus incorporated into the estimation problem. Not only the sensor location but also other factors are considered into the optimization criteria, such as the sensor shape. The problem is first stated formally, and then it is shown to be well-posed and to possess optimal solutions. The approach is illustrated with several examples.

Keywords:Distributed parameter systems, Stability of linear systems Abstract: This paper presents a novel approach for the development of boundary control laws for a class of linear, distributed port-Hamiltonian systems, with one dimensional spatial domain. Similarly to the control via generalised canonical transformations in the lumped parameter case, the idea is to determine a control action able to map the initial system into a target one, characterised not only by a different Hamiltonian function, but also by new internal dissipative and power-preserving interconnection structures. The methodology consists of two main steps, each associated to a generalised canonical transformation. In the first one, a coordinate change (based on a combination of a linear mapping and a backstepping transformation) is employed to modify the internal structure of the system. Then, in the second step, a generalised canonical transformation capable of properly shaping the Hamiltonian function is introduced. The proposed approach is illustrated with the help of a simple example, the boundary stabilisation of a lossless transmission line.

Keywords:Evolutionary computing, Optimization algorithms Abstract: A multi-objective multifactorial evolutionary algorithm has been proposed recently to address multi-objective multi-tasks optimization simultaneously. However, the approach only focuses on the improvement of algorithm convergence via knowledge transfer among the optimization tasks. To enhance the performance of both diversity and convergence which are important for evolutionary multi-objective optimization, this paper proposes a two-stage assortative mating method for multi-objective multifactorial evolutionary optimization. In the proposed algorithm, decision variables are first divided into two types using a decision variable clustering method: diversity-related variables and convergence-related variables. The two types of variables then undergo assortative mating with different parameters independently when offspring are generated. Experimental results on a variety of test instances show that the proposed algorithm is highly competitive as compared with existing multi-task and single-task algorithms.

Keywords:Sensor networks, Network analysis and control, Optimization algorithms Abstract: The problem of distributed connectivity optimization of an asymmetric sensor network represented by a weighted directed graph (digraph) is investigated in this paper. The notion of generalized algebraic connectivity is used to measure the connectivity of a time-varying weighted digraph. The generalized algebraic connectivity is regarded as a nonconcave and nondifferentiable continuous cost function, and a distributed approach, based on the subspace consensus algorithm, is developed to compute the supergradient vector of the network connectivity. By considering the above-mentioned network connectivity as a function of the transmission power vector of the network, a discrete-time update procedure is proposed to compute a stationary transmission power vector of the network which locally maximizes the network connectivity. The effectiveness of the developed algorithm is subsequently demonstrated by simulations.

Keywords:Optimization;Air traffic management, Optimization algorithms Abstract: We present a novel complex number formulation along with tight convex relaxations for the aircraft conflict resolution problem. Our approach combines both speed and heading control and provides global optimality guarantees despite non-convexities in the feasible region. We present a new characterization of the conflict separation condition in the form of disjunctive linear constraints. Using our approach, we are able to close a number of open instances and reduce computational time by up to two orders of magnitude on standard instances.

Keywords:Optimization, Estimation Abstract: This paper presents a novel Koopman operator theoretic approach for nonlinear constrained state estimation (CSE) with non-convex state constraints. Exploiting linear representation induced by Koopman operator, we show that under certain conditions the CSE problem can be transformed into a higher dimensional but convex problem. This could provide significant benefit in real time applications. We numerically demonstrate the efficacy of proposed approach and report superior performance compared to convexification based on successive linearization.

Keywords:Optimization, Network analysis and control, Optimal control Abstract: We consider the threshold model of cascading behavior in networks, in which a node fails if at least a certain fraction of its neighbors have failed in the previous time step. Our goal is to solve the optimal cascade seeding problem: For a given network and specified time horizon, find the set of nodes whose failure at time zero maximizes the failure amplification ratio -- the ratio between the number of final and initial failures. The optimal cascade seeding problem is combinatorial and thus intractable for large networks. We propose an approximation of the threshold model that lends itself to the application of tools from dynamical systems theory and convex optimization. Through a sequence of relaxations we write the approximate optimal cascade seeding problem as a linear program, which has the benefit of scaling gracefully in network size. Our approach retains the original network topology and accommodates the specification of a wide range of additional constraints on the initialization and propagation of failures, such as which nodes are immune from initial failure and which are required to be in failed state by the end of the time horizon.

Keywords:Optimization, Optimization algorithms, Agents-based systems Abstract: The problem of search by multiple agents to find and localize objects arises in many important applications. In this paper, we study a class of multi-agent search problems in which each agent can access only a subset of a discrete search space, with detection performance that depends only on the location. We show this problem can be reformulated as a minimum cost network optimization problem, and develop a fast specialized algorithm for the solution. We prove that our algorithm is correct, and has worst case computation performance that is faster than general minimum cost flow algorithms. We also address the problem where detection performance depends on both location and agent, which is known to be NP-Hard. We reduce the problem to a submodular maximization problem over a matroid, and provide an approximate algorithm with guaranteed performance. We illustrate the performance of our algorithms with simulations of search problems and compare it with other min-cost flow algorithms.

Keywords:Linear systems, Optimal control, Robust control Abstract: The objective is to find accurate open-loop controls for linear systems, which bring the state to the exact desired target in the absence of the disturbance (accurate), and minimize the worst case error at the final state (minimally sensitive) when disturbed. In particular, a suboptimal open-loop control is proposed for the multiplicative disturbance case. The proposed suboptimal control has a structural analogy to the Gramian based minimum energy controller but differs by using a weighted Gramian. Further analysis on this unconventional weighted Gramian shows that its inverse relates to the upper bound of the worst perturbation at the final state. A two dimensional heat exchanger example shows the effectiveness of the proposed control.

Keywords:Optimal control, Machine learning, Control of networks Abstract: We consider Generalized Additive Increase Multiplicative Decrease (G-AIMD) dynamics for resource allocation with alpha fairness utility function. This dynamics has a number of important applications such as internet congestion control, charging electric vehicles, and smart grids. We prove indexability for the special case of MIMD model and provide an efficient scheme to compute the index. The use of index policy allows us to avoid the curse of dimensionality. We also demonstrate through simulations for another special case, AIMD, that the index policy is close to optimal and significantly outperforms a natural heuristic which penalizes the strongest user.

Keywords:Optimal control, Constrained control, Variational methods Abstract: In this work impulsive control problems are investigated in that case in which matrix G that appears in the dynamics multiplying vector-valued control measure mu depends on the state variable, that is, G=G(x,t). The solution concept and the extension procedure in this non-linear case are not as trivial as in the case G=G(t). The key-point is to ensure robustness of the impulsive control system w.r.t. the control measure and regarding the approximations in the weak-* topology (``w.r.t.'' stands for ``with respect to'' here and further). Note that such approximations are required by applications. But this type of robustness is generally lost unless some extra assumptions on the matrix G w.r.t. the x-variable are imposed. It turns out that the weakest possible assumption, that still meets the robustness property, is the so-called Frobenius condition presented and discussed below. Under the Frobenius condition and without a priori regularity assumptions, we derive second-order necessary optimality conditions in a new form. This form and relations with previous results are discussed.

Keywords:Optimal control;Control applications;Power generation Abstract: We consider a wireless sensor node equipped with a piezoelectric vibration energy harvester, which is excited by a series of periodic base acceleration impulses. The magnitude and arrival times of the impulses are known a priori. The node also contains a finite energy storage system, a data queue, and a data transmitter. While most piezoelectric energy harvesters trickle-charge the storage system, in this study, we model a PWM-controlled H-bridge circuit at the transducer and energy storage system interface, which can realize any desired transducer current including two-way power flow. Our goal is to maximize the bits of data transmitted from the node over a fixed period of time through the control of the transmission power and transducer current. However, there are parasitic losses associated with the circuitry used to extract power, and therefore, the optimal scheduling policy must balance energy resources between the two energy-consuming tasks: harvesting energy and transmitting data. Using barrier methods, we develop the optimal off-line control policy to maximize data transmission, and compare how this optimal control policy behaves with a finite versus an infinite energy storage system. The resulting off-line control policy provides an upper bound on the performance of a real-time controller, and the analysis can be used for design purposes.

Keywords:Optimal control;Hybrid systems Abstract: This paper deals with robust minimum-time control of a class of asymptotically null-controllable with bounded input planar systems. A hybrid controller is proposed to robustly achieve global finite time stability of a set of points wherein the plant state is zero. The resulting controller provides time optimal response from initial conditions in a certain subset of the state space, and finite time convergence elsewhere. Finally, the effectiveness of the proposed methods is demonstrated in a numerical example.

Keywords:Variational methods, Optimal control;Nonholonomic systems Abstract: We introduce variational obstacle avoidance problems on Riemannian manifolds and derive necessary conditions for the existence of their normal extremals. The problem consists of minimizing an energy functional depending on the velocity and covariant acceleration, among a set of admissible curves, and also depending on a navigation function used to avoid an obstacle on the workspace, a Riemannian manifold.

We study two different scenarios: a general one on a Riemannian manifold and a sub-Riemannian problem. By introducing a left-invariant metric on a Lie group, we also study the variational obstacle avoidance problem on a Lie group. We apply the results to the obstacle avoidance problem of a planar rigid body and a unicycle.

Keywords:Sensor fusion, Game theory, Estimation Abstract: Consider a setup in which a central estimator seeks to estimate an unknown deterministic parameter using measurements from multiple sensors. Some of the sensors may be adversarial in that their utility increases with the Euclidean distance between the estimate of central estimator and their own local estimate. These sensors may misreport their measurements to the central estimator at a falsification cost. We formulate a Stackelberg game in which the central estimator acts as the leader and the adversarial sensors act as the follower. We present the optimal linear fusion scheme for the estimator and the optimal attack pattern for the adversarial sensors in the Nash equilibrium sense. Interestingly, the estimate at the central estimator may be better than if the measurements from the adversarial sensors were altogether ignored.

Keywords:Hybrid systems;Fault diagnosis Abstract: This paper addresses the problem of state estimation of a linear time-invariant system when some of the sensors or/and actuators are under adversarial attack. In our set-up, the adversarial agent attacks a sensor (actuator) by manipulating its measurement (input), and we impose no constraint on how the measurements (inputs) are corrupted. We introduce the notion of ``sparse strong observability" to characterize systems for which the state estimation is possible, given bounds on the number of attacked sensors and actuators. Furthermore, we develop an efficient secure state estimator based on Satisfiability Modulo Theory (SMT) solvers.

Keywords:Estimation, Linear systems, Networked control systems Abstract: We consider the problem of network-based attacks, such as Man-in-the-Middle attacks, on standard state estimators. To ensure graceful control degradation in the presence of attacks, existing results impose very strict integrity requirements on the number of noncompromised sensors. We study the effects of sporadic data integrity enforcement, such as message authentication, on control performance under stealthy attacks. We show that even with sporadic data integrity guarantees, the attacker cannot introduce an unbounded state estimation error while remaining stealthy. We present a design-time framework to derive safe integrity enforcement policies, and illustrate its use; we show that with even 20% of authenticated messages we can ensure satisfiable state estimation errors under attacks.

Keywords:Estimation, Robust control;Fault tolerant systems Abstract: In this paper, we consider the problem of sequential detection with m sensors in adversarial environment. An attacker intends to increase the detection error by modifying n out of m sensors' measurements. On the other hand, the detector needs to be designed to achieve the optimal performance during the attack. The problem is formulated as a game between detector and adversary in this paper. We study both cases where m > 2n and m ≤ 2n, and obtain an equilibrium strategy pair of detection rule and attack scheme for both cases. Furthermore, we investigate the efficiency of our proposed detection strategy in the absence of attacker.

Keywords:Estimation, Kalman filtering, Networked control systems Abstract: We study the problem of remote state estimation, in the presence of a passive eavesdropper. An authorized user estimates the state of an unstable linear plant, based on the packets received from a sensor, while the packets may also be intercepted by the eavesdropper. Our goal is to design a coding scheme at the sensor, which encodes the state information, in order to impair the eavesdropper's estimation performance, while enabling the user to successfully decode the sent messages. We introduce a novel class of codes, suitable for real-time dynamical systems, termed State-Secrecy Codes. By using acknowledgment signals from the user, they apply linear time-varying transformations to the current and previously received states. We prove that under minimal conditions, State-Secrecy Codes achieve perfect secrecy, namely the eavesdropper's minimum mean square error grows unbounded almost surely, while the user's estimation performance is optimal. These conditions require that at least once, the user receives the corresponding packet while the eavesdropper fails to intercept it. The theoretical results are illustrated in simulations.

Keywords:Estimation;Fault detection, Stochastic systems Abstract: This work investigates the effects of signal attacks possibly combined with network deception attacks injecting fake measurements on stochastic cyber-physical systems. The goal of the attacker is to maximize the estimation error based on the information available about the system and the measurement models, preferably without being detected. This problem is formulated following a worst-case approach characterizing the maximum degradation the attacker can induce at each time instant when a Bayesian filter developed within the random finite set (RFS) framework is employed for simultaneous attack detection and resilient state estimation. A novel concept of error which captures the switching (Bernoulli) nature of the signal attack is proposed as an appropriate distance measure for joint detection-estimation. Furthermore, the notion of stealthiness is introduced in order to derive attack policies useful to synthesize undetectable perturbations that can deceive a Maximum A posteriori Probability (MAP) detector implemented for security.

Keywords:Energy systems;Smart grid, Optimization Abstract: Residential Demand Response has emerged as a viable tool to alleviate supply and demand imbalances of electricity during times when the electric grid is strained. Demand Response providers bid reduction capacity into the wholesale electricity market by asking their customers under contract to temporarily reduce their consumption in exchange for a monetary incentive. This paper models consumer behavior in response to such incentives by formulating Demand Response in a Mechanism Design framework. In this auction setting, the Demand Response Provider collects the price elasticities of demand as bids from its rational, profit-maximizing customers, which allows targeting only the users most susceptible to incentives such that an aggregate reduction target is reached in expectation. We measure reductions by comparing the materialized consumption to the projected consumption, which we model as the "10-in-10"-baseline, the regulatory standard set by the California Independent System Operator. Due to the suboptimal performance of this baseline, we show, using consumption data of residential customers in California, that Demand Response Providers receive payments for "virtual reductions", which exist due to the inaccuracies of the baseline rather than actual reductions. Improving the accuracy of the baseline diminishes the contribution of these virtual reductions.

Keywords:Energy systems;Smart grid, Optimization Abstract: Load-serving entities which procure electricity from the wholesale electricity market to service end-users face significant quantity and price risks due to the volatile nature of electricity demand and quasi-fixed residential tariffs at which electricity is sold. This paper investigates strategies for load serving entities to hedge against such price risks. Specifically, we compute profit-maximizing portfolios of forward contract and call options as a function of uncertain aggregate user demand and wholesale electricity prices. We compare the profit to the case of Demand Response, where users are offered monetary incentives to temporarily reduce their consumption during periods of supply shortages. Using smart meter data of residential customers in California, we simulate optimal portfolios and derive conditions under which Demand Response outperforms call options and forward contracts. Our analysis suggests that Demand Response becomes more competitive as wholesale electricity prices increase.

Keywords:Energy systems;Smart grid;Power systems Abstract: We explore the integration of large-scale, grid-level energy storage into wholesale electricity markets. Since the operation of large-scale energy storage may influence wholesale electricity prices, it is important to design proper market integration mechanisms so as to mitigate the price manipulation resulting from strategic storage operation. We conduct a comparative analysis on three natural market mechanisms that have appeared in the literature: i) the centralized mechanism according to which all batteries are centrally operated to minimize the social cost, ii) the semi-centralized mechanism under which the batteries are centrally operated subject to the constraints specified by a single storage owner (on the maximum amount of withdrawn and charged energy in each period), and iii) the deregulated mechanism according to which the storage owner can freely operate batteries so as to maximize her profit. Under some mild assumptions, we establish the equivalence between the semi-centralized and the deregulated mechanisms: the two mechanisms result in the same storage operation and the same dispatch of generation. We conduct numerical experiments on a modified IEEE 14-bus test system to validate the established comparative results.

Keywords:Smart grid, Agents-based systems, Optimization algorithms Abstract: This paper presents distributed algorithms for finite-time convex optimization problems of networked multi-agent systems. The uncertain information comes from the noise corruption or interference in the communication as well as the computation performed by the agents. The objective is to design distributed algorithms such that a team of agents, each with its own private objective function and communicating over an undirected graph, seeks to minimize the sum of all local objective functions in finite time. Specifically, a distributed algorithm with robust consensus strategies is proposed to solve this distributed optimization problem so that the optimal solution can be estimated in finite time. The developed algorithm is applied to the distributed economic dispatch problem in smart grid and it shows that under the proposed algorithms, the optimal solution can be achieved in finite time, while satisfying both the global generation-demand constraints and local generation capacity constraints. Analytical convergence analysis of the developed algorithms is studied for both problems. The effectiveness of the proposed methods is illustrated by examples and numerical simulation.

Keywords:Smart grid;Control applications, Optimization algorithms Abstract: Uncontrolled or improperly controlled electric vehicle (EV) charging can negatively impact electric distribution networks. In this paper, we develop a decentralized event-driven EV charging control scheme to achieve "valley-filling" (i.e., flattening demand profile during overnight charging), meanwhile meeting heterogeneous individual charging requirements and satisfying distribution network constraints. This control scheme is capable of handling EVs' random arrivals and departures. The formulated problem is an optimization problem with a non-separable objective function and strongly coupled inequality constraints. We describe a novel shrunken-primal-dual subgradient (SPDS) algorithm to support the decentralized control scheme, and verify its efficacy and convergence with a simple distribution network model.

Keywords:Smart grid, Game theory, Optimization Abstract: We consider the problem of devising optimal bidding strategies for electricity suppliers in a day-ahead market where each supplier bids a linear non-decreasing function of its generating capacity for each of the 24 hours. The market operator schedules suppliers based on their bids to meet demand during each hour and determines hourly market clearing prices. Each supplier strives to submit bids that maximize her individual profit, conditional upon other suppliers bids. This process achieves a Nash equilibrium when no supplier is motivated to modify her bid. Solving the profit maximization problem requires information of rivals' bids which are typically not available. We develop an inverse optimization approach for estimating rivals' cost functions given historical market clearing prices and production levels, and use these functions to compute the Nash equilibrium bids. We propose sufficient conditions for the existence and uniqueness of the Nash equilibrium, and provide out-of-sample performance guarantees for the estimated cost parameters. Numerical experiments show that our approach achieves higher profit than an alternative approach in the literature, which relies instead on the assumption that other suppliers' bids are normally distributed.

Keywords:Automotive control;Automotive systems, Predictive control for nonlinear systems Abstract: Lean NOx Trap (LNT) is one of the most effective after-treatment technologies used to reduce NOx emissions of diesel engines. One relevant problem in this context is LNT regeneration timing control. This problem is indeed difficult due to the fact that LNTs are highly nonlinear systems, involving complex physical/chemical processes, that are hard to model. In this paper, a novel approach for regeneration timing of LNTs is proposed, allowing us to overcome these issues. This approach, named data-driven model predictive control (D2- MPC), does not require a physical model of the engine/trap system but is based on low-complexity polynomial prediction models, directly identied from data. The regeneration timing is computed through an optimization algorithm, which uses the identified models to predict the LNT behavior. Two D2-MPC strategies are proposed, and tested in a co-simulation study, where the plant is represented by a detailed LNT model, built using the well-known commercial tool AMEsim, and the controller is implemented in Matlab/Simulink.

Keywords:Automotive control, Optimal control Abstract: Diesel engines are of great challenges due to stringent emission and fuel economy requirements. Compared with the conventional turbocharger system, regenerative assisted system provides additional degree of freedoms for the turbocharger speed control. Hence, it significantly improves control capability for exhaust-gas-recirculation (EGR) and boost pressure. This paper focuses on control design for the diesel engine air-path system equipped with an EGR subsystem and a variable geometry turbocharger (VGT) coupled with a regenerative hydraulic assisted turbocharger (RHAT). The challenges lie in the inherent coupling among EGR, turbocharger performance, and high nonlinearity of engine air-path system. A linear quadratic (LQ) controller design approach is proposed in this paper for regulating the EGR mass flow rate and boost pressure simultaneously and the resulting closed-loop system performance can be tuned by properly selecting the LQ weighting matrices. Multiple LQ controllers with integral action are designed based on the linearized system models over a gridded engine operational map and the final gain-scheduling controller for a given engine operational condition is obtained by interpreting the neighboring LQ controllers. The gain-scheduling LQ controllers for both traditional VGT-EGR and VGT-EGR-RHAT systems are validated against the in-house baseline controller, consisting of two single-input and single-output controllers, using the nonlinear plant. The simulation results show that the designed multi-input and multi-output LQ gain-scheduling controller is able to manage the performance trade-offs between EGR mass flow and boost pressure tracking. With the additional assisted and regenerative power on turbocharger shaft for the RHAT system, engine transient boost pressure performance can be significantly improved without compromising the EGR tracking performance, compared with the baseline control.

Keywords:Automotive control;Control applications, Stochastic optimal control Abstract: We propose a cloud-aided scheme for electronically controlled suspensions. The cloud hosts a position dependent road model estimated from car measurements, which is used on the vehicle to parametrize a stochastic model predictive controller (MPC). Improving the current state of the art in suspension control is hindered by several factors. Suspension control faces an inherent trade-off between passenger comfort, road holding and suspension limits, and finding meaningful tuning can be a struggle with basic control techniques; uncertainty on the road conditions and actuators saturations further complicate the picture. We show how a stochastic MPC formulation can meaningfully handle these compromises, and how a cloud-aided update of the road model helps to maximize performance.

Keywords:Automotive control;Human-in-the-loop control, Constrained control Abstract: An assistant control scheme for the dynamic model of a car to help the driver track a given reference or to keep the car in a given lane while making sure that all the system states satisfy pre-defined constraints is given. The assistant control algorithm is based on a hysteresis switch and the formal properties of the closed-loop system are studied via a Lyapunov-like analysis. Simulation results showing the effectiveness of the driving assistance system are presented.

Keywords:Automotive control;Hybrid systems;Mechatronics Abstract: We consider the set-point regulation of a non-standard hydro-pneumatic suspension architecture used in commercial tractors, which allows regulating both the stroke and the pressure in the suspension. The model reveals an affine dynamic comprising two single integrators whose actuation is performed by way of suitably switching constant input selections. We design the switching input using a hybrid representation, providing necessary and sufficient conditions for the global stabilizability. Two constructive hybrid control laws are proposed: the first one solves the stabilization problem, while the second can be used to suitably reduce the number of switches of the input, thereby limiting the aging of the actuators. Both control laws are tested in simulation and assessed in terms of performance and robustness in the presence of parametric uncertainties.

Keywords:Automotive control;Mechatronics, Pattern recognition and classification Abstract: Knock is an undesired phenomenon occurring in spark ignited engines and is controlled acting on the spark timing. This paper presents a closed-loop architecture that makes possible to address the knock control problem with a standard model-based design approach. An engine knock margin estimate is feedback controlled through a PI regulator and its target value is computed starting from the desired knock probability. A black-box modelling approach is used to identify the dynamics between the spark timing and the knock margin and a traditional model-based controller synthesis is performed. Experimental results at the test bench show that, compared to a conventional strategy, the proposed approach allows for a better compromise between the controller speed and the variability of the spark timing. Moreover, another advantage w.r.t. the conventional strategies is that closed-loop performance prove to be constant for different reference probabilities, leading to a more regular engine behaviour.

Keywords:Adaptive control, Control applications, Estimation Abstract: Active ankle-foot orthoses are used to assist patients suffering from stroke, cerebral palsy etc. through providing them an external force supply to track normal gait cycles. In this paper, we propose a novel backstepping control design for active ankle-foot orthoses to track desired gait trajectories and to reduce the effects of unknown disturbances such as ground reaction force and weight of the foot. The actual system is modeled as two-degree-of-freedom mass-spring system. Disturbances are modeled as a finite sum of sinusoidal signals with unknown amplitudes, frequencies and phases, and an unknown constant. An adaptive backstepping control law is designed for force input to the system. It is proved that the equilibrium of the closed loop system is stable, and vertical position of the patient's heel tracks the desired trajectory. Finally, simulations are performed to show superiority of the proposed control architecture over a PID control.

Keywords:Adaptive control;Delay systems, Stochastic systems Abstract: Global adaptive control problem is addressed for switched stochastic time-delay nonlinear systems with uncertain output function and unknown nonlinear growth rates. By adding a power integrator technique, a delay-independent adaptive output-feedback controller is designed. According to Lyapunov-Krasovskii stability theorem, it is shown that all the states of switched stochastic time-delay nonlinear system asymptotically converge to zero almost surely while maintaining boundedness of the closed-loop system in probability. An example is provided to illustrate the validity of the proposed control method.

Keywords:Adaptive control, Estimation;Flight control Abstract: This paper presents an adaptive controller design for the attitude and altitude of UAV quadrotors which are subjected to wind disturbances. During the design, it is assumed that the total mass, inertia tensor, the arms’ length of the quadrotor and the thrust and drag coefficients of the propellers attached on the quadrotor are unknown. Moreover, the wind disturbances are assumed as a finite sum of sinusoidal functions with unknown frequencies, amplitudes and phases. It is proved that the equilibrium of the closed loop error system is stable, all signals are bounded and desired altitude and attitude control are achieved despite unknown wind disturbance and plant parameters. Finally, a simulation is performed to show the feasibility of the design.

Keywords:Adaptive control;Fault tolerant systems, Autonomous robots Abstract: This paper develops an adaptive actuator failure compensation scheme for landing of a helicopter with robotic legs. The adaptive control design uses an integration of multiple failure compensator controllers designed for each actuator failure pattern. Such a design effectively utilizes the actuation redundancy of the robotic manipulators, using for landing of a helicopter, to compensate for possible actuator failures with no knowledge of actuator failure pattern, failure time instant and failure values. With complete parameterization of system and actuator failure uncertainties and direct adaptation of controller parameters, the adaptive control scheme guarantees desired closed-loop stability and asymptotic output tracking, despite uncertain actuator failures. Simulation results are presented to verify the desired control system performance.

Keywords:Adaptive control, Linear systems;Distributed parameter systems Abstract: We solve an adaptive disturbance rejection problem for a class of linear 2 x 2 hyperbolic partial differential equations (PDEs) with uncertain system parameters, from a single boundary measurement anti-collocated with the actuation. The disturbance contains biased oscillators. This is done by transforming the system into a canonical form, from which filters are designed so that the states can be expressed as linear combinations of the filters and uncertain parameters, a representation facilitating for the design of adaptive laws. A stabilizing controller is then combined with the adaptive laws to achieve asymptotic convergence to zero of the measured signal, and pointwise boundedness of all signals in the closed loop. The theory is demonstrated in a simulation.

Keywords:Adaptive control, Linear systems, Optimal control Abstract: This paper develops disturbance rejection control schemes using a control separation based LQ design for output tracking of linear multivariable possibly nonminimum-phase systems with unmatched disturbances. A control separation based LQ control framework is constructed for rejection of unmatched disturbances and tracking of a reference signal. A three-component control signal is generated from such a LQ design with a new cost function, for desired system stability, disturbance rejection and output tracking. Using dynamic programming, finite-time and infinite-time control schemes are developed in details. A comparison with a traditional LQ control design is studied to show the advantages of the new control separation based LQ control method. Simulation results are presented to verify the effectiveness of the proposed LQ control based disturbance rejection method.

Keywords:Automotive control, Autonomous robots;Control applications Abstract: We consider a steering plan for an autonomous car as a function of path length. The initial state of a car is composed of its position, direction, and curvature corresponding to its front-wheel direction. In the case that the final state of the steering plan is taken as one point on a curved road, not only the position but also the direction of the car and curvature corresponding to the curved road are specified. Defining posture as a state that consists of the car's position, direction, and curvature, we consider this steering plan as a trajectory plan from the start posture to the end posture. In cars, the upper and lower limits of allowable curvature exist due to the minimum turning radius of the cars. Lateral acceleration and jerk, which affect ride quality, are respectively proportional to curvature and sharpness, which is the rate of change of curvature. We chose clothoid segments, for which curvature and sharpness are easily adjusted, as components of a trajectory. Single or double clothoid segments are not flexible enough to match the end posture. We propose a trajectory planning method that uses triple clothoid segments whose lengths are variable and introduce a four-parameter model for this method. We moreover show a concrete numerical solution method based on an optimization problem framework.

Keywords:Autonomous robots, Optimization, Distributed control Abstract: This paper studies the multi-vehicle task assignment problem where several dispersed vehicles need to visit a set of target locations in a time-invariant drift field with obstacles while trying to minimize the total travel time. The vehicles have different capabilities, and each kind of vehicles need to visit a certain type of target locations; each target location might have the demand to be visited more than once by different kinds of vehicles. To find approximate solutions for such a challenging problem, we first design a path planning algorithm to minimize the time for a single vehicle to travel between two given locations through the drift field while avoiding obstacles. The path planning algorithm provides the travel cost matrix for the target assignment, and generates routes once the target locations are assigned to the vehicles. Then, we propose an auction-based distributed task assignment algorithm to assign the target locations to the vehicles using only local communication. Finally, numerical simulations show that the algorithm can lead to solutions close to the optimal.

Keywords:Autonomous robots, Autonomous vehicles;Robotics Abstract: The paper presents a systematic strategy for implementing Hilberts space filling curve for use in online exploration tasks and addresses its application in scenarios wherein the space to be searched obstacles (or holes) whose locations are not known a priori. Using the self-similarity and locality preserving properties of Hilberts space filling curve, a set of evasive maneuvers are prescribed and characterized for online implementation. Application of these maneuvers in the case of non-uniform coverage of spaces and for obstacles of varying sizes is also presented. The results are validated with representative simulations demonstrating the deployment of the approach.

Keywords:Autonomous robots, Autonomous vehicles, Uncertain systems Abstract: Safety is the most important aspect of systems which have to perform collision-free motions in dynamic environments. Formal verification methods, such as reachability analysis, are capable of guaranteeing safety for a given model and given assumptions (e.g. bounded velocity and acceleration). However, certain assumptions can be violated by dynamic obstacles during the execution of the verified motion plan, exposing the system to potential collisions. To compensate for the invalidated verification, this paper introduces the Point of No Return (PNR) and the Point of Guaranteed Arrival (PGA) by incorporating invariably safe sets. These concepts allow one to divide the planned trajectory into safe sections and safety-critical passageways. For the former, we are able to provide safety guarantees for an infinite time horizon. For the latter, we present a method to minimize such safety-critical passageways prior to execution and thus reduce the risk of potential collisions if assumptions are violated during execution. The safety benefits are highlighted by a numerical example of overtaking maneuvers of self-driving vehicles.

Keywords:Autonomous robots, Cooperative control, Machine learning Abstract: We study the sparsity and optimality properties of crowd navigation and find that existing techniques do not satisfy both criteria simultaneously: either they achieve optimality with a prohibitive number of samples or tractability assumptions make them fragile to catastrophe. For example, if the human and robot are modeled independently, then tractability is attained but the planner is prone to overcautious or overaggressive behavior. For sampling based motion planning of joint human-robot cost functions, for nt agents and T step lookahead, O(2^{2ntT}) samples are needed for coverage of the action space. Advanced approaches statically partition the action space into free-space and then sample in those convex regions. However, if the human is moving into free-space, then the partition is misleading and sampling is unsafe: free space will soon be occupied. We diagnose the cause of these deficiencies—optimization happens over trajectory space—and propose a novel solution: optimize over trajectory distribution space by using a Gaussian process (GP) basis. We exploit the “kernel trick” of GPs, where a continuum of trajectories are captured with a mean and covariance function. By using the mean and covariance as proxies for a trajectory family we reason about collective trajectory behavior without resorting to sampling. The GP basis is sparse and optimal with respect to collision avoidance and robot and crowd intention and flexibility. GP sparsity leans heavily on the insight that joint action space decomposes into free regions; however, the decomposition contains feasible solutions only if the partition is dynamically generated. We call our approach O(2^nt)-sparse interacting Gaussian processes.

Keywords:Autonomous robots;Hybrid systems, Computational methods Abstract: Planning trajectories for multiple agents in a way to guarantee that their collective behavior satisfies a certain high-level specification is crucial in many application domains. Motivated by this problem, we introduce a new logic called counting linear temporal logic plus (cLTL+). This logic enables specifying multi-agent tasks over possibly infinite horizons in a compact manner. We then propose an optimization-based method that generates trajectories for individual agents that, when implemented together, guarantee the satisfaction of a given cLTL+ formula. In the second part of the paper, we discuss how these results can be extended to generate trajectories that can be asynchronously implemented by the agents while preserving the satisfaction of the desired cLTL+ specification. In particular, we show that when the asynchrony between agent trajectories is bounded, it is possible to generate trajectories robust against such asynchrony with an appropriate modification of the optimization problem. Finally, we demonstrate these ideas on selected examples.

Keywords:Estimation, Kalman filtering, Distributed control Abstract: This work considers the problem of selecting sensors in large scale system to minimize the state estimation mean-square error (MSE). More specifically, it leverages the concept of approximate supermodularity to derive near-optimality certificates for greedy solutions of this problem in the context of Kalman filtering. It also shows that in typical application scenarios, these certificates approach the typical 1/e guarantee. These performance bounds are important because sensor selection problems are in general NP-hard. Hence, their solution can only be approximated in practice even for moderately large problems. A common way of deriving these approximations is by means of convex relaxations. These, however, come with no performance guarantee. Another approach uses greedy search, although also in this case typical guarantees do not hold since the MSE is neither submodular nor supermodular. This issue is commonly addressed by using a surrogate supermodular figure of merit, such as the logdet. Unfortunately, this is not equivalent to minimizing the MSE. This work demonstrates that no change to the original problem is needed to obtain performance guarantees.

Keywords:Estimation;Automotive systems, Neural networks Abstract: This paper deals with sideslip angle estimation of powered two-wheeled vehicles. Since available sensors used to directly measure this variable are bulky and expensive, estimation algorithms based on on-board measurements have been developed. These algorithms are mainly devoted to four-wheeled vehicles whereas the sideslip estimation for two-wheeled vehicles is still an open topic. This paper presents a Neural Network estimation algorithm that uses on-board standard measures available in modern motorbikes and studies the role of the most significant signals for the estimation. The employed black-box approach does not require the derivation of any physics-based model of the motorcycle dynamics and thus is meant as a valid tool for a preliminary insight in such estimation problem. The experimental data collected cover a rich amount of manoeuvres that are used to train the network and several other manoeuvres have been used to analyse its performances.

Keywords:Estimation, Kalman filtering, Filtering Abstract: This paper investigates fundamental performance bounds on estimation error for general state estimation systems that are not necessarily linear time invariant with noises that are not necessarily white Gaussian. In the analysis, concepts from information theory such as entropy play an instrumental role. We first propose an information-theoretic notion termed Gaussianity-whiteness to measure how Gaussian and white an asymptotically stationary stochastic process is. Subsequently, we derive lower bounds on estimation error variance which can be quantified explicitly by the Gaussianity-whiteness of the noises. Furthermore, the bounds are found to be tight in the particular case of a scalar linear time-invariant system with white Gaussian noises, as verified by the benchmark given by the renowned Kalman filter.

Keywords:Estimation, Communication networks, Statistical learning Abstract: We consider the problem of estimating functions in a Gaussian regression distributed and nonparametric framework where the unknown map is modeled as a Gaussian random field whose kernel encodes expected properties like smoothness. We assume that some agents with limited computational and communication capabilities collect M noisy function measurements on input locations independently drawn from a known probability density. Collaboration is then needed to obtain a common and shared estimate. When the number of measurements M is large, computing the minimum variance estimate in a distributed fashion is difficult since it requires first to exchange all the measurements and then to invert an M times M matrix. A common approach is then to circumvent this problem by searching a suboptimal solution within a subspace spanned by a finite number of kernel eigenfunctions. In this paper we analyze this classical distributed estimator, and derive a rigorous probabilistic bound on its statistical performance that returns crucial information on the number of measurements and eigenfunctions needed to obtain the desired level of estimation accuracy.

Keywords:Estimation, Modeling, Markov processes Abstract: This paper derives stochastic realisation algorithms for a class of Gaussian Generalised Reciprocal Processes (GGRP). The paper exploits the interplay between reciprocal processes and Markov bridges which underpin the GGRP model, to derive forwards-backwards state equations for realisation of a GGRP. The form on the inverse covariance matrix for the GGRP is derived, and its Cholesky factorisation can used to also construct the optimal (MMSE) smoother of GGRP observed in noise. The paper claims that the associated smoothing error is also a GGRP with known covariance which may be used to assess the performance of smoothing as a function of the model parameters. Full details are provided in a forthcoming journal paper.

Keywords:Aerospace, Sensor networks, Estimation Abstract: GNSS denied IMU correction is a practical challenge in aerospace vehicle navigation. In the context of several vehicles flying in formation, navigation accuracy can be enhanced by communication between the vehicles. In this paper, a collaborative navigation strategy is presented to deal with coarse and ambiguous measurements. An absolute navigation filter provides a first estimate of the navigation solution, while a relative observer rebuilds the neighbors relative states from embedded seekers. A high-level Master Filter fuses information provided by those two low-level filters to enhance the navigation solution. Absolute navigation measurements are terrain elevation data correlated with a Digital Elevation Model map. Since they are highly ambiguous and nonlinear, they are processed by a Box Regularized Particle Filter. The relative measurements under consideration suffer a high level of uncertainty, especially on the relative distance between vehicles. By fusing all uncertain data, a complete and accurate navigation solution is obtained. Numerical results are presented and show an enhancement in navigation performance by exchanging information, in terms of RMS estimation error (63% more accurate in position), estimation confidence (78% more precise in position), and computational load (requires 83% less operations).

Keywords:Agents-based systems, Autonomous systems, Cooperative control Abstract: This paper proposes a continuous-time model for aggregating a team of agents in k-dimensional space and for establishing a reference tracking. Since the model is of kinematic nature, each agent is considered as an ideal point communicating without delay with the other components of the team. The proposed model ensures that the agents centroid path converges in finite-time to the imposed trajectory while the agents aggregate in finite-time in a hyper-ball moving around the reference path. The dimension of the hyper-ball is modulated by varying one of the free parameters of the model. This fact guarantees that the swarm can reduce or enlarge its dimension according to the environment in which it moves. Conditions are also provided to guarantee absence of agents clashes and static swarm configuration around the performed path.

Keywords:Agents-based systems, Autonomous systems;Robotics Abstract: This paper presents a persistent coverage algorithm for multiple agents subject to 3-D rigid body kinematics. Each agent uses a forward-facing sensing footprint, modeled as an anisotropic spherical sector, to cover a 2-D manifold. The manifold is subject to continual collisions by high speed particles. Particle trajectories are estimated online with an extended Kalman filter using noisy spherical coordinate position measurements. Predicted impact points for each particle, along with associated covariances, are used to generate normally distributed coverage decay. This directs agents to explore in the vicinity of both future and past impact points. The efficacy of the algorithm is demonstrated through simulation.

Keywords:Agents-based systems, Autonomous vehicles, Variable-structure/sliding-mode control Abstract: This paper investigates the adaptive platoon control for nonlinear vehicular systems with asymmetric nonlinear input deadzone and inter-vehicular spacing constraints. Vehicular platoon control encounters great challenges from unmodeled dynamic uncertainties, unknown external disturbances, unknown asymmetric nonlinear input deadzone and inter-vehicular spacing constraints. In order to avoid collisions between consecutive vehicles as well as the connectivity breaks owing to limited sensing capabilities, a symmetric barrier Lyapunov function is employed. Then, a neural-network-based terminal sliding mode control (TSMC) scheme with minimal learning parameters is developed to maintain inter-vehicles keep connectivity and imultaneously avoid collisions. The uniform ultimate boundedness of all signals in the whole vehicular platoon control system is proven via Lyapunov analysis. Finally, a numerical example is proposed to show the effectiveness of the proposed scheme.

Keywords:Agents-based systems, Compartmental and Positive systems, Sensor networks Abstract: In this paper, we propose a distributed estimation architecture for a class of networked systems characterized by three distinct groups of nodes: plants, sensors and agents. We address the problem of fusing information on the plants, provided by the sensors to the agents, via a formal analysis of the trustworthiness concept. To this end, the scheme exploits the trust arising amongst agent and sensor groups, which is evaluated by means of a novel adaptive reputation mechanism built-up with the aim of intercepting the sensor unit that maximizes a Quality of Service performance. Steady-state conditions of the trust model and convergence properties of the resulting estimation scheme are formally proved. A final example is provided to exemplify the use of the scheme.

Keywords:Agents-based systems, Cooperative control, Autonomous systems Abstract: Formation control is a key problem in the coordination of multiple agents. It arises new challenges to traditional formation control strategy when the communication among agents is affected by uncertainties. This paper considers the robust multi-task formation control problem of multiple non-point agents whose communications are disturbed by uncertain parameters. The control objectives include 1. achieving the desired configuration; 2. avoiding collisions; 3. preserving the connectedness of uncertain topology. To achieve these objectives, first, a condition of Linear Matrix Inequality (LMI) is proposed for checking the connectedness of an uncertain communication topology. Then, by preserving the initial topological connectedness, a gradient-based distributed controller is designed via Lyapunov-like barrier functions. Two numerical examples illustrate the effectiveness of the proposed method.

Keywords:Agents-based systems, Cooperative control, Autonomous systems Abstract: This paper addresses the problem of position- and orientation-based formation control of a class of second-order nonlinear multi-agent systems in a 3D workspace with obstacles. More specifically, we design a decentralized control protocol such that each agent achieves a predefined geometric formation with its initial neighbors, while using local information based on a limited sensing radius. The latter implies that the proposed scheme guarantees that the initially connected agents remain always connected. In addition, by introducing certain distance constraints, we guarantee inter-agent collision avoidance as well as collision avoidance with the obstacles and the boundary of the workspace. Finally, simulation results verify the validity of the proposed framework.

Keywords:Cellular dynamics, Systems biology, PID control Abstract: Feedback regulation in biochemical systems is fundamental to cellular homeostasis, with failure causing disease or death. Recent work has found that cooperation between feedback and buffering---the use of reservoirs of molecules to maintain molecular concentrations---is often critical for biochemical regulation, and that buffering can act as a derivative or lead controller. However, buffering differs from derivative feedback in important ways: it is not typically limited by stability constraints on the parallel feedback loop, for some signals it acts instead as a low-pass filter, and it can modify the topology of the closed-loop system. Here, we propose a frequency-domain framework for studying the regulatory properties of buffer-feedback systems. We determine standard single-output closed-loop transfer functions, discuss loop-shaping properties, and show that buffering can remove fundamental limits on feedback regulation. We apply the framework to study the fundamental limits of regulation for glycolysis (anaerobic metabolism) with creatine phosphate buffering.

Keywords:Genetic regulatory systems, Systems biology, Biomolecular systems Abstract: Time-series of high throughput gene sequencing data intended for gene regulatory network (GRN) inference are often short due to the high costs of sampling cell systems. Moreover, experimentalists lack a set of quantitative guidelines that prescribe the minimal number of samples required to infer a reliable GRN model. We study the temporal resolution of data vs quality of GRN inference in order to ultimately overcome this deficit. The evolution of a Markovian jump process model for the Ras/cAMP/PKA pathway of proteins and metabolites in the G1 phase of the Saccharomyces cerevisiae cell cycle is sampled at a number of different rates. For each time-series we infer a linear regression model of the GRN using the LASSO method. The inferred network topology is evaluated in terms of the area under the precision-recall curve (AUPR). By plotting the AUPR against the number of samples, we show that the trade-off has a, roughly speaking, sigmoid shape. An optimal number of samples corresponds to values on the ridge of the sigmoid.

Keywords:Nonlinear systems identification, Systems biology, Machine learning Abstract: Network reconstruction has become particularly important in systems biology, and is now expected to deliver information on causality. Systems in nature are inherently nonlinear. However, for nonlinear dynamical systems with hidden states, how to give a useful definition of dynamic networks is still an open question. This paper presents a useful definition of Boolean dynamic networks for a large class of nonlinear systems. Moreover, a robust inference method is provided. The well-known Millar-10 model in systems biology is used as a numerical example, which provides the ground truth of causal networks for key mRNAs involved in eukaryotic circadian clocks. In addition, as second contribution of this paper, we suggest definitions of linear network identifiability, which helps to unify the available work on network identifiability.

Keywords:Systems biology, Biomolecular systems Abstract: The analysis of cardiac damage biomarkers is crucial in the diagnosis and prognosis of acute myocardial infarction. The present work proposes a dynamical model for the analysis of the release in the blood of cardiac troponin T (cTnT). The model, tested against patients data, proves to be an effective tool to extrapolate information of interest to the clinician, like peaks and peak-times of the release curve. Furthermore, the model has been proven efficient to quantitatively differentiate patients with effective and non-effective thrombolysis response, which is a key information to guide revascularization.

Keywords:Systems biology, Stochastic systems, Metabolic systems Abstract: This note investigates a basic enzymatic scheme, with a substrate transforming into a product by means of the catalytic action of an enzyme. The focus is in the role of a feedback regulating the enzyme production. The novelty of the paper is in the choice of the feedback, acting from substrate accumulation differently from previous cases already studied in the literature, where the feedback acts from the product or from the enzyme. The feedback scheme is studied according to both a deterministic and stochastic approach: the former providing the existence of a unique meaningful asymptotically stable equilibrium; the latter investigating how noise propagates with or without the feedback. Regards to the stochastic approach, the metabolic noise is evaluated in terms of the coefficient of variation of the product of the enzymatic reaction, aiming at measuring its fluctuations around the average steady-state. Numerical results are carried out according to Chemical Master Equations, showing a clear improvement, in terms of noise reduction, when the negative feedback is applied. Linear Noise Approximation has been as well exploited with the aim of finding analytical solutions for the metabolic noise, relating it to the model parameters.

Keywords:Systems biology, Stochastic systems, Metabolic systems Abstract: A metabolic pathway made of a cascade of biochemical reactions is considered, with a substrate which is eventually transformed into the final product by means of a sequence of reactions, each catalyzed by the same enzyme. The amount of the enzyme varies according to discrete noisy processes of production and elimination. A feedback acts on the final product clearance rate, exerted by the final product accumulation itself: higher final product levels lead to a faster dynamics. The aim of this note is to investigate how the noise scales with the length of the cascade and how the feedback impacts on the noise propagation. To this end, a Stochastic Hybrid System (SHS) formulation is exploited, with the enzyme production/clearance processes constituting the noise source. The noise propagation is measured in terms of the square of the coefficient of variation of the final product, and computations are carried out by means of the equations of moments, which are estimated in closed form after linearizing the SHS. Analytical solutions allow to infer information and to relate the noise propagation to the model parameters. Similarly to recent results occurring in other types of enzymatic reactions, the results highlight the influential role of feedback in noise reduction.

Keywords:Optimization Abstract: It is well-known that any sum of squares (SOS) program can be cast as a semidefinite program (SDP) of a particular structure and that therein lies the computational bottleneck for SOS programs, as the SDPs generated by this procedure are large and costly to solve when the polynomials involved in the SOS programs have a large number of variables and degree. In this paper, we review SOS optimization techniques and present two new methods for improving their computational efficiency. The first method leverages the sparsity of the underlying SDP to obtain computational speed-ups. Further improvements can be obtained if the coefficients of the polynomials that describe the problem have a particular sparsity pattern, called chordal sparsity. The second method bypasses semidefinite programming altogether and relies instead on solving a sequence of more tractable convex programs, namely linear and second order cone programs. This opens up the question as to how well one can approximate the cone of SOS polynomials by second order representable cones. In the last part of the paper, we present some recent negative results related to this question.

Keywords:Decentralized control, Networked control systems, Network analysis and control Abstract: A broad class of networks of linear control systems is characterized by a unit time delay in communication between neighboring systems. Whenever the local systems are structurally controllable and observable, a generic decentralized dynamic feedback law ensures that each strongly connected component of such a network is structurally controllable and observable from any local plant-controller pair within the component. This leads to a simple pole placement design procedure that ensures generic, arbitrary assignability of the closed-loop system eigenvalues via decentralized dynamic feedback control regardless of the communication topology.

Keywords:Network analysis and control, Agents-based systems, Large-scale systems Abstract: We consider a network of interconnected dynamical systems. Spectral network identification consists in recovering the eigenvalues of the network Laplacian from the measurements of a very limited number (possibly one) of signals. These eigenvalues allow to deduce some global properties of the network, such as bounds on the node degree. Having recently introduced this approach for autonomous networks of nonlinear systems, we extend it here to treat networked systems with external inputs on the nodes, in the case of linear dynamics. This is more natural in several applications, and removes the need to sometimes use several independent trajectories. We illustrate our framework with several examples, where we estimate the mean, minimum, and maximum node degree in the network. Inferring some information on the leading Laplacian eigenvectors, we also use our framework in the context of network clustering.

Keywords:Network analysis and control, Decentralized control, Agents-based systems Abstract: The paper provides consensus value estimates in multi-agent systems with directed and time-varying interaction networks. First, we prove general results regarding the asymptotic consensus value which is obtained as a convex combination of the initial states. It is shown that the cut-balance assumption guarantees a strictly positive lower bound on the convex combination components. This means that each agent plays a non vanishing role in the asymptotic consensus value. Second, we analyze the case where interaction weights vary uniformly over time. Finally, we study the effect of time-vanishing perturbations on the systems with uniform variation of the interaction weights. We show that the convex combination components vary smoothly with the perturbation under smooth and sufficiently fast vanishing perturbations. Moreover, we show that in this case, these components reach a limit when time goes to infinity. We also provide an example where this limit does not exist when the perturbation does not respect the fast vanishing assumption although the system itself converges to a consensus. Some numerical examples illustrate our results.

Keywords:Network analysis and control, Algebraic/geometric methods, Optimization Abstract: Synchronization is crucial for the correct functionality of many natural and man-made complex systems. In this work we characterize the formation of synchronization patterns in networks of Kuramoto oscillators. Specifically, we reveal conditions on the network weights, structure and on the oscillators natural frequencies that allow the phases of a group of oscillators to evolve cohesively, yet independently from the phases of oscillators in different clusters. Our conditions are applicable to general directed and weighted networks of heterogeneous oscillators. Surprisingly, although the oscillators exhibit nonlinear dynamics, our approach relies entirely on tools from linear algebra and graph theory. Further, we develop a control mechanism to determine the smallest (as measured by the Frobenius norm) network perturbation to ensure the formation of a desired synchronization pattern. Our procedure allows us to constrain the set of edges that can be modified, thus enforcing the sparsity structure of the network perturbation. The results are validated through a set of numerical examples.

Keywords:Network analysis and control, Control of networks, Decentralized control Abstract: A classical model for coupled dynamical systems with identical linear components and structured linear couplings is enhanced to capture measurement and actuation of by an external player. Input-output properties of the enhanced model -- including observability and controllability, decentralized fixed modes, and output controllability -- are determined in terms of the components' internal dynamics, the network's interconnection topology, and the structured interfaces between components. Further analyses are also developed for the special case that the components are subsystems, which are coupled only through their inputs and outputs. As an illustration, these structural characterizations are used to study the manipulation of a canonical multi-agent-system model, namely a double-integrator-network model, by an external player.

Keywords:Network analysis and control, Control of networks, Distributed control Abstract: This paper presents a novel approach to form an interdependent network model from time-varying system data. The research incorporates system meta-data using k -means clustering to form a layered structure within the dynamics. To compactly encode the layering, a Cartesian product model is fit to time-varying data using convex optimization. We show that under special situations a closed form solution of this model can be acquired. The Cartesian form is particularly conducive to reasoning about the role of the interdependent network layers within the dynamics. This is illustrated through the derivation of a distributed LQR controller which requires only knowledge of local layers in the network to apply. To demonstrate the applicability of this work, the proposed methods and analysis is applied to time-series data from a high-fidelity interdependent infrastructure network simulation

Keywords:Robust control, Uncertain systems, Lyapunov methods Abstract: We have recently considered the problem of tuning a static plant described by a differentiable input-output function, which is completely unknown, but whose Jacobian takes values in a known polytope of matrices: to drive the output to a given desired value, we have suggested an integral feedback scheme, whose convergence is ensured if the polytope of matrices is robustly full row rank. The suggested tuning scheme may fail in the presence of parasitic dynamics, which may destabilize the loop if the tuning action is too aggressive. Here we show that such tuning action can be applied to dynamic plants as well if it is sufficiently "slow", a property that we can ensure by limiting the integral action. We provide robust bounds based on the exclusive knowledge of the largest time constant and of the matrix polytope to which the system Jacobian is known to belong. We also provide similar bounds in the presence of parasitic dynamics affecting the actuators.

Keywords:Uncertain systems, Computer-aided control design, LMIs Abstract: Polynomial chaos theory provides a computationally efficient tool for control system design subject to probabilistic parametric uncertainties. In most existing methods, Galerkin projection is used to approximate the original stochastic system by a deterministic projected system of higher dimensions, so that control synthesis can be performed within the projected space. These methods have two main limitations: (i) a nonconvex optimization problem is obtained for control synthesis; and (ii) due to approximation errors, stability derived for the projected approximation may not be automatically achieved by the original system. In this article, a new polynomial chaos based approach is proposed for stochastic discrete-time linear quadratic regulation. Instead of approximating the original system with Galerkin projection, a guaranteed cost problem is formulated and then approximated by using polynomial chaos. A tuning parameter is introduced to explicitly account for the approximation errors. A semidefinite program is then derived by exploiting orthogonality of the polynomial bases, in contrast to the non-convex optimization obtained by the Galerkin projection based methods. In particular, the general nonlinear parametric dependence can be effectively addressed by using its piecewise polynomial approximation. A numerical example illustrates the efficacy of our proposed approach.

Keywords:Uncertain systems, Optimization;Supervisory control Abstract: Aspects of a Stochastic MPC approach to water-level planning for automated irrigation channels are studied in this paper. Given an uncertain schedule of flow demands and a model of the channel dynamics under low-level feedback control, the planning problem is to determine water-level references that lead to the satisfaction of chance-constraints on the transient response to changes in flow load, as demand varies across time in a way that it can deviate from the schedule. Stochastic MPC is a receding horizon, optimal control based approach to solving such problems. The chance-constrained optimisation problems involved are difficult to solve in general, and a scenario based approach is typically used to find approximate solutions. The main contribution of the paper is an efficient reformulation of the scenario optimisation problem by discarding redundant scenarios to further reduce the computational cost. The approach is applicable to linear systems with an uncertain additive input. The proposed strategy is applied to an automated irrigation channel in a simulation example.

Keywords:Uncertain systems, Linear parameter-varying systems, Robust control Abstract: This paper addresses the design problem of continuous-time Gain-Scheduled (GS) controllers comprising GS observers and GS state-feedback controllers for continuous-time Linear Parameter-Varying (LPV) systems. In most of GS controller design for practical systems, several uncertainty blocks are introduced to represent various control requirements, similarly to scaled H infinity controller design. Then, the design problem of GS output feedback controllers is formulated in terms of a non-convex problem due to the simultaneous design of the scaling matrices for the multiple uncertainty blocks. For this practical design problem, we propose a design method in which GS observer and GS state-feedback gains as well as constant scaling matrices are simultaneously optimized by using dilated Linear Matrix Inequality (LMI) technique with some structural constraints for the matrices introduced in the dilation procedure. We also derive a design method for the same problem but only inexact scheduling parameters are available. A numerical example well demonstrates the effectiveness of our method with respect to the simultaneous design.

Keywords:Uncertain systems, Nonlinear output feedback, Robust control Abstract: The article revisits Aizerman and Kalman conjectures for absolute stability through the lens of a novel graphical interpretation. Even though these conjectures are false in the general case, such a graphical interpretation suggests natural ways to introduce additional conditions in order to obtain valid absolute stability criteria. As an illustration, the article proves a new absolute stability criterion obtained by the iterative application of a variation of the circle criterion.

Keywords:Uncertain systems, Optimal control, Adaptive control Abstract: Modern dynamical systems often operate in environments of high-dimensional uncertainties that modulate system dynamics in a complicated fashion. These high-dimensional uncertainties, non-Gaussian in many realistic scenarios, complicate real-time system analysis, design and control tasks. In this paper, we address the scalability of computation for systems of high-dimensional uncertainties by introducing new sampling methods, the multivariate probabilistic collocation method (M-PCM) and its extension called M-PCM-OFFD which integrates M-PCM with the orthogonal fractional factorial designs (OFFDs) to break the curse of dimensionality. We explore the capabilities of M-PCM and M-PCM-OFFD based optimal control and adaptive control using the reinforcement learning approach. The analyses and simulation studies illustrate the efficiency and effectiveness of these two approaches.

Keywords:Robust control, Linear systems;Supervisory control Abstract: In this paper, we investigate the reachability analysis and safety controller synthesis problem for linear discrete-time systems under additive bounded disturbances. We consider the following problem; design a state feedback controller such that any state trajectories starting from an initial set can be robustly controlled towards a target one in finite time, while at the same time avoiding any prohibited regions. One of the potential disadvantages of existing reachability algorithms when external disturbances are taken into account, may be that the solution to guarantee reachability becomes conservative. Motivated by this, this paper provides a new controller synthesis framework based on the notion of tube-based control strategy, in which a suitable sequence of polytopes is generated according to a convex feasibility problem. An illustrative simulation validates the effectiveness of our proposed method.

Keywords:Automata;Fault tolerant systems;Hybrid systems Abstract: In this paper, we study a class of hierarchical finite transition systems representing a set of fault configurations, and we consider synthesizing fault tolerant controllers for such systems that lead to a graceful degradation as faults occur. In previous work, the problem was solved under the assumptions that (i) the specification for each fault configuration is of ''reach-avoid-stay'' type, (ii) the knowledge of the fault occurrence is immediate. We extend the previous work in two aspects. First, we propose an algorithm that works for specifications given in a more general fragment of linear temporal logic. Secondly, we show how the proposed algorithm can be modified to synthesize controllers that guarantee satisfaction of the specification even in the presence of fault detection delays.

Keywords:Stochastic systems, Decentralized control;Automata Abstract: Controller synthesis techniques for continuous systems with respect to temporal logic specifications typically use a finite-state symbolic abstraction of the system. Constructing this abstraction for the entire system is computationally expensive, and does not exploit natural decompositions of many systems into interacting components. We have recently introduced a new relation, called (approximate) disturbance bisimulation for compositional symbolic abstraction to help scale controller synthesis for temporal logic to larger systems.

In this paper, we extend the results to stochastic control systems modeled by stochastic differential equations. Given any stochastic control system satisfying a stochastic version of the incremental input-to-state stability property and a positive error bound, we show how to construct a finite-state transition system (if there exists one) which is disturbance bisimilar to the given stochastic control system. Given a network of stochastic control systems, we give conditions on the simultaneous existence of disturbance bisimilar abstractions to every component allowing for compositional abstraction of the network system.

Keywords:Supervisory control;Discrete event systems;Automata Abstract: In this paper, we present a systematic approach to transform a set of plant models and requirement models into a tree-structured multilevel discrete-event system to which multilevel supervisory controller synthesis can be applied. By analyzing the dependencies between the plants and the requirements using dependency structure matrix techniques, a multilevel clustering can be calculated. Since one of the major drawbacks of synthesizing supervisory controllers is state space explosion, multiple attempts exist to overcome this computational difficulty, such as modular, hierarchical, decentralized, and, recently developed, multilevel supervisory control synthesis. Unfortunately, the modeler needs to provide additional information as input for most of these non-monolithic synthesis procedures. For those supervisory control synthesis procedures that require additional information, no systematic approach exists in literature to transform any set of plant models and requirement models to the appropriate input needed for a particular synthesis procedure. The presented approach is applied to a model of a lock and a model of an MRI scanner patient support table.

Keywords:Supervisory control Abstract: A common approach to controller design of large scale discrete-event systems or hybrid systems is to apply synthesis procedures on an abstraction that is realised on a significantly smaller state set. However, for every abstraction-based controller design, an inherent problem is to guarantee that the controller is also admissible to the actual plant. This paper addresses abstraction-based supervisory control for not-necessarily topologically closed omega-languages and upper-bound language-inclusion specifications. We refer to an abstraction as consistent for the purpose of controller design, if any controller obtained for the abstraction is also admissible to the actual plant. The main results of our study are sufficient and necessary conditions to characterise consistency.

Keywords:Switched systems, Automata, Hybrid systems Abstract: We study discrete time linear constrained switching systems with additive disturbances, in the general setting where the switching acts on the system matrices, the disturbance sets and the state constraint sets. Our primary goal is to extend the existing invariant set constructions when the switching signal is constrained by a given automaton. We achieve it by working with a relaxation of invariance, namely the multi-set invariance. By exploiting recent results on computing the stability metrics for these systems, we establish explicit bounds on the number of iterations required for each construction. Last, as an application, we develop new maximal invariant set constructions for the case of linear systems in far fewer iterations compared to the state-of-the-art

Keywords:Stability of nonlinear systems, Algebraic/geometric methods, Lyapunov methods Abstract: Necessary and sufficient condition of stability (stabilizability) of nonlinear homogeneous (control) system is obtained using topological equivalence of any asymptotically stable homogeneous system to a quadratically stable one.

Keywords:Stability of nonlinear systems, Computational methods, Systems biology Abstract: We consider contractive systems whose trajectories evolve on a compact and convex state-space. It is well-known that if the time-varying vector field of the system is periodic then the system admits a unique globally asymptotically stable periodic solution. Obtaining explicit information on this periodic solution and its dependence on various parameters is important both theoretically and in numerous applications. We develop an approach for approximating such a periodic trajectory using the periodic trajectory of a simpler system (e.g. an LTI system). Our approximation includes an error bound that is based on the input-to-state stability property of contractive systems. We show that in some cases this error bound can be computed explicitly. We demonstrate our results using several examples from systems biology.

Keywords:Stability of nonlinear systems, Constrained control Abstract: The use of multipliers is an important technique for absolute stability analysis. In continuous-time the RL and RC multipliers preserve the positivity of memoryless and monotone nonlinearities. We classify their discrete-time counterparts and analyse their phase properties. The classification of the discrete-time multipliers is richer than that of their continuous-time counterparts; their phase properties are less flexible.

Keywords:Stability of nonlinear systems, Control of networks, Lyapunov methods Abstract: We synthesize a feedback for a fully connected network of identical Lienard-type oscillators such that the phase-balanced equilibrium---the mode where the centroid of the coupled oscillators in polar coordinates is at the origin---is asymptotically stable, and the phase-synchronized equilibrium is unstable. Our approach hinges on a coordinate transformation of the oscillator dynamics to polar coordinates, and periodic averaging theory to simplify the examination of multiple time-scale behavior. Using Lyapunov- and linearization-based arguments, we demonstrate that the oscillator dynamics have the same radii and balanced phases in steady state for a large set of initial conditions. Numerical simulation results are presented to validate the analyses.

Keywords:Stability of nonlinear systems, Delay systems, LMIs Abstract: We present stability criteria for equilibria of a class of linear complementarity systems, subjected to discrete and distributed delay. We present necessary and sufficient conditions for local exponential stability, inferred from the spectrum location of a corresponding system of delay differential algebraic equations. Subsequently, we obtain sufficient LMI based conditions for global asymptotic stability using Lyapunov-Krasovskii functionals.

Keywords:Stability of nonlinear systems;Delay systems, Lyapunov methods Abstract: We provide a bounded backstepping result that ensures global asymptotic convergence for a broad class of partially linear systems with an arbitrarily large number of integrators. We use one artificial delay, and we assume that the nonlinear subsystems satisfy a converging-input-converging-state assumption. When the nonlinear subsystem is control affine with the state of the first integrator as the control, we provide sufficient conditions for our converging-input-converging-state assumption to holdmm{, using a Lyapunov function construction}. Our example illustrates the novelty and utility of our main result.

Keywords:Stochastic systems, Uncertain systems, Output regulation Abstract: It is well known that the classical proportional-integral-derivative(PID) controller is most widely used in engineering systems which are typically nonlinear with various uncertainties including random noises, and that almost all the existing study on PID controller focus on linear deterministic systems. Motivated by this significant gap between control theory and engineering practice, we will in this paper present some theoretical results on PID control for a class of second order nonlinear uncertain stochastic systems, based on our recent study on the corresponding deterministic systems. To be specific, we will show that an analytic design method can be constructed explicitly for the three PID parameters, so that the global stability and asymptotic regulation of the closed-loop control systems can be guaranteed, as long as some knowledge on the upper bounds of the derivatives of both the unknown nonlinear drift and diffusion terms are available.

Keywords:Markov processes, Stochastic systems, Optimization Abstract: Many stochastic systems in various applications are large and complex. It is difficult to find closed-form optimal control policies. In this paper, a representative of such systems is considered, namely, an optimal stopping problem driven by a finite state Markov chain. Although the state space is finite, it is large containing many elements resulting in computational complexity. To overcome the difficulty, we divide the states into a number of groups so that the chain jumps frequently within each group and jumps over to other groups only occasionally. Based on this model, we use a singular perturbation approach to reduce the overall dimensionality and design near-optimal strategies for the original problem. Examples will be provided to illustrate the results.

Keywords:Markov processes;Switched systems, LMIs Abstract: This paper deals with the class of linear systems subject to Poisson jumps, where the dwell-time between jumps is described by an exponential distribution with mode-dependent parameter. No probabilistic information on the sequence of modes is assumed available. This model can be viewed as an uncertain Markov Jump Linear System (MJLS) with a transition rate matrix belonging to a polytope. Thanks to this interpretation, we show that mean square stability is equivalent to stability under arbitrary switching of a deterministic system. This allows one to derive sufficient conditions for mean square stability based on common Lyapunov functions, easily testable via semidefinite programming. Conservatism of the proposed conditions is discussed along with the relative implications among them.

Keywords:Linear systems, Randomized algorithms, Stochastic systems Abstract: We consider the problem of shaping the distribution of the state of a discrete time linear system subject to a stationary disturbance so as to optimize a performance index while satisfying probabilistic constraints involving control input and state. The state is not available and a disturbance compensator is designed via a one-shot off-line computational approach to optimally operate the system in stationary conditions. The resulting control strategy is easy to implement, able to handle probabilistic constraints and guarantees optimality in the long run. Moreover, it does not require the on-line (re)computation of the control parameters. Interestingly, problems where the disturbance is cyclostationary and/or the control is periodic can be embedded in our formulation. This is the case of the numerical example presented in the paper, where the proposed methodology is applied to stochastic periodic control of a battery for peak shaving of the solar energy produced by a photovoltaic panel installation.

Keywords:Optimization, Learning Abstract: In learning problems, avoiding to overfit the training data is of fundamental importance in order to achieve good predictive capabilities. Regularization networks have shown to be an effective tool to find reliable models, however their tuning is all but straightforward. In this paper, we consider learning problems that can be formulated as random convex minimization programs, and leverage on recent results established within the Wait & Judge theory for scenario optimization. Our main result is that, within this framework, generalization is deeply connected to the number of so-called support points found in optimization. By suitably selecting the regularization parameter, one can adjust the support points set and thereby can tune the trade-off between performance and generalization of the solution on the ground of a rigorous and quantitative theory.

Keywords:Stochastic systems, Markov processes, Stochastic optimal control Abstract: Average-cost optimality inequalities imply the existence of stationary optimal policies for Markov Decision Processes with average costs per unit time, and these inequalities hold under broad natural conditions. Additional conditions are required for the validity of the average-cost optimality equations. Recently the authors showed that the equicontinuity of value functions for discounted costs is sufficient additional condition for the validity of average-cost optimality equations for problems with weakly continuous transition probabilities and with possibly unbounded one-step costs, and this condition holds for setup-cost inventory control problems with backorders and convex holding/backlog costs. This paper studies periodic-review setup-cost inventory control problem with backorders and with quasiconvex cost functions and general demands. It is shown that such problems satisfy the equicontinuity condition. Therefore, the optimality inequalities hold in the form of equalities with a continuous average-cost relative value function for this problem. In addition, this implies that average-cost optimal (s,S) policies for the inventory control problem can be derived from the average-cost optimality equation. With the additional assumption on the monotonicity of the cost function, we establish the convergence of discounted-cost optimal ordering thresholds, when the system should start ordering, and convergence of discounted-cost relative value functions, when the discount factor converges to 1, to the corresponding optimal threshold and optimal relative value function for the average-cost problem.

Keywords:Distributed parameter systems Abstract: Models coming from population dynamics with age structuring form a remarkable source of infinite dimensional dynamical systems where the controlled trajectories need to satisfy natural constraints (such as positivity). We discuss the controllability and the detectability of such systems taking in consideration theses constraints. Our main new results assert that we can find controls steering an equilibrium state to another equilibrium in an uniform time and preserving the positivity of the trajectory. This situation contrasts with the one encountered in the case in which the diffusion phenomenon is considered, when the above tasked can be managed only if the control time is large enough. We next discuss the reconstruction of the state from partial measures for models inspired by the Lotka-Mc Kendrick system with or without spatial diffusion.

Keywords:Distributed parameter systems, Networked control systems Abstract: This paper proposes synchronization controllers for networked systems whose dynamics are described by parabolic partial differential equations. The control design objectives are to ensure that each networked system agrees with each other (synchronization) and that each networked system follows the state of a partial differential equation (leader-following). The novelty here is that the leader is governed by time invariant partial differential equation and thus the leader-following controller ensures that each networked system is spatially homogenized. This allows each system to dynamically reach a spatial distribution which is the solution to the time invariance partial differential equation. To achieve both control objectives the control signals are decomposed into two parts; one addressing synchronization via an appropriate consensus protocol with adaptation of the synchronization gains, and the other via a regulation controller of an associate error equation. This state error equation is constructed via asymptotic embedding methods which embed the spatially-dependent and time-invariant dynamics of the leader into the dynamics of each networked system. Both the stability of the proposed controllers and the well-posedness of the resulting aggregate system are summarized and an example of five networked parabolic partial differential equations tasked with synchronization and following a spatially-dependent leader are presented to provide insights on the proposed spatial homogenization.

Keywords:Distributed parameter systems Abstract: Backstepping boundary control is investigated for a class of linear port-Hamiltonian systems. It is shown that by considering as target system an exponentially stable dissipative PHS, i.e., a PHS with a linear dissipation term and homogeneous boundary conditions, a coordinate transformation based on a multiplicative operator suffices to map the open-loop system into the target system. The condition for the existence of the transformation is algebraic. Hence, the backstepping transformation and the associated matching condition are simpler than the conventional ones that considers Volterra integral terms and kernel conditions in the form of partial differential equations. Since the controller has been developed for a general class of linear PHS it is applicable to a large class of physical systems, as for instance transport, beam and wave equations. The result is illustrated on the examples of a transport equation and a vibrating string on a 1D spatial domain.

Keywords:Distributed parameter systems;Delay systems Abstract: We consider the class of linear partial differential equation systems in 1-D involving two distinct families, hyperbolic and parabolic. The model is motivated by physical phenomena arising in extreme ultraviolet light generation (EUV) for next-generation photolithography, where the droplet transport stream is affected by the diffusion of plasma generated from droplet vaporization. Other systems that can exhibit this behavior are found in biological chemotaxis and simplified predator-prey models. The two PDEs are coupled in-domain, which brings additional complexity when compared with the boundary coupled case, which has been explored in previous literature by Krstic (2009). The coupling is considered in an unidirectional manner, where the controlled hyperbolic PDE modeling the droplet stream displacement exhibits an in-domain Volterra integral source driven by the parabolic PDE modeling the plasma diffusion, which itself is driven at the boundary via the hyperbolic PDE. A backstepping method is derived to transform the system into a chosen exponentially stable target system, in the L^2 x H^1 norm. The backstepping method gives rise to a coupled hyperbolic-parabolic gain kernel PDE which must be solved to determine the controller. Simulation studies are presented to illustrate the effectiveness of the control.

Keywords:Adaptive control;Distributed parameter systems, Nonlinear output feedback Abstract: We address the problem of adaptive output-feedback stabilization for flow-induced vibrations of a membrane at high Mach numbers. The aeroelastic instability is compensated by using boundary control and anti-collocated measurement. The membrane is infinite in spanwise and the streamwise vibrations are modeled by a one-dimensional wave Partial Differential Equation (PDE) with an aerodynamic forcing term. Based on Piston theory, the term is represented by an anti-damping term multiplying a constant coefficient and a convective term multiplying an unknown constant coefficient. We then transform the wave PDE to a one-dimensional 2 times 2 first-order hyperbolic PDEs with constant coupling coefficients. Before introducing an adaptive output feedback controller for the hyperbolic PDEs, we present a nonadaptive explicit state feedback controller. To deal with the absence of both full-state measurements and parameter knowledge, the adaptive output-feedback design is used; the design is based on an observer canonical form which is obtained through a change of variables and a backstepping transformation. The form enables us to design an explicit state observer. We employ gradient-based parameter estimators. For the closed loop system, we achieve convergence of the state of the wave PDE to zero. We validate our result with a simulation.

Keywords:Distributed parameter systems Abstract: In this paper we solve the output tracking and disturbance rejection problem for a plant described by an one-dimensional anti-stable wave equation, with reference and disturbance signals that are supposed to belong to W^{1,infty}(0,infty), L^infty(0,infty), respectively. Generally, these signals cannot be generated by an exogenous system. We explore an approach based on proportional control. It is shown that the proportional low gain controller can achieve exponential output tracking while rejecting the disturbance. More precisely, we split the problem considered into three steps. In the first step, we convert the original system without disturbance into the two transport equations with an ordinary differential equation by using Riemann variables, then we propose a proportional control law by making use of the properties of transport systems and time delay systems. In the second step, based on our recent result on the disturbance estimator, we apply the estimation/cancellion strategy to cancel to the external disturbance to track the reference asymptotically. In the third step, we design a controller for the state observer system. Since no explicit disturbance appears in this system, the disturbance is exactly compensated, and the output signal to be controlled is exponentially tracking the reference signal. As a byproduct, we obtain a new output feedback stabilizing control law by which the resulting closed-loop system is exponentially stable using only two displacement output signals. Numerical experiments demonstrate the effectiveness of the proposed control law.

Keywords:Optimization, Optimization algorithms, Machine learning Abstract: Nonconvex optimization problems with an L1-constraint are ubiquitous, and are found in many application domains including: optimal control of hybrid systems, machine learning and statistics, and operations research. This paper shows that nonconvex optimization problems with an L1-constraint can be approximately solved in polynomial time. We first show that nonlinear integer programs with an L1-constraint can be solved in a number of oracle steps that is polynomial in the dimension of the decision variable, for each fixed radius of the L1-constraint. When specialized to polynomial integer programs, our result shows that such problems have a time complexity that is polynomial in simultaneously both the dimension of the decision variables and number of constraints, for each fixed radius of the L1-constraint. We prove this result using a geometric argument that leverages ideas from stochastic process theory and from the theory of convex bodies in high-dimensional spaces. We conclude by providing an additive polynomial time approximation scheme (PTAS) for continuous optimization of Lipschitz functions subject to Lipschitz constraints intersected with an L1-constraint, and we sketch a generalization to mixed-integer optimization.

Keywords:Iterative learning control, Optimization algorithms Abstract: We propose novel iterative learning control algorithms to track a reference trajectory in resource-constrained control systems. In many applications, there are constraints on the number of control actions, delivered to the actuator from the controller, due to the limited bandwidth of communication channels or battery-operated sensors and actuators. We devise iterative learning techniques that create sparse control sequences with reduced communication and actuation instances while providing sensible reference tracking precision. Numerical simulations are provided to demonstrate the effectiveness of the proposed control method.

Keywords:Optimization;Smart grid, Optimal control Abstract: This paper considers optimization problems of energy demand networks including aggregators and investigates strategic behavior of the aggregators. The energy demand network including aggregators will be optimized through pricing. Under this optimization process, the aggregator acts as intermediate between energy supply sources and a large number of consumers and is expected to moderate tasks to solve a large scale optimization problem. We propose an optimization process that uses information exchange or aggregation by the aggregators, which is actually an intermediate model of the well-known two extremal models. From the consumer's point of view, the aggregator is expected to have enough negotiation power on behalf of the consumers. This will be a main theme of this paper and we investigate strategic behavior of the aggregators. We suppose that the aggregator will try to pursue the benefit as well as market power by choosing the design parameter in its cost function. The strategic decision making by the aggregators could provide useful insights in qualitative analysis of the energy demand network, and the results of numerical example indicate that, for example, oligopoly by the aggregator may not be beneficial to the consumers.

Keywords:Optimization algorithms, Optimization, Machine learning Abstract: We analyze the local convergence of proximal splitting algorithms to solve optimization problems that are convex besides a rank constraint. For this, we show conditions under which the proximal operator of a function involving the rank constraint is locally identical to the proximal operator of its convex envelope, hence implying local convergence. The conditions imply that the non-convex algorithms locally converge to a solution whenever a convex relaxation involving the convex envelope can be expected to solve the non-convex problem.

Keywords:Optimization algorithms, Optimization Abstract: In this paper, we study a deterministic coordinate descent algorithm for constrained smooth convex optimization, where each iteration involves updating a block of the decision vector via a block coordinate-wise gradient projection step. We establish the asymptotic convergence of the algorithm under a minimal assumption that all the blocks would be updated infinitely many times. Moreover, we derive an O(1/k) rate of convergence to optimality for the algorithm, provided that each block is updated at least once during any time interval of given length. The algorithm generalizes the cyclic block coordinate gradient projection method in terms of the block selection rule and the step-size choice, and is shown to have commensurate convergence rate guarantees. The convergence rate of the algorithm can further be accelerated to O(1/k^2) by integrating the algorithm into a multi-step optimal gradient method when the problem is unconstrained. Finally, extensive simulations illustrate the efficiency and scalability of the deterministic coordinate descent algorithm and its accelerated variant.

Keywords:Optimization algorithms, Optimization Abstract: We design and analyze a novel gradient-based algorithm for unconstrained convex optimization. When the objective function is m-strongly convex and its gradient is L-Lipschitz continuous, the iterates and function values converge linearly to the optimum at rates rho and rho^2, respectively, where rho = 1-sqrt{m/L}. These are the fastest known guaranteed linear convergence rates for globally convergent first-order methods, and for high desired accuracies the corresponding iteration complexity is within a factor of two of the theoretical lower bound. We use a simple graphical design procedure based on integral quadratic constraints to derive closed-form expressions for the algorithm parameters. The new algorithm, which we call the triple momentum method, can be seen as an extension of methods such as gradient descent, Nesterov's accelerated gradient descent, and the heavy-ball method.

LAAS-CNRS and Inst. of Mathematics, Univ. Oftoulouse

Keywords:Optimal control, LMIs, Nonlinear systems identification Abstract: We consider the class of control systems where the differential equation, state and control system are described by polynomials. Given a set of trajectories and a class of Lagrangians, we are interested to find a Lagrangian in this class for which these trajectories are optimal. To model this inverse problem we use a relaxed version of Hamilton-Jacobi- Bellman optimality conditions, in the continuity of previous work in this vein. Then we provide a general numerical scheme based on polynomial optimization and positivity certificates, and illustrate the concepts on a few academic examples.

Keywords:Optimal control, Compartmental and Positive systems, Optimization Abstract: In this paper we consider L1 optimal and H-infinity optimal control problems for a particular class of Positive Bilinear Systems that arise in drug dosage design for HIV treatment. Starting from existent characterizations of the L1-norm for positive systems, a convex formulation for the first problem is provided. As for the H-infinity case, we propose an algorithm based on the iterative solution of a convex feasibility problem, that approximates an H-infinity optimal controller with arbitrary accuracy. A numerical example illustrates the results.

Keywords:Optimal control, Numerical algorithms;Switched systems Abstract: We present a theoretical formulation, and a corresponding numerical algorithm, that can find Pontryagin-optimal inputs for general dynamical systems by using a direct method. Optimal control remains as a versatile and relevant framework in systems theory applications, many decades after being formally defined. Pontryagin-optimal inputs can be found for some classes of problems using indirect methods, but these are often slow or lack robustness. On the other hand, convergent direct optimal control methods are fast, but their solutions usually converge to first-order optimality conditions, which are weaker.

Our result, founded on the theory of relaxed inputs as defined by J. Warga, establishes an equivalence between Pontryagin-optimal inputs and optimal relaxed inputs. We also formulate a sampling-based numerical method to approximate the Pontryagin-optimal relaxed inputs using an iterative direct method. Finally, using a provably-convergent numerical method, we synthesize approximations of the Pontryagin-optimal inputs from the sampled relaxed inputs.

Keywords:Optimal control, Optimization algorithms, Variational methods Abstract: This paper deals with a further development of analytic techniques for Optimal Control Problems (OCPs) involving differential systems with the state suprema. Differential equations evolving with state suprema (maxima) provide a useful modelling framework for various real-world applications, namely, in electrical engineering and in biology. The corresponding dynamic models lead to Functional Differential Equations (FDEs) in the presence of state-dependent delays. We study some particular (but important) cases of optimal control processes governed by systems with sup-operator in the right hand sides of the differential equations and obtain constructive characterizations of optimal solutions. The constrained OCPs we examine are formulated assuming the (linear) feedback-type control law. The case study presented in this article constitutes a formal extension of the concept of positive dynamic systems to differential systems with the state suprema.

Keywords:Optimal control, Optimization algorithms Abstract: Obstacle avoidance problems are a class of optimal control problems for which derivative-based optimization algorithms often fail to locate global minima. The goal of this paper is to provide a tutorial on how to apply Branch & Lift algorithms, a novel class of global optimal control methods, for solving such obstacle avoidance problems to global optimality. The focus of the technical developments is on how Branch & Lift methods can exploit the particular structure of Dubins' models, which can be used to model a variety of practical obstacle avoidance problems. The global convergence properties of Branch & Lift in the context of obstacle avoidance are discussed from a theoretical as well as a practical perspective by applying it to a tutorial example.

Keywords:Optimal control;Power systems;Emerging control applications Abstract: When providing frequency regulation in a pay-for-performance market, batteries need to carefully balance the trade-off between following regulation signals and their degradation costs in real-time. Existing battery control strategies either do not consider mismatch penalties in pay-for-performance markets, or cannot accurately account for battery cycle aging mechanism during operation. This paper derives an online control policy that minimizes a battery owner's operating cost for providing frequency regulation in a pay-for-performance market. The proposed policy considers an accurate electrochemical battery cycle aging model, and is applicable to most types of battery cells. It has a threshold structure, and achieves near-optimal performance with respect to a offline controller that has complete future information. We explicitly characterize this gap and show it is independent to length of the time of operations. Simulation results with both synthetic and real regulation traces are conducted to illustrate the theoretical results.

Keywords:Large-scale systems, Game theory Abstract: Imitation dynamics for population games are studied and their asymptotic properties analyzed. In the considered class of imitation dynamics - that encompass the replicator equation as well as other models previously considered in evolutionary biology - players have no global information about the game structure, and all they know is their own current utility and the one of fellow players contacted through pairwise interactions. For potential population games, global asymptotic stability of the set of Nash equilibria of the sub-game restricted to the support of the initial population configuration is proved. These results strengthen (from local to global asymptotic stability) existing ones and generalize them to a broader class of dynamics. The developed techniques highlight a certain structure of the problem and suggest possible generalizations from the fully mixed population case to imitation dynamics whereby agents interact on complex communication networks.

Keywords:Cooperative control, Large-scale systems, Stochastic systems Abstract: We consider open multi-agent systems. Unlike the systems usually studied in the literature, here agents may join or leave while the process studied takes place. The system composition and size evolve thus with time. We focus here on systems where the interactions between agents lead to pairwise gossip averages, and where agents either arrive or are replaced at random times. These events prevent any convergence of the system.

Instead, we describe the expected system behavior by showing that the evolution of scaled moments of the state can be characterized by a 2-dimensional (possibly time-varying) linear dynamical system.

We apply this technique to two cases : (i) systems with fixed size where leaving agents are immediately replaced, and (ii) systems where new agents keep arriving without ever leaving, and whose size grows thus unbounded.

Keywords:Cooperative control, Network analysis and control, Distributed control Abstract: We study the consensus problem of discrete-time systems under persistent flow and non-reciprocal interactions between agents. An arc describing the interaction strength between two agents is said to be persistent if its weight function has an infinite l1 norm. We discuss two balance conditions on the interactions between agents which generalize the arc-balance and cut-balance conditions in the literature respectively. The proposed conditions require that such a balance should be satisfied over each time window of a fixed length instead of at each time instant. We prove that in both cases global consensus is reached if and only if the persistent graph, which consists of all the persistent arcs, contains a directed spanning tree. The convergence rates are also provided in terms of the number of node interactions that have taken place.

Keywords:Network analysis and control, Large-scale systems, Estimation Abstract: In this paper we are interested in the estimation of the social influence among n agents that interact in a sparse social network. In particular, we consider the classical Friedkin and Johnsens model, where agents discuss m ≪ n independent topics, take into account the other opinions but are not completely open-minded, and persistently are influenced by their initial prejudices. By observing the initial and final opinions profile, we propose a method based on the l0/l1 minimization to infer the topology of the social graph and the strength of the interconnections. Compared to the methods previously introduced in literature, our work does not assume partial knowledge on the social graph and does not consider an optimized placement of stubborn agents injecting inputs that change the terminal behavior of the opinion dynamics. Moreover, the proposed method is suitable for parallel implementation and the influence identification of each agent can be performed independently from the others. Under suitable assumptions on the distribution of the initial prejudices, we derive theoretical conditions that guarantee that the problem is well posed and sufficient requirements on the number of topics under discussion that ensure perfect recovery. Extensive simulations corroborate theoretical results and our findings.

Keywords:Network analysis and control, Neural networks, Stability of nonlinear systems Abstract: In this paper we provide necessary conditions for the existence of multiple equilibrium points for a class of nonlinear cooperative networked systems with saturating interactions which describe models of collective decision-making. The multiple steady states of the dynamics represent the possible outcomes of a decision process, and, except for one positive and one negative, have all mixed signs. The conditions we obtain can be formulated in terms of the algebraic connectivity of the network and are inspired by Perron-Frobenius arguments. It is also shown that the mixed-sign equilibria are contained in a ball of radius given by the norm of the positive equilibrium point and centered in the origin. Numerical examples are given to illustrate the results.

Keywords:Network analysis and control, Large-scale systems, Game theory Abstract: Conditions for nonexistence of stationary solutions in collective decision making are investigated via discrete-state continuous-time mean-field games. The study builds on a bio-inspired model in honeybee swarms. The ultimate goal is to find the best alternative decision in a collective fashion. A cross-inhibition signal, as the one observed in honeybee swarms, is used to capture different types of failures, including disrupted communication channels, computational errors or malevolent behaviour. The model is based on the hypotheses that players control their transition rates from one state to another to minimise a cost, under the presence of an adversarial disturbance. The cost to minimise involves a penalty on control and a congestion-dependent term. As a main result, we prove that the solution obtained as the asymptotic limit of the nonstationary one can be approximated by a closed orbit trajectory. This argument is used to prove the nonexistence of stationary solution under certain conditions.

Keywords:Smart grid, Kalman filtering, Estimation Abstract: We address the problem of power system state estimation based on information coming from ubiquitous power demand time series and a limited number of PMUs. The presence of time synchronization error in the PMU measurements is explicitly considered. It is shown how incorrect modeling of synchronization errors easily lead to incorrect results, ruining the estimation performance of standard approaches. Resorting to a novel linear approximation for the power flow equations, we propose a Kalman based algorithm for the simultaneous estimation of system state and synchronization error param- eters. Compelling numerical simulations, based on the IEEE C37.118.1 standard on PMUs, validate the proposed approach.

Keywords:Smart grid, Optimization algorithms, Robust control Abstract: We describe a robust multiperiod transmission planning model including renewables and batteries, where battery output is used to partly offset renewable output deviations from forecast. A central element is a nonconvex battery operation model plus a robust model of forecast errors and a linear control scheme. Even though the problem is nonconvex we provide an efficient and theoretically valid algorithm that effectively solves cases on large transmission systems.

Keywords:Smart grid, Optimization algorithms Abstract: In this paper, we design a bidding system for a multiperiod electricity market in which market players participate with power generators and energy storage resources. For the bidding system design, we first develop a sequential procedure to determine a separate multidimensional bid function, i.e., an ensemble of period-specific bid functions, which enables to regard the multiperiod electricity market as an ensemble of conventional period-specific electricity markets. This sequential determination also enables to construct a distributed approximate scheme for multiperiod electricity market clearing. Then, based on a basis transformation similar to the Fourier transformation, we propose a bidding system with explicit consideration of the pricing of energy shiftability. It is shown that, in the situation where the optimal price profile levels off due to high penetration of energy storage, the distributed approximate scheme in the Fourier-like basis can attain the optimal market clearing with the minimal social cost. In addition, we numerically investigate the resultant deadweight loss, i.e., an increase of social costs caused by approximation, varying the levels of energy storage penetration.

Keywords:Smart grid;Power systems;Energy systems Abstract: This paper deals with passivity-based stability analysis of dynamic electricity pricing considering power flow. In the near future electricity market, power consumers and generators will participate in electricity market trading as market players. For such a market trading system, the dynamic pricing procedure is required to consider the intermittent participation of power consumers and generators. Then, this paper discusses the stability of the electricity market trading system including power flow using passivity analysis. This paper also shows that the optimal power demand, supply and electricity prices are asymptotically stable and these values are derived in a distributed manner through market trading.

Keywords:Smart grid;Power systems Abstract: In this paper, we introduce a distributed control methodology that enables wind generators (WGs) to dynamically dispatch and regulate their power outputs to optimal equilibria in real-time. These equilibria are constructed such that the total mechanical fatigue loads experienced by WGs are minimized and a total assigned power demand is collectively met. We begin by posing the fatigue-load minimization constrained optimal control problem (FLMCOC) as a restricted agreement problem and then propose a fully distributed control methodology for recovering its solution that leverages a particular consensus+innovations algorithm. The distributed algorithm can be realized via any arbitrary peer-to-peer communication network and under any case, it can guarantee dynamic regulation of WGs power outputs to their optimal values. Collectively, this paper offers a distributed control methodology for attaining a solution to the FLMCOC problem for large-scale wind farms that is characterized by the following merits: a) computational efficiency, since the computational burden is uniformly distributed among all wind generators and therefore scalability, b) resilience to single-point communication or agent failures and, c) privacy preservation, since the proposed algorithm requires WGs to only exchange nonsensitive information. This is critical in the case where WGs within a wind farm are owned by different stakeholders. The theoretical results are validated through numerical simulations on the modified IEEE 24-bus power network.

Keywords:Smart grid;Power systems Abstract: The use of energy storage systems is widely recognized as a key tool to create a more resilient energy infrastructure. At the same time, new technologies such as soft-open points and on-load tap changers are deserving growing attention for their potential applications in smart grids. In this paper we consider the coordinated use of on-load tap changer and energy storage systems for voltage support in distribution networks. We first formulate the optimal control problem over a given time horizon as a multi-period optimal power flow. To cope with uncertainties such as inaccurate forecasts, the optimal control problem is then inserted into a receding horizon scheme. The proposed approach requires very limited information to predict possible voltage problems and counteract them in advance. The control algorithm is tested on real data from a low voltage network featuring over- and undervoltages in the absence of voltage control. The obtained results show that the coordinated use of on-load tap changer and storage devices allows one to dramatically reduce the size of installed the storage units required to alleviate voltage issues. The obtained results show that the coordinated use of on-load tap changer and storage devices allows one to dramatically reduce the size of the installed storage units required to alleviate voltage issues.

Keywords:Automotive control, Observers for nonlinear systems, Modeling Abstract: Modeling and control of ground vehicles have become a major research field in the last few years, due to the increasing diffusion of driver assistance technologies and the persistent need for guaranteeing safety and comfort of driver and passengers. Although vehicle control systems require a large set of measurements to perform accurate computations, due to the possible unavailability and the non-negligible cost of sensors, it is not always possible to assume the direct knowledge of some important dynamic quantities involved, among which a major role is taken by its lateral velocity.

In this work, we address the design and implementation of an asymptotic sampled-data state observer for the vehicle single-track model. The observer only exploits the knowledge of sparse yaw-rate samples, which are obtained by relatively cheap digital gyroscopic devices, to reconstruct the continuous behavior of lateral velocity and yaw rate. However, due to the inherent properties of the vehicle single-track model, the observer is theoretically guaranteed to work only in the presence of sufficiently bounded driver maneuvers. Consequently and in view of a practical exploitation in a realistic setting, we preliminarily validate the approach by means of simulations of the observer applied to a more general vehicle model, including parameter variations, unmodeled dynamics and quantization. The results seem to confirm the potential of the approach.

Keywords:Automotive control, Autonomous vehicles, Optimal control Abstract: In autonomous driving, it is often useful to plan trajectories in a curvilinear coordinate frame with respect to a given reference curve, such as a path produced by a high-level route planner. In this domain, standard planning methods rely on expensive coordinate transformations or on solving computationally intensive boundary value problems for computing motion primitives between states. This work develops efficient, approximate path coordinate motion primitives appropriate for fast planning in autonomous driving scenarios. We gain a 1000x speed-up in primitive computation time relative to standard approaches at the loss of some precision with respect to the position along the reference line, which we statistically quantify. Motion primitive properties like path length, acceleration, and the reference line offset are exactly preserved.

Keywords:Automotive control, Predictive control for linear systems Abstract: Controlling a diesel engine air path to achieve optimal engine performance is a challenging problem, given its multivariable nature and high degree of nonlinearity. Model-based control approaches like MPC have the potential for providing effective controller design, in the presence of operating constraints. However, conventional MPC formulations have too many tuning parameters for efficient calibration to meet transient performance specifications. Furthermore, they generally involve the solution of an online optimisation problem, making real-time implementation difficult for all but extremely short prediction horizons. These challenges may be addressed by introducing an MPC formulation suitable for real-time control of a diesel-engine air path, incorporating an appropriate cost-function parameterisation to aid calibration. In this paper, data-driven prediction models identified from engine bench tests are used within the proposed MPC formulation, and implemented on a production automotive diesel. Preliminary experiments show the efficacy of the implementation in tracking desired air path reference trajectories over the UDC and EUDC drive cycles.

Keywords:Automotive control, Predictive control for linear systems Abstract: In the development of model predictive controllers (MPC) for a diesel engine air path, tuning the parameters of the controllers to achieve satisfactory performance is challenging, especially whilst adhering to input and safety constraints in the presence of unknown disturbances. The novel MPC structure introduced in a companion paper reduces the number of effective tuning parameters to lower the calibration effort, but does not directly consider the robustness of the controller in handling modelling uncertainties. This paper addresses this challenge by detailing how a constraint tightening-like approach can be augmented to the control architecture through an additional calibration parameter, providing practical robustness to additive state disturbances at steady-state conditions. The robust controller is firstly implemented in simulation, with a comprehensive investigation of its calibration performance under step changes in the fuelling rate. Experimental validation of the controller architecture is then provided for selected tunings of the calibration parameters, showing a similar qualitative and quantitative performance to the simulations. The impact on the closed loop response of the engine through the inclusion of the robustness parameter is shown to be minor, whilst still allowing the remaining parameters to be adjusted for achieving desired output transient responses.

Keywords:Automotive control, Predictive control for nonlinear systems, Control applications Abstract: While there is still a long way to robustly operating fully automated vehicles on our roads, low speed autonomy might be a reasonable intermediate step. Especially highly automated parking systems are currently in the focus of interest. When we aim at leveraging those systems in everyday parking scenarios, we should also be able to park on sidewalks and as such be able to traverse curbs. However, those use cases might then be a major challenge for vehicle control systems. Therefore, this paper describes the design of a control scheme for longitudinal vehicle dynamics control which is capable of performing on-curb parking while lateral vehicle dynamics control is assumed to be performed by a separate controller. We rely on a model predictive control scheme which exploits information of an extended Kalman filter for the purpose of disturbance rejection when parking on curbs. The estimator aims at determining the related road resistance forces in those scenarios. The proposed control concept is compared to a proportional-integral controller in five typical parking scenarios. Simulation results demonstrate that with predictive control, we are able to finish parking faster, to avoid unintended stops and to better track the reference velocity.

Keywords:Automotive systems, Pattern recognition and classification, Nonlinear output feedback Abstract: In this paper an intelligent robust feedback control approach is proposed for the control of the nonlinear suspension system. Employing higher order integral sliding mode approach, robust controllers with parameters optimized using PSO for various road classes are designed. A novel classifier invariant to changes in control parametersis then developed to detect the road class. Subsequently in the real time, based on system responses the roadlevel is detected by the classifier and accordingly the optimized control parameters are selected to implement thecontroller. The closed loopstability of the proposed approach isestablished and simulation results for different road classed are presented to show improvement in passenger comfort.

Keywords:Direct adaptive control, Constrained control Abstract: This paper presents a closed-form approach to strict enforcement of control signal magnitude constraints in a model reference adaptive control system. The control constraint enforcement procedure is reactive---no modifications are made to the system until a limit is encountered. Enforcement is obtained by introducing a scaling parameter for the control input that only becomes non-unity when a constraint is violated. An explicit solution for the update of the scaling parameter is derived that does not require any iteration or optimization to be performed. The scaling parameter update law ensures that constraints are satisfied in both the transient and steady state. A Lyapunov stability argument is presented that demonstrates the procedure provides error convergence so long as the scaling parameter's rate of growth is limited. Comments are made regarding appropriate adaptive control robustness modifications. A numerical example is used to demonstrate the design and is shown to successfully stabilize the system even when the same system subject to pure control saturation is unstable.

Keywords:Direct adaptive control, Output regulation, Robust control Abstract: The problem of output control for MIMO systems is addressed. Taking full advantage of all controls and all available measurements, by appealing to a general notion of ``robust" minimum-phase, a design procedure is proposed. The results are complemented with the design, under appropriate assumption, of an adaptive (nonlinear) internal model so as to handle parametric uncertainties in the exosystem.

Keywords:Adaptive control;Automotive control;Automotive systems Abstract: Electro-hydraulic valve actuators capable of variable valve timing, duration and lift offer potential benefits for significantly improving engine performance. A model-based adaptive feedforward control strategy was developed to improve the accuracy of valve opening timing control with the presence of time-varying valve delay. A discrete-time adaptive estimation algorithm was employed to estimate the system supply pressure, which is the leading factor of the valve opening delay. To make the online estimation feasible, a linear time-invariant model was obtained based on previously developed mathematical model. The valve opening delay determined by the estimated supply pressure was further used for the feedforward control to track the desired valve opening timing. Both the open-loop and closed-loop control schemes with adaptive feedforward were studied in this paper. The discrete-time adaptive parameter estimation algorithm along with the developed control strategies were verified on the test bench under transient operational conditions. The parameter estimation converges in 6 engine cycles with a steady-state mean relative estimation error of 7.1% and the tracking error of valve opening timing is kept within 1 crank angle degree using combined feedforward and feedback control.

Keywords:Adaptive control;MEMs and Nano systems, Stability of nonlinear systems Abstract: In this paper, we propose the design of an adaptive conditional servocompensator along with approximate hysteresis inversion for a piezoelectric nanopositioner to track desired periodic trajectories. The nanopositioner is modeled with a linear system proceeded by a hysteresis operator, which is represented by a Modified Prandtl-Ishlinskii (MPI) operator. The adaptive law, which is equipped with smooth parameter projection for robustness against matched disturbances, is initiated only when the trajectory driven by a continuously-implemented sliding mode control (SMC) enters a boundary layer around the sliding manifold. To reduce the conservativeness of the SMC law, we analytically derive the bound on the hysteresis inversion error. It is shown that, under appropriate conditions, the closed-loop system is well-posed and the tracking error converges exponentially to a periodic solution in the neighborhood of the origin. Experiments conducted on a commercial nanopositioner confirm the theoretical analysis, and demonstrate the efficacy of the proposed controller in comparison with a continuously-implemented SMC without the adaptive internal model. In particular, for a 100 Hz reference trajectory, the mean tracking error is found to be less than 0.015 %, compared to 0.15 % for the case when the adaptive internal model is not used.

Keywords:Adaptive control, Output regulation, Robust adaptive control Abstract: This paper proposes an adaptive PFC design scheme for designing almost strictly positive real (ASPR) or output feedback exponential passivity (OFEP) based adaptive output feedback control system for nonlinear system. The nonlinear system considered in this paper is the one which can be modelled by a T-S fuzzy model representation. For the nonlinear system modelled by T-S fuzzy model but its membership functions are uncertain, an adaptive design scheme of PFC for maintaining the ASPR-ness (or OFEP-ness) of the system will be proposed. Furthermore, an adaptive output feedback based output tracking control system with adaptive PFC is proposed and stability of the obtained adaptive control system is analyzed.

Keywords:Adaptive control, Aerospace, Adaptive systems Abstract: A solution to the problem of spacecraft tracking a desired attitude using the contraction analysis is given in this paper. First, an ideal state feedback controller, assuming the knowledge of the inertial matrix and the total angular momentum, is devised and ensured to be contracting. Then the adaptive control law is designed in a certainty equivalence fashion substituting the controller parameter vector by its estimate. The overall system is shown to be contracting under a sufficient excitation condition, which is a strictly weaker con- dition than the persistent excitation required for most adaptive control schemes.

Keywords:Autonomous robots, Markov processes, Intelligent systems Abstract: Simultaneous Search and Monitoring (SSM) is studied in this paper for a single UAV searcher and multiple moving ground targets. Searching for unknown targets and monitoring known targets are two intrinsically related problems, but have mostly been addressed in isolation. We combine the two problems with a joint objective function in a Partially Observable Markov Decision Process (POMDP). An online policy planning approach is proposed to plan a reactive policy to solve the POMDP, using both Monte-Carlo sampling and Simulated Annealing. The simulation result shows that the searcher will successfully find unknown targets without losing known ones. We demonstrate, with a theoretical proof and comparative simulations, that the proposed approach can deliver a better performance than conventional foresight optimization methods.

Keywords:Autonomous robots;Automata, Agents-based systems Abstract: Temporal logic based synthesis approaches are often used to find trajectories that are correct-by-construction for systems with complex behavior. 7 However, the scalability of such approaches is of concern and at times a bottleneck when transitioning from theory to practice. In this paper, we identify a class of problems in the GR(1) fragment of linear-time temporal logic (LTL) where the synthesis problem allows for a decomposition that enables easy parallelization. This decomposition also reduces the alternation depth, resulting in more efficient synthesis. A multi-agent robot gridworld example with coordination tasks is presented to demonstrate the application of the developed ideas and also to perform empirical analysis for benchmarking the decomposition-based synthesis approach.

Keywords:Autonomous robots;Robotics;Aerospace Abstract: We propose a novel vector field based guidance scheme for tracking and surveillance of a convoy, moving along a possibly nonlinear trajectory on the ground, by an aerial agent. The scheme first computes a time varying ellipse that encompasses all the targets in the convoy using a simple regression based algorithm. It then ensures convergence of the agent to a trajectory that repeatedly traverses this moving ellipse. The scheme is analyzed using perturbation theory of nonlinear differential equations and supporting simulations are provided. Some related implementation issues are discussed and advantages of the scheme are highlighted.

Keywords:Autonomous robots, Uncertain systems, Optimization algorithms Abstract: Consider a scenario where robots traverse a graph, but crossing each edge bears a risk of failure. A team operator seeks a set of paths for the smallest team which guarantee the probabilities that at least one robot visits each node satisfy specified per-node visit thresholds, and the probabilities each robot reaches its destination satisfy a per-robot survival threshold. We present the RSC problem formally as an instance of the submodular set cover problem and propose an efficient cost-benefit greedy algorithm for finding a feasible set of paths. We prove that the number of robots deployed by our algorithm is no more than (lambda/p_s)(1+log(lambda*Delta_K/p_s)) times the smallest team, where Delta_K quantifies the relative benefit of the first and last paths, p_s is the per-robot survival probability threshold and 1/lambda < 1 is the approximation factor of an oracle routine for the well-known orienteering problem. We demonstrate the quality of our solutions by comparing to optimal solutions computed for special cases of the RSC and the efficiency of our approach by applying it to a search and rescue scenario where 225 sites must be visited, each with probability at least 0.95.

Keywords:Autonomous vehicles;Aerospace, Autonomous robots Abstract: We address 3D path- and motion-planning in cluttered environments for a quadrotor UAV using a 3D depth sensor with limited range and field-of-view. The 3D elevation map of obstacles in the environment is assumed a priori unknown, but a 2D projection of this map onto a horizontal plane is assumed a priori fully known. We specifically address path-planning to discover and traverse "3D shortcuts," namely, to achieve reductions in path costs using 3D depth sensor information, as compared to planning using the 2D projection map alone. We propose a 3D path-planning algorithm based on incremental repair of a constant-altitude seed path computed from the 2D map. Two strategies are employed to expedite the discovery of such repairs. We demonstrate the effectiveness of the proposed algorithm via a high-fidelity numerical simulation, which includes the proposed path-planning algorithm, dynamically feasible trajectory generation, trajectory tracking, and simulation of the depth sensor.

Keywords:Autonomous vehicles, Autonomous robots, Uncertain systems Abstract: This paper proposes a novel application of recent research on sums-of-squares (SOS) optimization to feedback motion planning. We use nonlinear programming (NLP) to provide open-loop control and dynamic trajectories for a vehicle in segments, and then consider the problem of generating global trajectories by using a probabilistic roadmap (PRM) or a rapidly-exploring random tree (RRT). Furthermore, we compute funnels (reachable sets) using SOS optimization along the trajectory in which the vehicles state is guaranteed to remain. Considering the expensive computation of SOS, we adopt a funnel library to pre-compute funnels. A vehicle is subjected to disturbances due to model uncertainty and sensor noise, and the funnel library is computed without any knowledge of the severity of noise before motion planning. Therefore, we propose to use the Pontryagin difference method to shrink the funnels to account for noise-corrupted measurements, whose availability varies spatially throughout the state space. Our major contribution is to take into account the effect of measurement and model uncertainty in funnel computation, and we propose two efficient algorithms, feedback belief roadmap (FBRM) motion planning and feedback rapidly exploring random belief trees (FRRBT) motion planning, to generate safe trajectories. Our algorithms are demonstrated in simulated experiments showing their advantages over others.

Keywords:Estimation, Adaptive control, Stability of nonlinear systems Abstract: We present a sufficient condition for global asymptotic stability of linear time-varying systems of the form dx/dt=Ax+Bf(t)'z, dz/dt=-f(t)C'x with strictly positive real transfer function W(s)=C'inv(sI-A)B and the vector f(t) not satisfying the well-known persistent excitation condition. It is also shown that the criterion is optimal in some well-defined sense - making the condition "almost" necessary as well. This class of systems arise in many control applications including system identification and adaptive control.

Keywords:Estimation, Chaotic systems Abstract: Recently, Liberzon and Mitra established the notion of estimation entropy as a measure for the smallest information rate about the state of a system above which an exponential state estimation with a given exponent is possible. This paper shows that estimation entropy is closely related to the alpha-entropy, a concept introduced by Thieullen. Using this relation, we provide a lower estimate for estimation entropy in terms of Lyapunov exponents under the assumption of an absolutely continuous invariant measure with a bounded density, which includes in particular Hamiltonian and symplectic systems.

Keywords:Estimation, Identification, Nonlinear systems identification Abstract: The paper deals with the estimation of the noise covariance matrices of nonlinear state-space models, which are linearised for the purpose of the estimation. A special attention is focused on an analysis of the linearisation error effect on the quality of the covariance matrix estimates. For the analysis, typical representatives of four fundamental approaches to noise covariance matrix estimation, i.e., a correlation method, a maximum-likelihood method, a covariance matching method, and a Bayesian method are selected and briefly introduced. The analysis is performed using a navigation example with an additional assessment of the direct and indirect impact of the linearisation error on the state estimate.

Keywords:Estimation, Identification, Stochastic systems Abstract: The estimation of nonrandom pole and residue parameters from impulse-response data is revisited. Specifically, for an expository example (a one-pole discrete-time system), the Hammersley-Chapman-Robbins lower bound (HCRB) on the estimation error variance is derived, and compared with the widely-used Cramer-Rao bound (CRB). The HCRB is found to be significantly tighter than the CRB over a range of parameter values. Simplifications of the HCRB which admit analytical expressions but are guaranteed to outperform the CRB are also derived. The results indicate that CRB-based confidence intervals for pole-residue estimates, which are being used in several mode monitoring applications, need to be examined with caution.

Keywords:Estimation;Fault detection Abstract: In a recent publication there are new results concerning the polytopic set of possible states of a linear discrete-time SISO system subject to bounded disturbances from measurements corrupted by bounded noise. Using these results we construct an algorithm which, for the special case of a plant with a lag, recursively updates these polytopic sets when new measurements arrive.

Keywords:Estimation, Filtering, Kalman filtering Abstract: Nonlinear filtering based on Gaussian densities is commonly performed using so-called Linear Regression Kalman Filters (LRKFs). These filters rely on sample-based approximations of Gaussian densities. We propose a novel sampling scheme that is based on decomposing the problem of sampling a multivariate Gaussian into sampling a univariate Gaussian and sampling uniformly on the surface of a hypersphere. The proposed sampling scheme has significant advantages compared to existing methods because it produces a user-selectable number of samples with uniform, nonnegative weights and it does not require any numerical optimization. We evaluate the novel method in simulations and provide comparisons to multiple state-of-the-art approaches.

Keywords:Agents-based systems, Cooperative control;Emerging control applications Abstract: In this paper we investigate the problem of containing an outbreak using multiple cooperative agents. We present a general mathematical description of outbreak dynamics, which models the behaviour of many real-world situations including outbreaks of epidemic diseases, wild fires, riots, insect spreads, etc. Based on the outbreak dynamics we provide conditions on the positions of the control agents that guarantee that an outbreak can be contained before a deadline. A coverage control law that maximizes the area in which agents are able to contain a future unknown outbreak is deduced from these conditions. Simulation results illustrate the potential of the approach.

Keywords:Agents-based systems, Cooperative control;Hybrid systems Abstract: This paper presents a fully automated procedure for controller synthesis for a general class of multi-agent systems under coupling constraints. Each agent is modeled with dynamics consisting of two terms: the first one models the coupling constraints and the other one is an additional bounded control input. We aim to design these inputs so that each agent meets an individual high-level specification given as a Metric Interval Temporal Logic (MITL). Furthermore, the connectivity of the initially connected agents, is required to be maintained. First, assuming a polyhedral partition of the workspace, a novel decentralized abstraction that provides controllers for each agent that guarantee the transition between different regions is designed. The controllers are the solution of a Decentralized Robust Optimal Control Problem (DROCP) for each agent. Second, by utilizing techniques from formal verification, an algorithm that computes the individual runs which provably satisfy the high-level tasks is provided.

Keywords:Agents-based systems, Cooperative control, Sensor networks Abstract: In this paper, we study a distributed approach based on consensus algorithms for clock synchronization in wireless sensor networks. The sensor nodes face two types of uncertainties. One is that some of the nodes in the network can be faulty or even malicious and transmit arbitrary signals by not following the given protocol. The other is that the communication is unreliable and the packets exchanged among nodes may become lost, which results in bounded time delays in the neighbors' information. To deal with them, we propose a resilient algorithm where each normal node ignores the outliers in the clock data collected from its neighbors and also make updates based on data received in the past if new data has not arrived yet. We establish network connectivity conditions in terms of graph robustness for the proposed algorithm to attain resilient properties.

Keywords:Agents-based systems, Cooperative control, Stability of nonlinear systems Abstract: This paper addresses formation control of reduced attitudes in which a continuous protocol is proposed for achieving and stabilizing all regular polyhedra (also known as Platonic solids) under a unified framework. The protocol contains only relative reduced attitude measurements and does not depend on any particular parametrization as is usually used in the literature. A key feature of the control proposed is that it is intrinsic in the sense that it does not need to incorporate any information of the desired formation. Instead, the achieved formation pattern is totally attributed to the geometric properties of the space and the designed inter-agent connection topology. Using a novel coordinates transformation, asymptotic stability of the desired formations is proven by studying stability of a constrained nonlinear system. In addition, a methodology to investigate stability of such constrained systems is also presented.

Keywords:Agents-based systems, Cooperative control, Time-varying systems Abstract: In this paper we investigate the control of leader-follower swarms with time-varying objective functions and under balanced communication topologies. Motivated by shared control strategies for centralized systems, we formulate a control framework for distributed systems in which a leader agent and follower agents are interconnected via virtual cohesive forces in a balanced directed network, and the influence of the leader on the follower agents is regulated through time-varying inter-agent coupling dynamics. For such multi-agent systems, we investigate the stability under the proposed control framework and establish a connection between the bounds on the time-varying coupling and the ultimate swarm size. These results are obtained by studying the algebraic connectivity properties of the underlying weighted communication graph of the multi-agent system. Next, the application of our results to systems with switching communication topologies are discussed, with examples presented in swarm cohesion maintenance and collision avoidance problems. The theoretical results developed in this work are verified through numerical simulations.

Keywords:Systems biology Abstract: Synthetic biology is a rapidly expanding field at the interface of the engineering and biological sciences which aims to apply rational design principles in biological contexts. Many natural processes utilise regulatory architectures that parallel those found in control and electrical engineering, which has motivated their implementation as part of synthetic biological constructs. Tools based upon control theoretical concepts can be used to design such systems, as well as to guide their experimental realisation. In this paper we provide examples of biological implementations of negative feedback systems, and discuss progress made toward realisation of other feedback and control architectures. We then outline major challenges posed by the design of such systems, particularly focusing on those which are specific to biological contexts and on which feedback control can have a significant impact. We explore future directions for work in the field, including new approaches for theoretical design of biological control systems, the utilisation of novel components for their implementation, and the potential for application of automation and machine learning approaches to accelerate synthetic biological research.

Keywords:Distributed control, Estimation;Hybrid systems Abstract: A hybrid observer is described for estimating the state of an m>0 channel, n-dimensional, continuous-time, linear system of the form dot{x} = Ax,;y_i =C_ix,;iin{1,2,ldots, m}. The system's state x is simultaneously estimated by m agents assuming each agent i senses y_i and receives appropriately defined data from each of its current neighbors. Neighbor relations are characterized by a time-varying directed graph mathbb{N}(t) whose vertices correspond to agents and whose arcs depict neighbor relations. Agent i updates its estimate x_i of x at ``event times'' t_1,t_2,ldots using a local continuous-time linear observer and a local parameter estimator which for each jgeq 1, iterates q times during the time interval [t_{j-1},t_j) to obtain an estimate of x(t_j). Subject to the assumptions that none of the C_i are zero, the neighbor graph mathbb{N}(t) is strongly connected for all time, and the system whose state is to be estimated is jointly observable, it is shown that for any number lambda >0 it is possible to choose q and the local observer gains so that each estimate x_i converges to x as fast as e^{-lambda t} converges to zero.

Keywords:Distributed control, Agents-based systems Abstract: This paper establishes a general theorem concerning the eigenvalue invariance of certain inhomogeneous matrix products with respect to changes of individual multiplicands' orderings. Instead of detailed entries, it is the zero-nonzero structure that matters in determining such eigenvalue invariance. The theorem is then applied in analyzing the convergence rate of a distributed algorithm for solving linear equations over networks modelled by undirected graphs.

Keywords:Agents-based systems, Optimal control, Decentralized control Abstract: Leader selection for a single-leader, continuous-time multi-agent system, with single-integrator agents, is considered. A network of single integrator agents interact with each other according to the well studied asymptotic consensus law proposed by Olfati-Saber and Murray. In addition to the input prescribed by this consensus law, it is assumed that a bounded external input is allowed to act on only one (called the leader) of the agents. For each choice of leader, this bounded external input can be optimized to drive all the agents to a consensus state in the minimum possible time. This paper presents an algorithm for selecting a leader such that the time taken to reach consensus is the least among the minimum consensus times achievable by each leader. Recently developed Groebner basis based algorithms are used to calculate explicit set of polynomials which partitions each hyper-sphere in the state-space, centered at the origin; where each partition is identified with a particular leader node. The Groebner basis needs to be computed only once. To select the minimum time leader, these demarcating polynomials need to be evaluated at given initial condition exactly one time.

Keywords:Networked control systems, Stability of nonlinear systems, Robust control Abstract: A networked control system (NCS) consisting of cascaded two-port communication channels between the plant and controller is modeled and analyzed. It is shown that the robust stability of the two-port NCS can be guaranteed when the nonlinear uncertainties in the transmission matrices are sufficiently small in norm. The stability condition, given in the form of ``arcsin'' of the uncertainty bounds, is both necessary and sufficient.

Keywords:Network analysis and control, Distributed control, Control of networks Abstract: This paper presents a first-order continuous-time distributed step-size algorithm for computing the least squares solution to a linear equation over networks. Given the uniqueness of the solution and nonintegrable step size, the convergence results are provided for fixed graphs. For the nonunique solution and square integrable step size, the convergence is shown for constantly connected switching graphs. We also validate the results and illustrate possible impacts on the convergence speed using a few numerical examples.

Keywords:Network analysis and control, Large-scale systems Abstract: To achieve control objectives for extremely complex and very large scale networks using standard methods is a challenging, if not intractable, task. In this paper, we propose a novel way to approximately control network systems which lie in a sequence with a well defined limit by the use of graphon theory and the theory of infinite dimensional systems. The general controllability problem is analyzed for the infinite system and then the control performance in terms of the upper bound for the L2 state error between the limit system and the sequence of network systems is given. Finally, an example of the application of the minimum energy control methodology for network systems with sampled weightings is demonstrated.

Keywords:Network analysis and control, Control of networks, Linear systems Abstract: Control-channel interactions in a linear diffusive network model are studied, with the aim of highlighting the role of the network's topology in such interactions. Specifically, the influence of a built controller on the infinite and finite zero structure of a second control channel is characterized. The analysis shows how the network's graph topology, the relative positions of the control channels, and the specifics of the built controller influence the zero structure of the second control channel. In particular, it is shown that the some control architectures can introduce undesirable non-minimum-phase dynamics at remote locations, while others are guaranteed to maintain or promote minimum-phase dynamics.

Keywords:Network analysis and control, Agents-based systems, Stochastic systems Abstract: A stochastic multi-agent opinion dynamics model is proposed and analyzed, in which, the multi-leveled opinion of each agent is influenced by a random neighbor's binary action, determined by its opinion level. This model is shown to asymptotically produce consensus with a finite number of connected agents. On the other hand, when the number of agents is large, the time to achieve consensus can become exponentially high, potentially resulting in other equilibrium points based on the structure of the connectivity graph. Numerical simulations validate the proposed analysis and demonstrate these other equilibrium points, that exist when a large number of agents are present.

Keywords:Network analysis and control, Distributed control, Agents-based systems Abstract: In this paper, we propose a distributed algorithm that relies on a strongly connected (but possibly directed) communication topology to achieve admissible and balanced flows in a given network. More specifically, we consider a flow network that is described by a digraph (physical topology), each edge of which can admit a flow within a certain interval. The paper proposes and analyzes a distributed iterative algorithm for computing admissible and balanced flows, i.e., flows that are within the given interval at each edge and balance the total in-flow and the total out-flow at each node. Unlike previous work that required a communication topology with bidirectional exchanges between pairs of nodes that are physically connected (i.e., nodes that share an edge in the physical topology), the distributed algorithm we propose only requires a communication topology that matches the physical topology (which is, in general, directed). The proposed algorithm allows the nodes to asymptotically (with geometric rate) compute a set of admissible and balanced flows, as long as such solution exists.

Keywords:Network analysis and control, Distributed control, Estimation Abstract: In this paper, we study a problem of target tracking and circumnavigation with a network of autonomous agents. We propose a distributed algorithm to estimate the position of the target and drive the agents to rotate around it while forming a regular polygon and keeping a desired distance. We formally show that the algorithm attains exponential convergence of the agents to the desired polygon if the target is stationary, and bounded convergence if the target is moving with bounded speed. Numerical simulations corroborate the theoretical results and demonstrate the resilience of the network to addition and removal of agents.

Keywords:Network analysis and control, Distributed control, Filtering Abstract: This paper revisits the problem of multi-agent consensus from a graph signal processing perspective. By defining the graph filter from the consensus protocol, we establish the direct relation between average consensus of multi-agent systems and filtering of graph signals. This relation not only provides new insights of the average consensus, it also turns out to be a powerful tool to design effective consensus protocols for uncertain networks, which is difficult to deal with by existing time-domain methods. In this paper, we consider two cases, one is uncertain networks modeled by an estimated Laplacian matrix, the other is connected graphs with unknown topology. The consensus protocols are designed by interpolation methods for both cases based on the protocol filter. Several numerical examples are given to demonstrate the effectiveness of our methods.

Inst. of Problems of Mechanical Engineering Russian Acad

Keywords:Linear systems, Uncertain systems Abstract: In the paper the algorithm with compensation of parametric uncertainties, external disturbances and measurement noises for linear time-invariant plants is proposed. It is assumed, that the dimension of the noise can be equal to the state vector dimension and the disturbance can be presented in any equation of the plant model. Analytical condition for algorithm feasibility is proposed. The simulations show the efficiency of the proposed algorithm.

Keywords:Stochastic optimal control, Uncertain systems, Robust control Abstract: The design of controllers for systems whose dynamics is uncertain or poorly known is a recurrent theme in control systems theory. Usually the mathematical models for control design are approximations of the dynamics of the real systems, and uncertainties arise naturally in this context. In the field of control systems, the theory of robust control is one typical approach for such systems, where the goal is to guarantee some features for the designed controller such as stability and a satisfactory performance against a set of possible uncertainties. Other common approach in the literature is found in the theory of stochastic control, where the uncertainties affecting the system are modeled as stochastic processes. In the literature, a recent proposal to control uncertain stochastic systems is the so called CVIU --- Control Variation Increases Uncertainties --- approach. This approach makes use of stochastic state- and control- dependent noise, and the corresponding control problem involves minimization of a discounted quadratic function. The representation of uncertainties in the CVIU approach bears similarities with models used in robust control theory, which motivates our discussion on the relations between the two approaches. A correspondence between the H_{2} stochastic norm and the expected value of a discounted functional bridges the different cost criteria.

Keywords:Uncertain systems, Stochastic systems, LMIs Abstract: New linear matrix inequality (LMI) based conditions are proposed in this paper to solve the problems of designing H-infinity robust state feedback controllers and full- or reduced-order H-infinity filters for polytopic discrete-time linear systems affected by state-multiplicative noise. As a novelty, the uncertainties that affect the multiplicative noise matrices are considered to belong to a polytopic set which is distinct from the polytope where the other state space matrices lie. Consequently, the decision variables of the optimization problems, fixed as polynomials, can depend with distinct arbitrary degrees on the uncertain parameters, providing flexibility to trade-off computational complexity and accuracy of the computed H-infinity guaranteed costs in both control and filter designs. The merits of the proposed technique are illustrated by numerical examples and comparisons with other methods from the literature.

Keywords:Uncertain systems, Robust control, Lyapunov methods Abstract: AbstractThis paper provides a comprehensive framework for local stability analysis of uncertain feedback interconnections within the integral quadratic constraints theory using general dynamic multipliers. It is shown how so-called hard and soft constraints can be effectively combined in order to (locally) capture the action of the uncertainty. This is illustrated for Zames-Falb multipliers, where it is proven that the subclasses of causal and anticausal multipliers can easily be factorized into hard constraints and thus individually be incorporated into the framework without introducing conservatism.

Keywords:Uncertain systems, Robust control, Randomized algorithms Abstract: A new method to plan guaranteed to be safe paths in an uncertain environment, with an uncertain initial and final configuration space, while avoiding static obstacles is presented. First, two improved versions of the previously proposed BoxRRT algorithm are presented: both with a better integration scheme and one of them with the control input selected according to a desired objective, and not randomly, as in the original formulation. Second, a new motion planner, called towards BoxRRT*, based on optimal Rapidly-exploring Random Trees algorithm and using interval analysis is intro- duced. Finally, each of the described algorithms are evaluated on a numerical example. Results show that our algorithms make it possible to find shorter reliable paths with less iterations.

Keywords:Uncertain systems, Estimation, Stochastic systems Abstract: We introduce the problem of protecting the privacy of textit{time-varying} sensitive data using differential privacy. Contrary to prior work that considers fixed private data, we wish to design a privacy-preserving mechanism that, at each time and given the observations so far, keeps the textit{current} state of a dynamical system private. Our work protects dynamical systems from being tracked by an adversary by providing differentially private guarantees.

Specifically, we propose a mechanism which adds artificial noise to (i) the input of the system and (ii) the measurements which are then published. In particular, two scenarios are considered: for a scalar dynamical system under epsilon--differential privacy, we derive a mechanism that, at each time, publishes the most accurate approximation of the current state while preserving privacy. Next, for a general linear system under (epsilon,delta)--differential privacy, we propose a Gaussian--based privacy--preserving mechanism with a quadratic cost.

Keywords:Predictive control for linear systems, Optimization algorithms, Optimization Abstract: We propose a primal-dual interior-point (PDIP) method for solving quadratic programming problems with linear inequality constraints that typically arise from MPC applications. We show that the solver converges (locally) quadratically to a suboptimal solution of the MPC problem. PDIP solvers rely on two phases: the damped and the pure Newton phases. Compared to state-of-the-art PDIP methods, our solver replaces the initial damped Newton phase (usually used to compute a medium-accuracy solution) with a dual solver based on Nesterov's fast gradient scheme (DFG) that converges with a sublinear convergence rate of order O(1/k^2) to a medium-accuracy solution. The switching strategy to the pure Newton phase, compared to the state of the art, is computed in the dual space to exploit the dual information provided by the DFG in the first phase. Removing the damped Newton phase has the additional advantage that our solver saves the computational effort required by backtracking line search. The effectiveness of the proposed solver is demonstrated on a 2-dimensional discrete-time unstable system and on an aerospace application.

Keywords:Computational methods, Autonomous robots Abstract: We present an efficient algorithm for multi-robot motion planning from linear temporal logic (LTL) specifications. We assume that the dynamics of each robot can be described by a discrete-time, linear system together with constraints on the control inputs and state variables. Given an LTL formula ψ, specifying the multi-robot mission, our goal is to construct a set of collision-free trajectories for all robots, and the associated control strategies, to satisfy ψ. We show that the motion planning problem can be formulated as the feasibility problem for a formula φ over Boolean and convex constraints, respectively capturing the LTL specification and the robot dynamics. We then adopt a satisfiability modulo convex (SMC) programming approach that exploits a monotonicity property of φ to decompose the problem into smaller subproblems. Simulation results show that our algorithm is more than one order of magnitude faster than state-of-the-art sampling-based techniques for high-dimensional state spaces while supporting complex missions.

Keywords:Information theory and control, Markov processes, Stochastic optimal control Abstract: In this semi-tutorial paper, we first review the information-theoretic approach to account for the computational costs incurred during the search for optimal actions in a sequential decision making problem. The traditional (MDP) framework ignores computational limitations while searching for the optimal policies, essentially assuming that the acting agent is perfectly rational, aiming for exact optimality. Using the so-called free-energy, a variational principle is then introduced that accounts not only for the value of a policy alone, but also considers the cost of finding this optimal policy. The solution of the variational equations arising from this formulation can be obtained using familiar Bellman-like value iterations from dynamic programing and the Blahut-Arimoto (BA) algorithm from rate distortion theory. Finally, we demonstrate the utility of the approach for generating hierarchies of state abstractions that can be used to best exploit the available computational resources. A numerical example showcases these concepts for a path-planning problem in a grid world environment.

Keywords:Optimal control, Autonomous vehicles;Switched systems Abstract: Collisions, if they are planned appropriately, can enable more effective navigation for robots capable of handling them. A mixed integer programming (MIP) formulation demonstrates the computational practicality of optimizing trajectories that comprise planned collisions. A novel framework is proposed to incorporate a physically realistic model of the hybrid contact dynamics as constraints in the optimization problem. Precise bounds are placed on the error from the simplifying assumptions, and it is shown that the error is driven to zero with finer temporal resolution. Implementation issues are considered in the context of regulation and damage upon contact. In particular, a damage quantification function is proposed. A simulated case study demonstrates that an increase in performance is achieved under this schema as compared to collision-free optimal trajectories.

Keywords:Optimal control, Constrained control, Autonomous robots Abstract: This paper develops a convex optimization-based method for real-time path planning onboard an autonomous vehicle for environments with cylindrical or ellipsoidal obstacles. Obstacles render the state space non-convex, thus a constrained, non-convex optimal control problem must be solved to obtain a feasible trajectory. A technique known as Successive Convexification is used to solve the non-convex optimal control problem via a convergent sequence of convex optimization problems. The paper has two main contributions: first, constraints for ensuring that the computed trajectories do not cross obstacles between discrete states are developed for a class of dynamics; second, the theory of successive convexification is extended to allow for a general class of non-convex state constraints. Finally, simulations for a relevant example are presented to demonstrate the effectiveness of the proposed method.

Keywords:Iterative learning control, Uncertain systems, Learning Abstract: We present a Robust Learning Model Predictive Controller (RLMPC) for constrained uncertain systems performing iterative tasks. The proposed controller builds on earlier work of Learning Model Predictive Control (LMPC) for deterministic systems.The main idea behind RLMPC is to collect data from previous iterations and use it to estimate the current value function and build a robust safe set. We demonstrate that the proposed RLMPC algorithm is able to iteratively improve its control performance and robustly satisfy system constraints. The efficacy and limitations of the proposed RLMPC approach are illustrated on a numerical example.

Max Planck Inst. for Dynamics of Complex Tech. Systems

Keywords:Stability of nonlinear systems;Fluid flow systems, Computational methods Abstract: The stabilization or set point control of incompressible laminar flows has been under vivid investigation since long. All linearization based approaches suffer from the conceptual shortcoming of a possibly small domain of attraction. In order to get the system into the regime where, e.g., Riccati-based feedback stabilization works, nonlinear control laws are necessary. Therefore, we propose a scheme that continuously updates an initial feedback, that guarantees decay of solutions under locally checkable conditions, and that can be realized through solving large-scale linear equations.

Keywords:Stability of nonlinear systems, Linear systems, Numerical algorithms Abstract: The Sector Stability Theorem is an intuitive condition for the stability of feedback loops that unifies many lines of research including robust control, passivity theory, dissipativity theory, and integral quadratic constraints (IQC) theory. This theorem plays a central role in deriving a frequency-domain test for general sector bounds and is used to develop efficient numerical algorithms for checking and enforcing sector bounds on linear time-invariant (LTI) systems. The notion of relative and directional indices are also developed. Two application examples illustrate the potential of the tool and techniques discussed in the paper.

By considering the tracking control of a quadrotor UAV on SE(3) we avoid singularities of Euler angles and ambiguity of quaternions and by explicitly taking into account the constraint of non-zero total thrust in our controller design, we do not achieve a local result but almost global asymptotic stability of the tracking controller. Second, we consider the position tracking error in the body-frame of the reference UAV. As a result, contrary to most existing tracking controllers, our control action becomes independent of the definition of the inertial frame.

We illustrate by simulations that even in the presence of small disturbances and sampled, delayed, and noisy measurements the controller achieves stable tracking error dynamics for which errors converge to some region near the origin.

Keywords:Stability of nonlinear systems, Lyapunov methods, LMIs Abstract: Estimating the Domain of Attraction (DA) of non-polynomial systems is a challenging problem. Taylor expansion is widely adopted for transforming a nonlinear analytic function into a polynomial function, but the performance of Taylor expansion is not always satisfactory. This paper provides solvable ways for estimating the DA via Chebyshev approximation. Firstly, for Chebyshev approximation without the remainder, higher order derivatives of Lyapunov functions are used for estimating the DA, and the largest estimate is obtained by solving a generalized eigenvalue problem. Moreover, for Chebyshev approximation with the remainder, an uncertain polynomial system is reformulated, and a condition is proposed for ensuring the convergence to the largest estimate with a selected Lyapunov function. Numerical examples demonstrate that both accuracy and efficiency are improved compared to Taylor approximation.

Keywords:Stability of nonlinear systems, Lyapunov methods, Stability of linear systems Abstract: Passivity indices are a pair of real numbers that quantitatively measure the shortage/excess of passivity of a system, which provide us with a useful tool for the analysis and design of compositional systems. For a system whose passivity indices are known, it can be passivated by adding the feedforward and/or feedback loop(s), such that its passivity indices both become non-negative. We investigate the achievable bounds of passivity indices of the passivated system and the corresponding bounds for the feedforward/feedback gains. Three cases depending on the sign of the original indices are discussed separately.

Keywords:Stability of nonlinear systems, Lyapunov methods, Uncertain systems Abstract: The small-gain paradigm has long been used to verify stability of feedback interconnected systems. For component systems that are integral input-to-state stable (iISS), available small-gain results require the component systems to be strongly iISS. We remove this restriction by using a recently proposed Lyapunov characterization of iISS that allows cross terms between external inputs and states in the Lyapunov decrease condition. This novel formulation extends previously available iISS small-gain arguments, which is demonstrated in an example.

Keywords:Air traffic management, Optimization, Stochastic systems Abstract: Adverse weather can reduce airport capacity. When the number of arriving aircraft exceeds this reduced capacity, flights can get delayed. A Ground Delay Program (GDP) is a strategy by which aircraft landing slots can be redistributed so that the flights are delayed on the ground itself and not in the air. This increases safety, reduces the fuel consumption and hence the operating costs for airlines. In this paper, we present six algorithms that perform this slot reassignment. These algorithms differ in the extent to which slots can get re-arranged in real-time and the amount of information that the airlines must reveal to the central planner during the implementation. These two features of the algorithm are called as stability and privacy respectively. The efficiency of these six algorithms, measured in terms of the expected delay cost for flights, is compared using operational data for La Guardia Airport in New York. A two-step Receding Horizon Static (2-step RHS) model is shown to be a good compromise based on present expectations of privacy and stability in the system.

Keywords:Biomolecular systems, Markov processes, Optimization Abstract: Model-based prediction of stochastic noise in biomolecular reactions often resorts to approximation with unknown precision. As a result, unexpected stochastic fluctuation causes a headache for the designers of biomolecular circuits. This paper proposes a convex optimization approach to quantifying the steady state moments of molecular copy counts with theoretical rigor. We show that the stochastic moments lie in a convex semi-algebraic set specified by linear matrix inequalities. Thus, the upper and the lower bounds of some moments can be computed by a semidefinite program. Using a protein dimerization process as an example, we demonstrate that the proposed method can precisely predict the mean and the variance of the copy number of the monomer protein.

Keywords:Chaotic systems, Stochastic systems, Neural networks Abstract: This paper deals with asynchronous synchronization for two arrays of coupled jumping neural networks with both a constant leakage delay and discrete time-varying delays in a master-slave configuration, where jumping instants of network modes and controller modes are asynchronous. The asynchronous control, which isgoverned by a finite piecewise homogeneous Markov process and involves the leakage delay and the bounds of the time-varying delays, is proposed. The resultant synchronization error system becomes a piecewise homogeneous Markovian jump nonlinear system with delays. By constructing a suitable mode-dependentLyapunov-Krasovskii functional and employing some matrixinequality techniques combined with Finsler's lemma, a sufficient condition guaranteeing the mean-square exponential stability of the synchronization error system is developed. Finally, a numerical example is provided to demonstrate the theoretical analysis and an image encryption algorithm based on the synchronized drive-response complex networks is also proposed.

Keywords:Control applications;Power generation, Stochastic systems Abstract: Recent research into wind farm control promises the ability to create more densely populated wind farms and improved power production of existing wind farms by controlling for wake interactions between turbines. In this paper, a computationally efficient Discrete time Stochastic and Dynamic model (DStoDyn) is developed using of a wide sense stationary random variable with deterministic mean to model wind direction uncertainties in a wind farm. Comparisons to results obtained from the large eddy simulation software SOWFA show that general wake displacement trends may be represented by DStoDyn.

Keywords:Distributed parameter systems, Fuzzy systems;Fault tolerant systems Abstract: This paper investigates a robust fuzzy fault tolerant control (FTC) problem for a class of coupled systems described by nonlinear ordinary differential equations (ODEs) and two nonlinear beam equations. A robust fuzzy FTC, consisting of a fuzzy FTC for the ODE subsystem and a robust boundary FTC for the beam, is developed in terms of bilinear matrix inequalities (BMIs) by Lyapunovs direct method to guarantee the exponential stability of the closed-loop coupled system in both the normal and failure cases while the unique existence of mild solution of the closed-loop normal coupled system is discussed. Finally, the simulation study of the flexible spacecraft is given to show the effectiveness of the proposed method.

Shenyang Inst. of Automation, Chinese Acad. Ofsciences

Keywords:Fuzzy systems;Fault tolerant systems, Markov processes Abstract: This paper investigates the reliable control for T-S fuzzy delayed systems using a semi-Markov processThe aim is to design a fuzzy reliable controller such that the closed-loop system is stochastically stable even if the appearance of actuator failures. A mode-dependent Lyapunov-Krasovskii functional is employed and some novel integral inequalities are utilized in order to reduce the conservatism. In this case, some criteria are established and the desired controller can be achieved by settling an optimization issue in view of the proposed criteria. Finally, an example is presented to show the effectiveness of the given results.

Keywords:Distributed parameter systems, Stability of linear systems, Lyapunov methods Abstract: This article considers systems coupling an ordinary differential equation (ODE) with a wave equation through its boundary data. The main focus is put on the role of different time scales for each equation on the stability of the coupled system. A fast wave equation coupled to an ODE is proven to be stable if each subsystem is stable. However, we show examples of stable subsystems generating an unstable full system when coupling a wave equation to a fast ODE.

Keywords:Distributed parameter systems;Delay systems, Stability of nonlinear systems Abstract: This paper presents a control design for the one-phase Stefan problem under actuator delay via a backstepping method. The Stefan problem represents a liquid-solid phase change phenomenon which describes the time evolution of a material's temperature profile and interface position. The actuator delay is modeled by a first-order hyperbolic partial differential equation (PDE), resulting in a cascaded transport-diffusion PDE system defined on a time-varying spatial domain described by an ordinary differential equation (ODE). Two nonlinear backstepping transformations are utilized for the control design. The setpoint restriction is given by the initial internal energy of the physical system and the stored energy injected by past input heat arising from the delay initial condition, which guarantees a physical constraint on the proposed controller for the melting process. This constraint ensures the exponential convergence of the moving interface to a setpoint and exponential stability of the temperature equilibrium profile and the delayed controller in the H1 norm.

Keywords:Distributed parameter systems;Delay systems, Networked control systems Abstract: We consider a reaction-diffusion PDE under continuously applied boundary control that contains a constant delay. The point measurements are sampled in time and transmitted through a network with a time-varying delay. We construct an observer that predicts the value of the state allowing to compensate for the constant boundary delay. Using a time-varying injection gain, we ensure that the estimation error vanishes exponentially with a desired decay rate if the delays and sampling intervals are small enough while the number of sensors is large enough. The stability conditions, obtained via a Lyapunov-Krasovskii functional, are formulated in terms of linear matrix inequalities. By applying the backstepping transformation to the future state estimation, we derive a boundary controller that guarantees the exponential stability of the closed-loop system with an arbitrary decay rate smaller than that of the observer. The results are demonstrated by an example.

Keywords:Distributed parameter systems;Flexible structures, Estimation Abstract: The disturbance estimator design proposed in [IEEE Trans. Automat. Control, 10.1109/TAC.2016.2636571] is a systematic method to deal with the control-matched uncertainty. There are two main highlights for this approach: the disturbance estimator is not invoking high-gain and the derivative of disturbance is not required to be bounded. In this paper, we propose an output feedback control to stabilize an Euler Bernoulli beam equation by following the idea of [IEEE Trans. Automat. Control,10.1109/TAC.2016.2636571]. The main difficulty is that the boundary of the beam contains both interior uncertainty and the external disturbance. The well-posedness and the asymptotical stability of the closed-loop are proved by a novel transformation from which the nonlinear problem can be solved by method for linear ones.

Keywords:Distributed parameter systems, Lyapunov methods, Communication networks Abstract: This paper deals with dynamic boundary control synthesis of communication networks which are modeled under fluid-flow modeling and compartmental representation. The boundary control synthesis of the resulting linearized coupled hyperbolic PDE-ODEs is carried by means of Lyapunov techniques and LMIs formulation. Two specific control functions with constraints are studied. Input-to state stability of the linearized system of an optimal equilibrium is guaranteed while minimizing the asymptotic gain due to the control actions.

Keywords:Distributed parameter systems, Lyapunov methods, Sampled-data control Abstract: With the growing utility of hyperbolic systems in modeling physical and controlled systems, this paper considers the problem of stabilization of boundary controlled hyperbolic partial differential equations where the output measurements are communicated after being time-sampled and space-quantized. Static and dynamic controllers are designed, which establish stability in different norms with respect to measurement errors using Lyapunov-based techniques. For practical purposes, stability in the presence of event-based sampling and quantization errors is analyzed. The design of sampling algorithms ensures practical stability.

Keywords:Distributed parameter systems, Estimation, Optimization Abstract: In this paper we investigate the use of Stochastic Reduced Order Models (SROMs) for solving Stochastic Source Identification (SSI) problems in steady-state transport phenomena given statistics of the system state at a small number of locations. We capture the physics of the transport phenomenon by a Partial Differential Equation (PDE) which we discretize using the finite element method. The SSI problem is then formulated as a stochastic optimization problem constrained by the PDE, and then transformed into a deterministic one after representing the random quantities with a low-dimensional discrete SROM. The small number of samples given by SROMs requires only a small number of PDE solves at each optimization iteration in order to obtain a solution to the SSI problem, defined as a distribution of possible source locations and intensities. We provide simulations to demonstrate the effectiveness of SROMs in capturing uncertainty. We also demonstrate the ability of SROMs to capture multiple independent sources of uncertainty, in particular, we consider uncertainty in the location of the measurements which has practical implications in robotics applications.

Keywords:Optimization, Optimization algorithms Abstract: We present a Matlab toolbox that automatically computes tight worst-case performance guarantees for a broad class of first-order methods for convex optimization. The class of methods includes those performing explicit, projected, proximal, conditional and inexact (sub)gradient steps.

The toolbox relies on the performance estimation (PE) framework, which recently emerged through works of Drori and Teboulle and the authors. The PE approach is a very systematic manner of obtaining non-improvable worst-case guarantees for first-order numerical optimization schemes. However, using the PE methodology requires modelling efforts from the user, along with some knowledge of semidefinite programming. The goal of this work is to ease the use of the performance estimation methodology, by providing a toolbox that implicitly does the modelling job. In short, its aim is to (i) let the user write the algorithm in a natural way, as he/she would have implemented it, and (ii) let the computer perform the modelling and worst-case analysis parts automatically.

Keywords:Identification, Optimization Abstract: In the context of direct data-driven design, we propose a controller design procedure on the basis of a set of experimental input/output data, with no identification of the plant model. The objective of the control problem is to make the closed-loop system to match the behavior of an assigned reference model as close as possible. As is well known, the presence of one of more non-minimum phase zeros in the plant transfer function makes the direct data-driven design procedure significantly harder since, no matter what is the considered approach among the ones proposed in the literature, the designed controller commonly leads to an unstable closed-loop system due to unstable pole-zero cancellations. In this paper we propose a new approach for performing the design of direct data-driven controller when the unknown plant may or may not have non-minimum phase zeros. The problem is formulated in the context of the set-membership estimation theory, and previous results from some ot the authors on errors-in-variables identification are exploited to compute the controller parameters. The effectiveness of the presented technique is demonstrated by means of two simulation examples.

Keywords:Control system architecture, Optimization Abstract: Many real-world control systems, such as the smart grid and human sensorimotor control systems, have decentralized components that react quickly using local information and centralized components that react slowly using a more global view. This paper seeks to provide a theoretical framework for how to design controllers that are decomposed across timescales in this way.The framework is analogous to how the network utility maximization framework uses optimization decomposition to distribute a global control problem across independent controllers, each of which solves a localproblem; except our goal is to decompose a global problem temporally, extracting a timescale separation. Our results highlight that decomposition of a multi-timescale controller into a fast timescale, reactive controller and a slow timescale, predictive controller can be near-optimal in a strong sense. In particular, we exhibit such a design, named Multi-timescale Reflexive Predictive Control (MRPC), which maintains a per-timestep cost within a constant factor of the offline optimal in an adversarial setting.

Keywords:Identification, Optimization, Optimization algorithms Abstract: In this paper, a novel optimization method for the data-driven local coordinates approach to a prediction error method, which is one of system identification methods, is developed. In the proposed method, parameters of system matrices to be estimated are kept as their original forms of matrices whereas they are converted into a vector in the literature. Optimization with respect to the matrix variables can improve the computational efficiency. Furthermore, it is effective to identify input-output equivalent systems with each other since they attain the same value of the objective function. To this end, a Riemannian quotient manifold is introduced. The geometry of the proposed manifold is investigated and a novel Riemannian conjugate gradient method on the manifold is provided. Numerical experiments show that the difference of the proposed Riemannian conjugate gradient method from Euclidean one greatly improves the efficiency of the algorithm.

Keywords:Optimization algorithms, Distributed control, Randomized algorithms Abstract: In this paper, we consider a network of processors aiming at cooperatively solving a convex feasibility problem in which the constraint set is the intersection of local uncertain sets, each one known only by one processor. We propose a randomized, distributed method---using concepts borrowed from a centralized ellipsoid algorithm---having finite-time convergence and working under asynchronous, time-varying and directed communication topologies. At every communication round, each processor maintains a "candidate" ellipsoid for the global problem and performs two tasks. First, it verifies---in a probabilistic sense---if the center of the candidate ellipsoid is robustly feasible for its local set and, if not, constructs a new ellipsoid with smaller volume. Second, it exchanges its ellipsoid with neighbors, and then selects the one with smallest volume among the collected ones. We show that in a finite number of communication rounds, the processors reach consensus on a common ellipsoid whose center is---with high confidence---feasible for the entire set of uncertainty except a subset having an arbitrary small probability measure. We corroborate the theoretical results with numerical computations in which the algorithm is tested on a multi-core platform of processors communicating asynchronously.

Keywords:Iterative learning control, Optimal control, Learning Abstract: Reinforcement learning belongs to a class of artificial intelligence algorithms which can be used to design adaptive optimal controllers learned online. These methods have mostly been based on state feedback, which limits their application in practical scenarios. In this paper, we present an output feedback Q-learning algorithm to solve the discrete-time linear quadratic regulator (LQR) problem. An output feedback Q-learning scheme is proposed that learns the optimal controller online without requiring any knowledge of system dynamics, making it completely model-free. Both policy iteration (PI) and value iteration (VI) algorithms are developed, where the later does not require an initially stabilizing policy. The convergence of these algorithms has been shown. The proposed method does not require a discounting factor which is typically introduced in the cost function to trade-off between the excitation noise bias and system stability. The method is therefore exact and converges to the actual LQR control solution obtained by solving the Riccati equation. Simulation results have been used to show the effectiveness of the scheme.

Keywords:Optimal control;Quantum information and control, Numerical algorithms Abstract: The objective of this work is to study time-minimum and energy-minimum global optimal control for dissipative open quantum systems whose dynamics is governed by the Lindblad equation. The controls appear only in the Hamiltonian.

Using recent results regarding the decoupling of such dissipative dynamics into intra- and inter-unitary orbits, we transform the control system into a bi-linear control system on the Bloch ball (the unitary sphere together with its interior). We thendesign a numerical algorithm to construct an optimal path to achieve a desired point given initial states close to the origin (the singular point) of the Bloch ball. This is done both for the minimum-time and minimum -energy control problems.

Keywords:Optimal control, Stochastic optimal control;Energy systems Abstract: In this paper, we consider the problem of dynamic programming when supremum terms appear in the objective function. Such terms can represent overhead costs associated with the underlying state variables. Specifically, this form of optimization problem can be used to represent optimal scheduling of batteries such as the Tesla Powerwall for electrical consumers subject to demand charges - a charge based on the maximum rate of electricity consumption. These demand charges reflect the cost to the utility of building and maintaining generating capacity. Unfortunately, we show that dynamic programming problems with supremum terms do not satisfy the principle of optimality. However, we also show that the supremum is a special case of the class of forward separable objective functions. To solve the dynamic programming problem, we propose a general class of optimization problems with forward separable objectives. We then show that for any problem in this class, there exists an augmented-state dynamic programming problem which satisfies the principle of optimality and the solutions to which yield solutions to the original forward separable problem. We further generalize this approach to stochastic dynamic programming problems and apply the results to the problem of optimal battery scheduling with demand charges using a data-based stochastic model for electricity usage and solar generation by the consumer.

Keywords:Optimal control;Switched systems, Computational methods Abstract: Kraus maps (completely positive trace preserving maps) arise classically in quantum information, as they describe the evolution of noncommutative probability measures. We introduce tropical analogues of Kraus maps, obtained by replacing the addition of positive semidefinite matrices by a multivalued supremum with respect to the L"owner order. We show that non-linear eigenvectors of tropical Kraus maps determine piecewise quadratic approximations of the value functions of switched optimal control problems. This leads to a new approximation method, which we illustrate by two applications: 1) approximating the joint spectral radius, 2) computing approximate solutions of Hamilton-Jacobi PDE arising from a class of switched linear quadratic problems studied previously by McEneaney. We report numerical experiments, indicating a major improvement in terms of scalability by comparison with earlier numerical schemes, owing to the "LMI-free" nature of our method.

Keywords:Optimal control, Time-varying systems, Computational methods Abstract: A state constrained optimal control problem subject to continuous-time linear time-varying dynamics is decomposed into a family of linear quadratic regulator (LQR) problems via convex duality and a game formalism. By addressing these LQR problems directly, a feedback characterisation for the optimal control is given in terms of the solution of a two-point boundary value problem (TPBVP). This characterisation is illustrated via its application in a simple example.

Keywords:Optimal control, Linear systems, Markov processes Abstract: This paper studies finite-horizon optimal control of a class of degradable systems modeled by acyclic semi-Markov jump linear systems. The Cox distribution is used to Markovianize the underlying semi-Markov jump process. Control design challenges in optimal control of Markov jump linear systems with partial or no mode observation are discussed and by exhibiting a numerical example it is shown that unlike the full-mode observable case, if some jumps cannot be observed the necessary optimality condition may not be sufficient for the optimality of the linear state-feedback control law. The optimal control of an acyclic semi-Markov jump linear system is then investigated through Markovianization by Coxian models. Furthermore, some insights are provided on the problem of Cox model order reduction in order to reduce the computational complexity associated with the control design.

Keywords:Sampled-data control, Networked control systems;Emerging control applications Abstract: Zero dynamics attack is lethal to cyber-physical systems in the sense that it is stealthy and there is no way to detect it. Fortunately, if the given continuous-time physical system is of minimum phase, the effect of the attack is negligible even if it is not detected. However, the situation becomes unfavorable again if one uses digital control by sampling the sensor measurement and using the zero-order-hold for actuation because of the `sampling zeros.' When the continuous-time system has relative degree greater than two and the sampling period is small, the sampled-data system must have unstable zeros (even if the continuous-time system is of minimum phase), so that the cyber-physical system becomes vulnerable to `sampling zero dynamics attack.' In this paper, we begin with its demonstration by a few examples. Then, we present an idea to protect the system by allocating those discrete-time zeros into stable ones. This idea is realized by employing the so-called `generalized holder' which replaces the zero-order-holder.

Keywords:Fault detection, Distributed control, Optimization Abstract: We consider the design and analysis of robust distributed control systems (DCSs) to ensure the detection of integrity attacks. DCSs are often managed by independent agents and are implemented using a diverse set of sensors and controllers. However, the heterogeneous nature of DCSs along with their scale leave such systems vulnerable to adversarial behavior. To mitigate this reality, we provide tools that allow operators to prevent zero dynamics attacks when as many as p agents and sensors are corrupted. Such a design ensures attack detectability in deterministic systems while removing the threat of a class of stealthy attacks in stochastic systems. To achieve this goal, we use graph theory to obtain necessary and sufficient conditions for the presence of zero dynamics attacks in terms of the structural interactions between agents and sensors. We then formulate and solve optimization problems which minimize communication networks while also ensuring a resource limited adversary cannot perform a zero dynamics attacks. Polynomial time algorithms for design and analysis are provided.

Keywords:Optimization, Optimization algorithms;Fault tolerant systems Abstract: In this paper, we focus on applications in machine learning, optimization, and control that call for the resilient selection of a few elements, e.g. features, sensors, or leaders, against a number of adversarial denial-of-service attacks or failures. In general, such resilient optimization problems are hard, and cannot be solved exactly in polynomial time, even though they often involve objective functions that are monotone and submodular. Notwithstanding, in this paper we provide the first scalable algorithm for their approximate solution, that is valid for any number of attacks or failures, and which, for functions with low curvature, guarantees superior approximation performance. Notably, the curvature has been known to tighten approximations for several non-resilient maximization problems, yet its effect on resilient maximization had hitherto been unknown. We complement our theoretical analyses with supporting empirical evaluations.

Keywords:Hybrid systems, Estimation Abstract: In this paper, we study a security problem for attack detection in a class of cyber-physical systems consisting of discrete computerized components interacting with continuous agents. We consider an attacker that may inject recurring signals on both the physical dynamics of the agents and the discrete interactions. We model these attacks as additive unknown inputs with appropriate input signatures and timing characteristics. Using hybrid systems modeling tools, we design a novel hybrid attack monitor and, under reasonable assumptions, show that it is able to detect the considered class of recurrent attacks. Finally, we illustrate the general hybrid attack monitor using a specific finite time convergent observer and show its effectiveness on a simplified model of a cloud-connected network of autonomous vehicles.

Keywords:Networked control systems;Fault detection, Linear systems Abstract: Securing cyber-physical systems is vital for our modern society since thy are widely used in critical infrastructure like power grid control and water distribution. One of the most sophisticated attacks on these systems is the covert attack, where an attacker changes the system inputs and disguises his influence on the system outputs by changing them accordingly. In this paper an approach to detect such an attack by extending the original system with a switched auxiliary system is proposed. Furthermore, a detection system using a switched Luenberger observer is presented. The effectiveness of the proposed method is illustrated by a simulation example.

Keywords:Stochastic systems, Adaptive control;Fault tolerant systems Abstract: In this paper, we propose a novel adaptive control architecture for addressing security and safety in cyber-physical systems subject to exogenous disturbances. Specifically, we develop an adaptive controller for time-invariant, state-dependent adversarial sensor and actuator attacks in the face of stochastic exogenous disturbances. We show that the proposed controller guarantees uniform ultimate boundedness of the closed-loop dynamical system in a mean-square sense. We further discuss the practicality of the proposed approach and provide a numerical example involving the lateral directional dynamics of an aircraft to illustrate the efficacy of the proposed adaptive control architecture.

Keywords:Smart grid, Distributed control, Game theory Abstract: This paper proposes a novel distributed control strategy for large-scale deployment of flexible demand. The devices are modelled as competing players that respond to iterative broadcasts of price signals, scheduling their power consumption to operate at minimum cost. By describing their power update at each price broadcast through a multi-valued discrete-time dynamical system and by applying Lyapunov techniques, it is shown that the proposed control strategy always converges to a stable final configuration, characterized as a Wardrop (or aggregative) equilibrium. It is also proved that such equilibrium is socially efficient and optimizes some global performance index of the system (e.g. minimizes total generation costs). These results are achieved under very general assumptions on the electricity price and for any penetration level of flexible demand. Practical implementation of the proposed scheme is discussed and tested in simulation on a future scenario of the UK-grid with large numbers of flexible loads.

Keywords:Power systems;Smart grid;Control applications Abstract: Transmitting a large file across the internet requires breaking up the file into smaller packets of data. Packetized energy management (PEM) leverages similar concepts from communication theory to coordinate distributed energy resources by breaking up deferrable residential consumer demands into smaller fixed-duration/fixed-power packets of energy. Each individual load is managed by a probabilistic automaton that stochastically requests energy packets as a function of its local dynamic state (e.g., temperature or state-of-charge). Based on the aggregate request rate from packetized loads and grid conditions, the PEM coordinator will modulate the rate of accepting requests, which permits tight tracking of a reference (load-shaping or market) signal. This paper presents a state bin transition (macro) model suitable for characterizing a diverse population of electric water heaters (EWHs) and energy storage systems (ESSs) under a single PEM coordinator that is validated against an agent-based simulation of the diverse loads. The resulting model illustrates how diversity of packetized load types enhances the level of flexibility offered by the coordinator.

Keywords:Power systems;Smart grid, Hierarchical control Abstract: This paper focuses on the problem of controlling an ensemble of heterogeneous resources connected to an electrical grid at the same point of common coupling (PCC). The controller receives an aggregate power setpoint for the ensemble in real time and tracks this setpoint by issuing individual optimal setpoints to the resources.The resources can have continuous or discrete nature (e.g., heating systems consisting of a finite number of heaters that each can be either switched on or off) and/or can be highly uncertain (e.g., photovoltaic (PV) systems or residential loads). A naive approach would lead to a stochastic mixed-integer optimization problem to be solved at the controller at each time step, which might be infeasible in real time. Instead, we allow the controller to solve a continuous convex optimization problem and compensate for the errors at the resource level by using a variant of the well-known error diffusion algorithm. We give conditions guaranteeing that our algorithm tracks the power setpointat the PCC on average while issuing optimal setpoints to individual resources. We illustrate the approach numerically by controlling a collection of batteries, PV systems, and discrete loads.

Keywords:Power systems;Smart grid, Distributed control Abstract: Flexible loads such as residential air-conditioners (ACs) can be directly controlled to provide demand-side regulation and balancing services to the grid. In aggregation, an ensemble of ACs may be seen as a distributed energy storage resource with a capacity modulated by ambient temperature and the AC temperature set-points. Existing research has predominantly focused on modelling and controlling the aggregate demand response of such ensembles, but relatively little work has been devoted to quantifying controllable energy resource as a function of ensemble diversity. This paper investigates analytic bounds on the aggregate energy demand transients induced by step changes in temperature set-points for ensembles of ACs. An analytic characterisation of the transient demand response of homogeneous ensembles is used to bound the controllable energy demand of heterogeneous ensembles constructed by aggregation of clusters of identical loads. The analysis shows that the transient energy demand of a heterogeneous ensemble can be bounded by that of an associated mean homogeneous ensemble as a function of the set-point step size relative to the ACs hysteresis regulation band width. The proposed analytic bounds are numerically evaluated for the simulated demand responses of AC ensembles with various degrees of heterogeneity.

Keywords:Decentralized control;Smart cities/houses, Markov processes Abstract: We discuss the applicability of classical control theory to problems in smart grids and smart cities. We use tools from iterated function systems to identify controllers with desirable properties. In particular, controllers are identified that can be used to design not only stable closed-loop systems, but also to regulate large-scale populations of agents in a predictable manner. We also illustrate by means of an example and associated theory that many classical controllers are not suitable for deployment in these applications.

Keywords:Smart grid;Smart cities/houses, Optimization Abstract: This paper formulates an optimal station assignment problem for electric vehicle (EV) battery swapping that takes into account both temporal and spatial couplings. The goal is to reduce the total EV cost and station congestion due to temporary shortage in supply of available batteries. We show that the problem is reducible to the minimum weight perfect bipartite matching problem. This leads to an efficient solution based on the Hungarian algorithm. Numerical results suggest that the proposed solution provides a significant improvement over a greedy heuristic that assigns nearest stations to EVs.

Keywords:Control applications, Computational methods;Hybrid systems Abstract: Rendezvous is a fundamental maneuver in autonomous space operations in which an active chaser spacecraft is required to navigate safely to the proximity of a second passive target spacecraft. Ensuring safety of such control maneuvers is challenging and design errors can be expensive. We present the first verified control solution to a benchmark formulation of spacecraft autonomous rendezvous in the form of a hybrid LQR controller verified using a data-driven algorithm. Our hybrid LQR scheme is motivated by enforcing safety constraints rather than optimizing performance, and the control law is formulated by periodically solving optimization problems that depend on the current state. The resulting hybrid system presents a challenge for existing automated formal verification tools due to its lack of a closed-form model description. We overcome this challenge by using a data-driven approach (implemented in the new verification tool DryVR). DryVR relies on simulation traces to compute reachable states of the system over bounded time horizon and initial conditions to rigorously verify that the system does not violate any safety requirements.

Keywords:Control applications, Constrained control;Power systems Abstract: This paper presents a control strategy to perform healthy fast charging of a lithium-ion (Li-ion) battery cell. The control law is based on a two-step approach. First, the battery cell is controlled using an aggressive pre-stabilization loop. Then, constraint satisfaction is ensured by augmenting the resulting system with an explicit reference governor able to handle the (possibly nonlinear) constraints arising from the physics of the battery. The control law is designed using a reduced model of the battery dynamics and is then validated on a highly accurate simulator of the battery cell. Comparisons with existing strategies show that the proposed control scheme exhibits better performances while maintaining a low computational cost.

Keywords:Control applications;Electrochemical processes, Simulation Abstract: Leakage of hydrogen due to formation of pinholes endangers the membrane longevity in a polymer electrolyte membrane fuel cell (PEMFC). In this work, based upon a novel approach, mitigation of the hydrogen transfer leak rate is achieved via controlling the speed of the hydrogen recirculation blower (HRB) as well as fuel overpressure control. The problem is formulated as a constrained control problem. Considering the multivariable nature of the control problem, a model predictive controller is employed to meet with the objectives. Moreover, the control limitation in presence of large transfer leaks is discussed. In order to evaluate the controller performance, an experimental model of a Ballard 3kW test station equipped with an HRB is utilized, where the model is derived on the basis of pneumatic modeling technique with inclusion of the hydrogen transfer leak model. Simulation results demonstrate the controller's ability for reducing the leak rate while handling the constraints, which leads to an improved durability for the membrane. Furthermore, it confirms the controller limitation.

Keywords:Power generation;Control applications, Predictive control for linear systems Abstract: We propose a new strategy for wind turbines generator torque control to enhance the overall wind energy capture and fatigue loads mitigation by using the information provided by light detection and ranging (LIDAR) system. Numerical time-series of wind speed information generated by LIDAR are used to obtain closed-form mathematical models for the upcoming wind signal and are employed within the exact output regulation control architecture. Simulation studies employing the FAST models in operating conditions below the turbines rated wind speed show that energy capture can be improved while preserving or even reducing the tower fatigue load measures.

Keywords:Maritime control;Control applications;Robotics Abstract: This paper presents a reactive collision avoidance algorithm, which avoids both static and moving obstacles by keeping a constant avoidance angle between the vehicle velocity vector and the obstacle. In particular, we consider marine vehicles with underactuated sway dynamics, which cannot be directly controlled. This gives an underactuated component in the vehicle velocity, which the proposed algorithm is designed to compensate for. The algorithm furthermore compensates for the obstacle velocity. Conditions are derived under which the sway movement is bounded and collision avoidance is mathematically proved. The theoretical results are supported by simulations. The proposed algorithm makes only limited sensing requirements on the vehicle, is intuitive and suitable for a wide range of vehicles. This includes vehicles with heavy forward acceleration constraints, which is demonstrated by applying the algorithm to a vehicle with constant surge speed.

Keywords:Adaptive control;Robotics;Aerospace Abstract: In this paper, we investigate the task-space adaptive control problem for free-floating space manipulators with uncertain kinematics and dynamics and with an unmodifiable inner joint control loop. The existence of an unmodifiable inner joint control loop makes most torque-based control algorithms in the literature inapplicable. We propose a dynamic modularity (DM) approach to resolve this problem, and this is hopeful for bridging the potential gap between the advanced control theory for (free-floating) space manipulators and practical engineering applications. Adaptive outer loop controllers are developed and shown to be able to guarantee the convergence of the task-space tracking errors. The performance of the proposed DM approach is shown by a numerical simulation.

Keywords:Adaptive control, Robust adaptive control, Uncertain systems Abstract: Majority of contributions in adaptive control literature assume that the system dynamics is linearly parametrizable, and a certainty equivalence principle is exploited to guarantee global stability and asymptotic convergence of tracking error to zero. Although linear-in-the-parameters (LIP) assumption is reasonable for a large class of dynamics, there exists a considerable number of real world systems, involving complex dynamics, where nonlinear parametrizations are inevitable. Previous research has shown that classical gradient-based adaptive designs with the certainty equivalence principle do not perform satisfactorily for NLIP systems, and may, in fact, cause instability in many situations. This work is an attempt towards addressing this issue by a novel non-certainty equivalence adaptive control design, where the classical gradient-based adaptive algorithm is used to tackle the LIP component of the NLIP dynamics, while a robust compensator, appended to the controller, accounts for the linearization error. The designed controller ensures a global uniformly ultimately bounded (UUB) stability of the error dynamics. Simulation results on two different models of NLIP dynamics are provided to validate the theoretical development.

Keywords:Adaptive systems, Stochastic systems, Optimization Abstract: Multitask diffusion and consensus algorithms have been proposed to solve distributed optimization problems in real time from streaming data, where the nodes cooperate to estimate node-dependent parameters. A fundamental question motivating their development is: how do standard diffusion LMS and real time consensus (RTC) algorithms perform in such environments? Previously, only moment stability has been studied via energy conservation arguments which require unrealistic white regressor assumptions. We present realization-wise stability results for the first time, under both correlated regressors and noise. This allows us to give an explicit expression for the limit point of these algorithms in the slow adaptation regime. We see that the Adapt-Then-Combine (ATC), Combine-Then-Adapt (CTA) and RTC algorithms all converge to a common Pareto optimal solution of the distributed MMSE problem.

Keywords:Output regulation, Identification for control, Robust adaptive control Abstract: This paper deals with the problem of adaptive output regulation for single-input single-output nonlinear systems, with respect to uncertainties in the exosystem. We endow a recently developed post-processing internal model design with a hybrid adaptive structure, which allows to use different identification schemes to adaptively tune the internal model at runtime. Practical regulation results are presented, with the regulation error that is proved to be linearly related to the prediction capabilities of the identifier.

Keywords:Output regulation, Lyapunov methods, Robust adaptive control Abstract: In this paper, we present a method of applying integral action to enhance the robustness of energy shaping controllers for underactuated mechanical systems with matched disturbances. Previous works on this problem have required a number of technical assumptions to be satisfied, restricting the class of systems for which the proposed solution applies. The design proposed in this paper relaxes some of these technical assumptions.

Keywords:Robust adaptive control, Game theory, Optimization algorithms Abstract: In this paper, we present a class of learning dynamics for distributed adaptive pricing in affine congestion games. We consider the setting where a large population of users is faced with the problem of choosing between a finite number of available resources, each resource having a particular cost function that depends only on the share of users using that particular resource. Since the mass of users is constant, their individual decisions affect the performance of all the available resources, thus generating a population game where each resource can be seen as a particular strategy in the game. Given the well-known fact that Nash equilibria in population games may not be socially optimal, a social planner is faced with the challenge of designing incentive mechanisms that induce a socially optimal Nash equilibrium. To achieve this, we present in this paper a class of model-free distributed pricing algorithms that guarantee convergence to the set of optimal tolls that induce a socially optimal Nash equilibrium. Our results allow us to consider populations of users that react instantaneously to tolls, as well as populations with social dynamics. Since the algorithms are data-driven, they can be implemented in settings where full information of the game is not available. By combining tools from game theory, robust set-valued dynamical systems, and adaptive control, a convergence result is established.

Keywords:Autonomous systems, Agents-based systems, Autonomous robots Abstract: This paper presents a method for deriving optimal controls and assigning attacker-defender pairs in a target-attacker- defender differential game between an arbitrary numbers of attackers and defenders, all of which are modeled using double integrator dynamics. It is assumed that each player has perfect information about the states and controls of the players within a certain range of themselves, but they are unaware of any players outside of this range. Isochrones are created based on the time-optimal trajectories needed for the players to reach any point in the shortest possible time. The intersections of the players' isochrones are used to determine whether a defender can intercept an attacker before the attacker reaches the target. Sufficient conditions on the detection range of the defenders and the guaranteed capture despite perturbations of the attackers off the nominal trajectories are derived. Then, in simulations with multiple players, attacker-defender pairs are assigned so that the maximum number of attackers are intercepted in the shortest possible time.

Keywords:Autonomous systems, Biological systems, Cooperative control Abstract: We extend the Speeding Up and Slowing Down (SUSD) strategy for distributed source seeking from a three agent group to a swarm of any number of agents without communicating frame coordinates or gradient estimates among agents. We integrate a nonlinear time varying consensus-on-a-sphere control law with the SUSD strategy in a leader-follower frame-work, which is inspired by source seeking behavior of certain fish species. We provide Lyapunov-based convergence analysis for the leader-follower SUSD strategy integrated with the consensus law. We demonstrate the efficiency of the proposed method through simulated source seeking behavior in three dimensional scalar fields.

Keywords:Autonomous systems, Intelligent systems, Markov processes Abstract: This work develops novel strategies for optimal planning with semantic observations using continuous state Partially Observable Markov Decision Processes (CPOMDPs). We propose two major innovations to Gaussian mixture (GM) CPOMDP policy approximation methods. While these state of the art methods have many theoretically nice properties, they are hampered by the inability to efficiently represent and reason over hybrid continuous-discrete probabilistic models. The first major innovation is the derivation of closed-form variational Bayes (VB) GM approximations of PBVI Bellman policy backups, using softmax models of continuous-discrete semantic observation probabilities. The second major innovation is a new clustering-based technique for mixture condensation that scales well to very large GM policy functions and belief functions. Simulation results for a target search and interception task with binary semantic observations show that the GM policies resulting from these innovations are more effective than those produced by other state of the art GM approximations, but require significantly less modeling overhead and runtime cost.

Keywords:Autonomous systems, Optimal control, Robust control Abstract: Fast and safe navigation of dynamical systems through a priori unknown cluttered environments is vital to many applications of autonomous systems. However, trajectory planning for autonomous systems is computationally intensive, often requiring simplified dynamics that sacrifice safety and dynamic feasibility in order to plan efficiently. Conversely, safe trajectories can be computed using more sophisticated dynamic models, but this is typically too slow to be used for real-time planning. We present the new algorithm FaSTrack: Fast and Safe Tracking. A path or trajectory planner using simplified dynamics to plan quickly can be incorporated into the FaSTrack framework, which provides a safety controller for the vehicle along with a guaranteed tracking error bound. This bound captures all possible deviations due to high dimensional dynamics and external disturbances. FaSTrack is modular and can be used with most current path or trajectory planners. We demonstrate this framework using a 10D nonlinear quadrotor model tracking a 3D path obtained from an RRT planner.

Keywords:Filtering, Autonomous systems, Stochastic optimal control Abstract: Optimizing measures of the observability Gramian as a surrogate for the estimation performance may provide irrelevant or misleading trajectories for planning under observation uncertainty.

Keywords:Hybrid systems, Autonomous systems;Discrete event systems Abstract: This paper discusses Hamel'sformalism for simple hybrid systems and explores the role of reversing symmetries in these system with a continuous-discrete combined dynamics.

By extending Hamel's formalism to the class of simple hybrid systems with impulsive effects, we derive, under some conditions, the dynamics of Lagrangian hybrid systems and Hamiltonian hybrid systems. In particular, we derive Euler-Poincar'e and Lie-Poisson equations for systems with impulsive effects as a simple hybrid system.

A reversing symmetry in the phase-space permits one to construct a time reversible hybrid Hamiltonian system. Based on the invariance of a Hamiltonian function by a reversing symmetry, we can find sufficient conditions for the existence of periodic solutions for these simple hybrid systems.

Keywords:Estimation, Kalman filtering;Energy systems Abstract: Li-ion batteries require advanced Battery Management Systems (BMSs). The estimation of the cells internal quantities (residual energy, temperature, ions concentrations) is paramount for the correct and safe operation of Li-Ion batteries. Accurate estimation of these quantities is however a challenging task. This work addresses the internal state estimation of a Li-ion cell applying the Unscented Kalman Filter (UKF) approach to the complete P2D model. The use of the complete P2D model allows for the estimation of the spatial distribution of Li-ions, along with the estimate of the bulk State of Charge (SoC). The paper illustrates how the UKF can address the two main issues involved in using the P2D model in estimation:weak observability and computational load. The observability issue is addressed imposing a soft mass conservation constraint in the UFK particles computation while a parallelized implementation softens the computational burden. Extensive simulations validates the approach with currents up to 50C.

Keywords:Estimation, Identification, Energy systems Abstract: This paper investigates the fundamental relationship between the estimation accuracy of the equivalent circuit dynamics and the measurement data, i.e. input current and output voltage. Specifically, the Cramer-Rao bounds of the model parameter estimation are derived analytically as explicit functions of generic input/output data. The derivation is performed in both discrete-time and Laplace representation, and for both single- and multi-variable estimation scenarios. The sinusoidal current input is then used as an example for illustration. The analytic results could benefit the estimation practice in multiple ways, including the estimation reliability/robustness evaluation, offline experiment design for system identification, and online data selection.

Keywords:Estimation, Kalman filtering, Nonlinear systems identification Abstract: State estimation is applicable to almost all areas of engineering and science. Applications that include a physical-parametric model of a system are candidates for state estimation. These estimators reconstruct the system states based on a system model and information received from the system sensors. The most widely applied state estimators are the Kalman Filter (KF) derivatives. These filters use a parametric system model, system measurements and input information, and require knowledge about the noise statistics affecting the system. These noise statistics are often unknown and inaccurate filter tuning may lead to decreased filter performance or even filter divergence. These estimators can be extended to estimate parameters. However, insufficient system excitation can cause parameter estimation drifts. In this paper, a sensitivity-based adaptive Square-Root Unscented Kalman Filter (SRUKF) is presented. This filter estimates system states, parameters and noise covariances online. Moreover, local sensitivity analysis is performed to prevent parameter estimation drifts during phases of insufficient system excitation. The filter is evaluated on two testbeds based on an axis serial mechanism and compared with the joint SRUKF.

Keywords:Estimation, Kalman filtering Abstract: In this paper we introduce the a fortiori expectation-maximization (AFEM) algorithm for computing the parameters of a distribution from which unlabeled, correlated point sets are presumed to be generated. Each unlabeled point is assumed to correspond to a target with independent probability of appearance but correlated positions. We propose replacing the expectation phase of the algorithm with a Kalman filter modified within a Bayesian framework to account for the unknown point labels which manifest as uncertain measurement matrices. We also propose a mechanism to reorder the measurements in order to improve parameter estimates. In addition, we use a state-of-the-art Markov chain Monte Carlo sampler to efficiently sample measurement matrices. In the process, we indirectly propose a constrained k-means clustering algorithm. Simulations verify the utility of AFEM against a traditional expectation-maximization algorithm in a variety of scenarios.

Keywords:Estimation, Identification for control, Linear systems Abstract: mathcal{H}_{infty}-norm estimation is usually an important aspect of robust control design. The aim of this paper is to develop a data-driven estimation method exploiting iterative input design, without requiring parametric modeling. More specifically, the estimation problem is formulated as a emph{sequential game}, whose solution is derived within the emph{prediction with expert advice} framework. The proposed method is shown to be competitive with the state-of-the-art techniques.

Keywords:Estimation, Nonlinear output feedback, Stochastic optimal control Abstract: This paper presents state estimation and stochastic optimal control gathered in one global optimization problem generating dual effect i.e. the control can improve the future estimation. As the optimal policy is impossible to compute, a sub-optimal policy that preserves this coupling is constructed thanks to the Fisher Information Matrix (FIM) and a Particle Filter. This method has been applied to the localization and guidance of a drone over a known terrain with height measurements only. The results show that the new method improves the estimation accuracy compared to nominal trajectories.

Keywords:Agents-based systems, Estimation, Sensor networks Abstract: This paper considers the problem of localising a signal source using a team of mobile agents that can only detect the presence or absence of the signal. A background false detection rate and missed detection probability are incorporated into the assumptions. An estimation algorithm is proposed that discretises the search environment into cells, and uses Bayesian techniques to approximate the posterior probability of each cell containing the source. Analytical results are presented for a range of specific cases, and simulations are used to investigate more complex scenarios.

Keywords:Agents-based systems, Distributed control, Networked control systems Abstract: This paper presents two bearing-only control laws that guarantee almost global convergence of the desired formation in finite time. For each control law, the equilibrium set is firstly studied. Then, we provide rigorous analysis on asymptotic convergence as well as finite time convergence of the system to the desired equilibrium. Finally, numerical simulations are provided to validate our analysis.

Keywords:Agents-based systems, Distributed control, Optimization algorithms Abstract: In this paper we present a novel distributed coverage control framework for a network of mobile agents, in charge of covering a finite set of points of interest (PoI), such as people in danger, geographically dispersed equipment or environmental landmarks. The proposed algorithm is inspired by C-Means, an unsupervised learning algorithm originally proposed for non-exclusive clustering and for identification of cluster centroids from a set of observations. To cope with the agents limited sensing range and avoid infeasible coverage solutions, traditional C-Means needs to be enhanced with proximity constraints, ensuring that each agent takes into account only neighboring PoIs. The proposed coverage control framework provides useful information concerning the ranking or importance of the different PoIs to the agents, which can be exploited in further application-dependent data fusion processes, patrolling, or disaster relief applications.

Keywords:Agents-based systems, Distributed control, Lyapunov methods Abstract: The first contribution of this paper is to compute the dynamics of the mass and of the position of the center of mass of Voronoi cells for a given multi-agent spatial distribution. These two results are then used in the design of a distributed backstepping control law for a multi-agent coverage problem. The agents are assumed to have second order dynamics and will be moving on a plane inside 3D space. The analytic expressions for the rate of change of the mass and center of mass of the Voronoi cells, valid for non-uniform density functions, are new to the best of the authors' knowledge. For the particular case of uniform density, the result of the rate of change of area was known before but a new proof is presented in the paper based on a geometric argument and small perturbations. Simulation results are provided to show the effectiveness of the approach.

Keywords:Agents-based systems, Iterative learning control, Markov processes Abstract: Online learning is the process of providing online control decisions in sequential decision-making problems given (possibly partial) knowledge about the optimal controls for the past decision epochs. The purpose of this paper is to apply the online learning techniques on finite-state finite-action Markov Decision Processes (finite MDPs). We consider a multi-agent system composed of a learning agent and observed agents. The learning agent observes from the other agents the state probability distribution (pd) resulting from a stationary policy but not the policy itself. The state pd is observed either directly from an observed agent or through the density distribution of the multi-agent system. We show that using online learning, the learned policy performs at least as well as the one of the observed agents. Specifically, this paper shows that if the observed agents are running an optimal policy, the learning agent can learn the optimal average expected cost MDP policies via online learning techniques by using a descent gradient algorithm on the observed agents pd data.

Keywords:Agents-based systems, Network analysis and control, Decentralized control Abstract: This work presents the design of a decentralized control strategy that allows singularly perturbed multi-agent systems to achieve synchronization with global performance guarantees. The study is mainly motivated by the presence of two features that characterize many physical systems. The first is the complexity in terms of interconnected subsystems and the second is that each subsystem involves processes evolving on different time-scales. The main difficulty that we have to overcome is that we have to avoid the use of centralized information related to the interconnection network structure. This problem is solved by rewriting the synchronization problem in terms of stabilization of a singularly perturbed uncertain linear system. The singularly perturbed dynamics of subsystems generates theoretical challenges related to the stabilizing controller design but also numerical issues related to the computation of the controller gains. We show that these problems can be solved by decoupling the slow and fast dynamics. Our theoretical developments are illustrated by some numerical examples.

Keywords:Biological systems, Distributed parameter systems, Distributed control Abstract: Several stains of the intracellular parasitic bacterium Wolbachia limit severely the competence of the mosquitoes Aedes aegypti as a vector of dengue fever and possibly other arboviroses. For this reason, the release of mosquitoes infected by this bacterium in natural populations is presently considered a promising tool in the control of these diseases. Following works by M. Turelli and subsequently M. Strugarek et al., we consider a simple scalar reaction-diffusion model describing the evolution of the proportion of infected mosquitoes, sufficient to reveal the bistable nature of the Wolbachia dynamics. A simple distributed feedback law is proposed, whose application on a compact domain during finite time is shown to be sufficient to invade the whole space. The corresponding stabilization result is established for any space dimension.

Keywords:Biological systems, Markov processes, Stochastic systems Abstract: Nullclines provide a convenient way of characterising and understanding the behaviour of low dimensional nonlinear deterministic systems, but are, perhaps not unsurprisingly, a poor predictor of the behaviour of discrete state stochastic systems in the low numbers regime. Such models are appropriate in many biological systems. In this paper we propose a graphical discrete `nullcline-like' construction, inspired by the Markov chain tree theorem, and investigate its application to the original genetic toggle switch, which is a feedback interconnection of two mutually repressing genes. When the feedback gain (the `cooperativity') is sufficiently large, the deterministic system exhibits bistability, which shows itself as a bimodal stationary distribution in the discrete stochastic system for sufficiently large numbers. However, at small numbers a third mode appears corresponding to roughly equal numbers of each molecule. Without cooperativity, on the other hand (i.e. low feedback gain), the deterministic system has just one stable equilibrium. Nevertheless, the stochastic system can still exhibit bimodality. In this paper, we illustrate that the discrete `nullclines' proposed can, without the need to calculate the steady state distribution, provide an efficient graphical way of predicting the shape of the stationary probability distribution in different parameter regimes, thus allowing for greater insights in the observed behaviours.

Keywords:Biological systems, Modeling Abstract: Major challenges exist in the design of gene regulatory networks. Some of these can be addressed by the in silico modelling and design of systems prior to implementation. However, reliable modelling of a given system is predicated upon a range of simplifying assumptions which may only be valid for a limited range of architectures and experimental conditions. In this paper we study the autorepressor, also referred to as the negative autoregulator, a genetic motif common both in natural and synthetic circuits. A number of approaches to modelling the autorepressor are presented, and one of these is extended to include the impact of inducer consumption, a phenomenon frequently observed in experiments. We implement this system using the tet-repressor (TetR), and compare the in vivo data with the results of simulations using nominal parameters taken from the literature. We demonstrate that a modelling approach that considers inducer sequestration due its binding with a transcription factor may be required to qualitatively replicate experimental results. We conclude by drawing comparisons between experimental and simulated results, and discuss means by which modelling could be extended to better represent observed behaviours.

Keywords:Biological systems;Robotics, Autonomous systems Abstract: This paper presents a simple-structure micromanipulator for grasping and orienting zebrafish (Danio rerio) larva. Compared with complicated handling systems that are based on microfluidic chip, the designed 4-DOF manipulator that has three translations and one rotation allows operators to manipulate larva automatically in a more controllable manner. One glass pipette is mounted at the end of manipulator to rotate larva (about the microscope optical axis) in two dimensions to appropriate gestures where larva's tail is parallel with pipette. Pipette tip is then driven to approach the tail, and the micro pump that is connected with the pipette runs to hold part of larva's tail. Precisely rotating manipulator arm effectively ensures flexible orientation of grasped larva in the third dimension. In order to suppress the rotation oscillation of pipette tip, we have developed an online calibration method to compensate rotation error. We have also provided a simple extremum searching algorithm to automatically rotate larva body to special gestures that are commonly used in experiments (such as dorsal or lateral gestures). Experimental results show the performance of designed manipulator and verify the validity of presented control methods.

Keywords:Biological systems, Stochastic systems, Robust control Abstract: Possible sources of instabilities in the cochlea are investigated by letting the cochlear active gain be a stochastic process which enters the dynamics multiplicatively. The theory of structured stochastic uncertainty in dynamical systems is employed by reformulating a generalized class of biomechanical models of the cochlea as an LTI system in feedback with a diagonal stochastic gain. A simulation-free, Mean Square Stability (MSS) analysis is then carried out to predict possible unstable basilar membrane vibration modes. These modes suggest a mechanism explaining the frequencies of linearized instabilities that give rise to limit cycles due to a spatially varying inhomogeneity and temporal perturbations along the cochlear partition. In fact, we show that the range of unstable frequencies is controlled by the shape of the nominal cochlear active gain. This analysis suggests an explanation of vibrations in the ear that occur in the absence of any stimulus such as Spontaneous Otoacoustic Emissions (SOAEs) and tinnitus.

Keywords:Modeling, Biological systems, Systems biology Abstract: The evolution of parasites and pathogens are important to human, agricultural, and wildlife systems. Mathematicians have attempted to theorize how infection mechanisms may evolve. Since phage-bacteria interactions are the most abundant in nature, they have become the object of intensive study. The way in which these phages evolved to moderate temperateness - the propensity of the phage to enter lysogeny - remains poorly understood. To gain a more extensive and concrete understanding of the likelihood of a bacteriophage to display temperateness, we have examined the advantages of the lysogenic pathway over the lytic path under fluctuating environments. Multiple iterations over different periods of good and bad conditions allowed us to exemplify the behavior and predispositions of these organisms. We explored how a multiplicity of infection (MOI) - the ability of a phage to infect an already infected cell - drives these seemingly stochastic decisions. We found that temperate phages might use the lysogenic path to protect themselves from extended periods of detrimental conditions.

Keywords:Game theory, Randomized algorithms, Networked control systems Abstract: This paper considers a stochastic potential game in which each player solves a parameterized stochastic convex optimization problem. We propose a randomized inexact best- response (BR) scheme to compute the Nash equilibrium (NE). In each iteration, while the other players keep their strategies invariant, a single player is randomly chosen to update its equilibrium strategy by computing an inexact proximal BR by solving a player-specific stochastic program since exact solutions are generally unavailable in finite time. By imposing suitable conditions on the inexactness sequences, we prove the almost sure (a.s.) convergence and mean convergence of the iterates generated by the scheme to an NE. Finally, we present some preliminary numerics on the problem of congestion control.

Keywords:Identification, Randomized algorithms;Materials processing Abstract: The Sign-Perturbed Sums (SPS) randomized algorithm is adapted to the procedure of data treatment of dynamic fracture tests. The original method is modified and applied for nonlinear regression function describing the strain rate dependence of material strength at the framework of structuretemporal approach. Ordinary there are few observation points of goal parameter with random noises with unknown statistical distribution, hence this point stipulates the choice of SPSalgorithm for this problem. It is proved that SPS-procedure permit to define a confidence intervals for dynamic strength parameter with proper accuracy in this case. The applicability of this method is demonstrated on example of experimental data treatment of dynamic fracture of a concrete.

Keywords:Networked control systems, Randomized algorithms, Control over communications Abstract: A consensus problem for multi-agent systems under jamming attacks is considered. Specifically, the agents are assumed to communicate over a shared network, where transmissions may fail at certain times due to jamming. We propose stochastic communication protocols so that the agents attempt to communicate with each other at random time instants that are unknown by the attacker. We obtain sufficient finite-time practical consensus conditions. Through a probabilistic analysis, we show that our communication protocols allow consensus under a class of attacks that were previously not considered. We demonstrate the efficacy of our results by considering two different strategies of the attacker: a deterministic attack strategy and a more malicious communication-aware strategy.

Keywords:Power systems, Randomized algorithms, Uncertain systems Abstract: We consider a power capacity optimization problem where a consumer has to decide the amount of electrical power capacity to purchase for the following year, which includes an amount that is constant over the year (yearly capacity), and an additional surplus per month (monthly capacity). The cost per power unit of the yearly capacity is lower than that of the monthly capacity. A high violation cost is paid when the actual power consumption in a month exceeds the pre-allocated capacity. Given that future power consumption is uncertain, we propose a solution that consists in the minimization of the average expected cost, which includes also the violation costs. By replacing the average with its empirical mean, we can compute an approximate solution to the original problem with a pre-defined level of accuracy by extracting a sufficiently large number of power consumption realizations, which is here set via the uniform convergence of empirical means theory. Extractions are obtained based on a stochastic model that is built from available historical data. The effectiveness of the approach is shown on a real case study.

Keywords:Randomized algorithms, Uncertain systems, Filtering Abstract: The traditional Monte Carlo method (called FMC in this paper) is widely used for initial uncertainty forecasting, but continues to face fundamental questions regarding its transient performance. In particular, following discretization of the initial state probability density function (pdf) into a particle ensemble, it is not clear how well the propagated samples continue to represent the true state-uncertainty at future times. The objective of this paper is to evaluate the transient performance of FMC with a fixed number of samples. The following question is asked: under what conditions could the propagated FMC ensemble have been generated by a direct sampling of the unknown true state-pdf? To answer this question, the propagated ensemble is viewed as the realization of a Markov chain and the FMC process as the evolution of the associated transition kernel. An equation governing the evolution of FMC transition kernel is derived. It is shown that for systems with "zero-divergence" in their force field, the true evolved state pdf is the invariant distribution of the propagated FMC transition kernel at all times. No such equivalence is guaranteed for systems with non-zero divergence. Numerical simulations are provided to support theoretical claims about ensemble quality for both types of dynamic systems.

Keywords:Robust control, Randomized algorithms, Autonomous robots Abstract: We investigate a path planning algorithm for generating robust and safe paths, which satisfy mission requirements specified in linear temporal logic (LTL). When robots are deployed to perform a mission, there can be disturbances which can cause mission failures or collisions with obstacles. Hence, a path planning algorithm needs to consider safety and robustness against possible disturbances. We present a robust path planning algorithm, which maximizes the probability of success in accomplishing a given mission by considering disturbances in robot dynamics while minimizing the moving distance of a robot. The proposed method can guarantee the safety of the planned trajectory by incorporating an LTL formula and chance constraints in a hierarchical manner. A high-level planner generates a discrete plan satisfying the mission requirements specified in LTL. A low-level planner builds a sampling-based RRT search tree to minimize both the mission failure probability and the moving distance while guaranteeing the probability of collision with obstacles to be below a specified threshold. We validate the robustness and safety of paths generated by the algorithm in simulation and experiments using a quadrotor.

Keywords:Control of networks Abstract: Radio transmission at millimeter wave carrier frequencies will be a central technology in the new 5G wireless systems that are in standardization. To obtain a sufficient coverage, multi-point transmission is needed to compensate for the severe radio shadowing that occurs at these frequencies. Incoming downlink data streams must then be split and sent on to the radio base stations over multiple data paths, often with different delay properties. This paper presents a new MIMO delay skew control algorithm that operates over these paths to secure simultaneous transmission over the corresponding wireless interfaces. This secures redundancy gains for ultra-reliable communication applications. The paper also presents an analysis of disturbance rejection and reference signal tracking properties, arriving at conditions that decouple these properties between the control channels. These conditions provide guidelines for network design.

Keywords:Network analysis and control, Distributed control, Networked control systems Abstract: In this paper we investigate the performance of linear networked dynamical systems over digraphs with a globally reachable node. We consider first and second order systems subject to distributed disturbances and define an output that quantifies the performance through the input-output H2 norm of the system. We develop a generalized framework for computing the H2 norm for this class of systems, and apply this framework to evaluate two performance measures for systems whose underlying network graphs result in normal weighted graph Laplacian matrices. We find closed-form solutions for the measure that quantifies the total deviation of the states from the average, and bounds on the measure that quantifies the weighted squared difference between the states of neighboring nodes. Numerical examples indicate that a second order system connected over a cycle graph may have better performance when its underlying graph is directed due to complex eigenvalues of the Laplacian. The results also indicate that the H2 norm of a symmetric system is less than or equal to that of the corresponding perturbed non-symmetric system for either line or complete graphs when the network size is sufficiently large.

Keywords:Network analysis and control, Identification, Stochastic systems Abstract: The interconnectivity structure of many complex systems can be modeled as a network of dynamically interacting processes. Identification of mutual dependencies amongst the agents is of primary importance in many application domains that include internet-of-things, neuroscience and econometrics. Moreover, in many such systems it is not possible to deliberately affect the system and thus passive methods are of particular relevance. However, for an effective framework that identifies influence pathways from dynamically related data streams originating at different sources it is essential to address the uncertainty of data caused by possibly unknown time-origins of different streams and other corrupting influences including packet drops and noise. In this article, a method of reconstructing the network topology from corrupt data streams is provided with emphasis on the characterization of the effects of data corruption on the reconstructed network. The structure of the network is identified by observing the sparsity pattern in the joint power spectrum of the measurements.

Keywords:Network analysis and control, Markov processes Abstract: We examine the influence of time-varying interactions, which are modeled by a Markov switching graph (MSG), on noisy multi-agent dynamics. Our focus is on the robustness of both consensus and leader-follower tracking dynamics in the presence of stochastic noise, and we derive expressions for the steady-state covariance of the system's deviation from consensus and tracking error, respectively. We use these measures to quantify individual and group performance as functions of the interaction graphs and graph switching matrix. We extend notions of robustness and joint centrality indices for static graphs to MSGs.

Keywords:Network analysis and control, Agents-based systems;Emerging control applications Abstract: We consider how asynchronous networks of agents who imitate their highest-earning neighbors can be efficiently driven towards a desired strategy by offering payoff incentives, either uniformly or targeted to individuals. In particular, if for each available strategy, agents playing that strategy receive maximum payoff when their neighbors play that same strategy, we show that providing incentives to agents in a network that is at equilibrium will result in convergence to a textit{unique} equilibrium. When a uniform incentive can be offered to all agents, one can compute the optimal incentive using a binary search algorithm. When incentives can be targeted to individuals, we propose an algorithm to select which agents should be chosen based on iteratively maximizing a ratio of the number of agents who adopt the desired strategy to the payoff incentive required to get those agents to do so. Simulations demonstrate that this algorithm computes near-optimal targeted payoff incentives for a range of networks and payoff distributions in coordination games.

Keywords:Network analysis and control, Sensor networks, Estimation Abstract: This paper pertains to the analysis and design of decentralized estimation schemes that make use of limited communication. Briefly, these schemes equip the sensors with scalar states that iteratively merge the measurements and the state of other sensors to be used for state estimation. Contrarily to commonly used distributed estimation schemes, the only information being exchanged are scalars, there is only one common time-scale for communication and estimation, and the retrieval of the state of the system and sensors is achieved in finite-time. We extend previous work to a more general setup and provide necessary and sufficient conditions required for the communication between the sensors that enable the use of limited communication decentralized estimation schemes. Additionally, we discuss the cases where the sensors are memoryless, and where the sensors might not have the capacity to discern the contributions of other sensors. Based on these conditions and the fact that communication channels incur a cost, we cast the problem of finding the minimum cost communication graph that enables limited communication decentralized estimation schemes as an integer programming problem.

Keywords:Observers for Linear systems;Delay systems Abstract: This paper deals with the observability problem of a sort of singular systems with commensurate time-delays in the trajectory of the state, in the time derivative of the trajectory of the state (neutral terms), and in the output system. By using a recursive algorithm, sufficient conditions (easy testable) are proposed for guaranteeing the backward and the algebraic observability of the system.

Keywords:Observers for Linear systems;Delay systems Abstract: For linear singular time-delay systems, the most existing results focus on the simple case, i.e. Edot{x}(t) = A0x(t)+A1x(t-tau). Few results have been stated for the general linear singular time-delay systems of the form E(t-tau)dot{x}(t-tau) = Ax(t-tau), which covers also neutral delay systems. For such a general case, this paper deduced sufficient conditions, with which a simple Luenberger-like observer can be designed in order to exponentially estimate the states.

Keywords:Observers for Linear systems, Large-scale systems, Estimation Abstract: In this paper, the problem of distributed estimation for a linear large-scale system is studied. A nonlinear distributed observer is proposed, whose estimation error converges to zero in a finite time. A fixed-time converging version of the observer is also presented. The efficiency of estimators is demonstrated by computer simulations.

Keywords:Observers for Linear systems, Lyapunov methods;Stability of hybrid systems Abstract: In this paper we propose a time-varying observer for a linear continuous-time plant with asynchronous discrete-time measurements. The proposed observer is contextualized in the hybrid systems framework providing an elegant setting for the proposed solution. In particular some theoretical tools are provided, in terms of LMIs, certifying asymptotic stability of a certain compact set where the estimation error is zero. Moreover the case of asynchronous measurements is considered, i.e. when the measurements are not provided in well defined time instants, but they occur at an arbitrary time in a certain time interval. A design procedure based on the numerical solution of an infinite-dimensional LMI is also proposed, leading to a time-varying observer gain. Finally a numerical example shows the effectiveness of the proposed approach.

Keywords:Observers for Linear systems, Optimization algorithms;Fault tolerant systems Abstract: The problem of output redundancy in discrete-time linear plants is addressed, wherein the presence of redundant sensors is motivated by unknown bias or faults affecting the measurement equation. In this context, we focus on the design of a nonlinear estimation procedure consisting in a bias estimator together with a linear Luenberger structure augmented with an adaptive weighted pseudo-inverse combination of the available measurements. It is shown that the proposed scheme is characterized by higher performances compared to the classical compensation of the observer output injection using the estimated bias. Simulation results are given to illustrate the potential behind the proposed solution.

Fraunhofer Inst. for Industrial Mathematics (ITWM)

Keywords:Observers for Linear systems;Switched systems;Fault diagnosis Abstract: To determine the switching signal and the state of a switched linear system, one usually requires mode observability. This requires that all individual modes are observable and that the modes are distinguishable. In theory, it allows to determine the active mode in an arbitrarily short time. If one enlarges the observation to an interval that contains a switch, both assumptions (observability of each mode and clearly distinct dynamics) can be relaxed. In [1] this concept, called switch observability, was formalized. It is of particular interest for fault identification. Based on switch observability, we propose an observer. This observer combines the information obtained before and after a switching instant to determine both the state and the switching signal. It is analyzed and illustrated in an example.

Keywords:Optimal control, Optimization, LMIs Abstract: We revisit the linear programming approach to deterministic infinite horizon discounted optimal control problems. In the first part, we relax the original problem to an infinite-dimensional linear program over a measure space and prove equivalence of the two formulations under mild assumptions, significantly weaker than those found in the literature until now. The proof is based on duality theory and mollification techniques for constructing approximate smooth subsolutions to the associated Hamilton-Jacobi- Bellman equation. In the second part, we assume polynomial data and use Lasserres hierarchy of primal-dual moment-sum- of-squares semidefinite relaxations to approximate the value function and design an approximate optimal feedback controller. We conclude with an illustrative example.

Keywords:Computer-aided control design, Numerical algorithms, Optimal control Abstract: We study a class of leavable, undiscounted, minimax optimal control problems for perturbed, continuous-valued, nonlinear control systems. Leaving or ``stopping'' is mandatory and the costs are assumed to be non-negative, extended real-valued functions. In a previous contribution, we have shown that this class of optimal control problems is amenable to the solution based on symbolic models of the plant in the sense that an arbitrarily precise upper bound on the value function (measured in terms of its hypograph) can be computed from a given abstraction with prescribed precision on every compact subset of state space. In this work, we propose an algorithm to compute arbitrarily precise abstractions of discrete-time plants that represent the sampled behavior of continuous-time, perturbed, nonlinear control systems and establish the convergence rate of the precision in dependence of the discretization parameters of the algorithm. We illustrate the algorithm by approximately solving an optimal control problem involving a two dimensional version of the cart-pole swing-up problem.

Keywords:Computational methods, Numerical algorithms, Estimation Abstract: We suggest a method for significantly reducing the so-called wrapping effect, i.e., the accumulation of approximation errors incurred during reach-set computation of differential equations when repeatedly over-approximating intermediate reach sets by tractable computational representations of sets in the R^{n} . Our method can be implemented on top of any known reach-set computation method and generalizes bracketing systems suggested by Ramdani et al. by being based on dimension-wise enclosures of the reach sets of appropriate lower-dimensional surfaces of the initial set selected due to monotonicity properties. Thus exploring just low-volume sub-sets rather than the entire initial and intermediate reach sets, accuracy is enhanced as the approximation error tends to be correlated with set volume. At the same time, the curse of dimensionality that set partitioning methods are prone to is avoided by resorting to a number of subsets linear in the problem dimension. Technically, we first conduct sensitivity analysis of the solution mapping with respect to initial states based on a simulation-based technique, and then determine subsets which are extracted from the boundary of the initial set for performing reachability analysis. We test our method by using it on top of the validated ODE solver VNODE-LP and demonstrate its effect by comparison with existing methods, using illustrative examples of non-linear dynamics.

Keywords:Hybrid systems, Nonlinear output feedback Abstract: Symbolic controller synthesis offers the ability to design controllers enforcing a rich class of specifications such as those expressible in temporal logic. Despite the promise of symbolic controller synthesis and correct-by-design control software, this design methodology is not yet widely applicable due to the complexity of constructing finite-state abstractions for large continuous systems. In this paper we investigate a compositional approach to the construction of abstractions by exploiting the cascading structure of partially feedback linearizable systems. We show how the linearized part and the zero dynamics can be independently abstracted and subsequently composed to obtain an abstraction of the original continuous system. We also illustrate through examples how this compositional approach significantly reduces the time required for the construction of abstractions.

Keywords:Hybrid systems, Adaptive control;Automata Abstract: We develop a method to control discrete-time systems with constant but initially unknown parameters from linear temporal logic (LTL) specifications. We introduce the notions of (non-deterministic) parametric and adaptive transition systems and show how to use tools from formal methods to compute adaptive control strategies for finite systems. For infinite systems, we first compute abstractions in the form of parametric finite quotient transition systems and then apply the techniques for finite systems. Unlike traditional adaptive control techniques, our method is correct-by-design, does not require a reference model, and can handle a much wider range of systems and specifications. Illustrative examples are included.

Keywords:Hybrid systems;Switched systems Abstract: In this paper, we present a methodology that facilitates the integration of formal verification techniques into model-based design. The focus is on set-based reachability analysis and on control systems that are described by hybrid dynamics and nonlinear components. Starting with a standard simulation model, e.g. in MATLAB/Simulink, we transform it into an equivalent verification model, formally a network of hybrid automata. This verification model complies with the SX format, which is a formalism used by several reachability tools. A major obstacle encountered is that highly scalable reachability algorithms and tools exist for piecewise affine (PWA) dynamical models, but not for nonlinear ones. To obtain PWA over-approximations of nonlinear dynamics, we use an abstraction method known as hybridization. Hybridization consists in partitioning the state-space into a set of domains and for each domain approximating the nonlinear dynamics by simpler ones. Nondeterministic inputs are added to account for the abstraction error. Existing hybridization procedures operate on the composed (flattened) system, so the number of partitions is exponential in the number of variables. This quickly leads to intractably large models, even for small systems. To mitigate this problem, we decompose the original dynamics and carry out the state-space partitioning and PWA approximation on the components. The number of partitions in each PWA component is at most quadratic in the abstraction error, thus largely avoiding an explosion in the number of partitions. Since the SX format can handle templates, several components may share the same abstraction. The result is a highly compact model that retains the modular structure of the original simulation model. If only a small subset of the partitions is reachable, the bottleneck of having excessively large PWA models can be avoided by composing the model on-the-fly during the reachability analysis.

Keywords:Stability of nonlinear systems, Lyapunov methods Abstract: In this paper, we propose an iterative method for using SOS programming to estimate the region of attraction of a polynomial vector field, the conjectured convergence of which necessitates the existence of polynomial Lyapunov functions whose sublevel sets approximate the true region of attraction arbitrarily well. The main technical result of the paper is the proof of existence of such a Lyapunov function. Specifically, we use the Hausdorff distance metric to analyze convergence and in the main theorem demonstrate that the existence of an n-times continuously differentiable maximal Lyapunov function implies that for any epsilon>0, there exists a polynomial Lyapunov function and associated sub-level set which together prove stability of a set which is within epsilon Hausdorff distance of the true region of attraction. The proposed iterative method and probably convergence is illustrated with a numerical example.

Keywords:Stability of nonlinear systems, Network analysis and control;Discrete event systems Abstract: Network formation models explain the dynamics of the structure of connections using mechanisms that operate under different principles for establishing and removing edges. The Jackson-Rogers model is a generic framework that applies the principle of triadic closure to growing networks. Past work describes the asymptotic behavior of the degree distribution based on a continuous-time approximation. Here, we introduce a discrete-time approach that provides a more accurate fit of the dynamics of the in-degree distribution of the Jackson-Rogers model. Furthermore, we characterize the limit distribution and the expected value of the average degree as equilibria, and prove that both equilibria are asymptotically stable.

Keywords:Stability of nonlinear systems, Nonlinear output feedback;Robotics Abstract: In this article, controller design for a class of nonlinear systems is considered. The strict feedback form is a special case of this class and the proposed method is an extension to the backstepping method. In general form, the proposed method suggests a dynamical controller which has one state less than the system. However, the controller order is not fixed and it may be less than the general form. In a special case, the proposed controller reduces into a static function which is the original backstepping method. The proposed method can be used for stabilization and output tracking for this class which may be quite complicated or even impossible with regular methods. The proposed control strategy is based on the stability of the augmented states. In case that the assumption does not hold, another strategy is suggested to be used for stabilization.

Keywords:Stability of nonlinear systems, PID control;Aerospace Abstract: We propose a control law for stabilization of a bar tethered to two aerial vehicles, and provide conditions on the control law's gains that guarantee exponential stability of the equilibrium. Given the proposed control law, we analyze the stability of the equilibrium for two cases, specifically, for a bar of known and unknown mass. We provide lower bounds on the attitude gains of the UAVs' attitude inner loop that guarantee exponential stability of the equilibrium. We also include an integral action term in the control law, so as to compensate for battery drainage and model mismatches, and we provide a lower bound on the integral gain that guarantees stability of the equilibrium. We present an experiment that demonstrates the stabilization and that validates the robustness of the proposed control law.

Keywords:Stability of nonlinear systems;Power systems Abstract: This paper considers a system of ordinary differential equations subject to a parameter-dependent disturbance. The goal is to find the boundary in parameter space between parameter values for which the system will recover from the disturbance to a desired stable equilibrium point, and parameter values for which it will not recover. If the system state when the disturbance clears, call it the initial condition, depends continuously on parameter value, then it seems plausible that this parameter space boundary would consist of parameter values whose corresponding initial conditions lie on the boundary of the region of attraction (RoA) of the desired stable equilibrium point (SEP). Unfortunately, this is not true in general since, even when the system's vector field varies smoothly with parameter value, the boundary of the RoA of the SEP may not vary even continuously with respect to small parameter variations. This work shows that, for a large class of vector fields which generalize Morse-Smale vector fields, the RoA boundary varies continuously in an appropriate sense with respect to small parameter variations. Furthermore, it has been shown elsewhere that the RoA boundary for these vector fields is equal to the union of the stable manifolds of the equilibria and periodic orbits they contain. A complete argument is provided here that this decomposition into stable manifolds persists under small changes in parameter for the vector fields under consideration. The above results are applied to provide a theoretical basis for a numerical algorithm which computes parameter values which lie on the desired parameter space boundary.

Keywords:Stability of nonlinear systems, Uncertain systems;Aerospace Abstract: Two approaches to tackle the nonlinear robust stability problem of an aerospace plant are examined. The first employs a combination of the Describing Function method and mu analysis, while the second makes use of Integral Quadratic Constraints. The model analyzed consists of an airfoil subject to freeplay and LTI parametric uncertainties. The key steps required to apply the two methodologies and their main features are highlighted and discussed. Emphasis is given to quantitatively determine the post-critical behaviour known as Limit Cycle Oscillations. An important aim of the study is to understand how the conservatism usually associated with IQCs can be tackled by means of an informed selection of the multipliers and the search of local stability certificates. As for the latter, a restricted sector bound condition is proposed.