Showing papers in "IEEE Transactions on Automatic Control in 2012"

Nonlinear Feedback Design for Fixed-Time Stabilization of Linear Control Systems

Abstract: Two types of nonlinear control algorithms are presented for uncertain linear plants. Controllers of the first type are stabilizing polynomial feedbacks that allow to adjust a guaranteed convergence time of system trajectories into a prespecified neighborhood of the origin independently on initial conditions. The control design procedure uses block control principles and finite-time attractivity properties of polynomial feedbacks. Controllers of the second type are modifications of the second order sliding mode control algorithms. They provide global finite-time stability of the closed-loop system and allow to adjust a guaranteed settling time independently on initial conditions. Control algorithms are presented for both single-input and multi-input systems. Theoretical results are supported by numerical simulations.

Distributed Event-Triggered Control for Multi-Agent Systems

Abstract: Event-driven strategies for multi-agent systems are motivated by the future use of embedded microprocessors with limited resources that will gather information and actuate the individual agent controller updates. The controller updates considered here are event-driven, depending on the ratio of a certain measurement error with respect to the norm of a function of the state, and are applied to a first order agreement problem. A centralized formulation is considered first and then its distributed counterpart, in which agents require knowledge only of their neighbors' states for the controller implementation. The results are then extended to a self-triggered setup, where each agent computes its next update time at the previous one, without having to keep track of the state error that triggers the actuation between two consecutive update instants. The results are illustrated through simulation examples.

Dual Averaging for Distributed Optimization: Convergence Analysis and Network Scaling

Abstract: The goal of decentralized optimization over a network is to optimize a global objective formed by a sum of local (possibly nonsmooth) convex functions using only local computation and communication. It arises in various application domains, including distributed tracking and localization, multi-agent coordination, estimation in sensor networks, and large-scale machine learning. We develop and analyze distributed algorithms based on dual subgradient averaging, and we provide sharp bounds on their convergence rates as a function of the network size and topology. Our analysis allows us to clearly separate the convergence of the optimization algorithm itself and the effects of communication dependent on the network structure. We show that the number of iterations required by our algorithm scales inversely in the spectral gap of the network, and confirm this prediction's sharpness both by theoretical lower bounds and simulations for various networks. Our approach includes the cases of deterministic optimization and communication, as well as problems with stochastic optimization and/or communication.

Strict Lyapunov Functions for the Super-Twisting Algorithm

Abstract: A method to construct a family of strict Lyapunov functions, i.e., with negative definite derivative, for the super-twisting algorithm, without or with perturbations, is provided. This second order sliding modes algorithm is widely used to design controllers, observers and exact differentiators. The proposed Lyapunov functions ascertain finite time convergence, provide an estimate of the convergence time, and ensure the robustness of the finite-time or ultimate boundedness for a class of perturbations wider than the classical ones for this algorithm. Since the Lyapunov functions and their derivatives are quadratic forms, the operation with them is as simple as for linear time invariant systems.

Stability and Stabilization of Switched Linear Systems With Mode-Dependent Average Dwell Time

Abstract: In this paper, the stability and stabilization problems for a class of switched linear systems with mode-dependent average dwell time (MDADT) are investigated in both continuous-time and discrete-time contexts. The proposed switching law is more applicable in practice than the average dwell time (ADT) switching in which each mode in the underlying system has its own ADT. The stability criteria for switched systems with MDADT in nonlinear setting are firstly derived, by which the conditions for stability and stabilization for linear systems are also presented. A numerical example is given to show the validity and potential of the developed techniques.

Output-Based Event-Triggered Control With Guaranteed ${\cal L}_{\infty}$ -Gain and Improved and Decentralized Event-Triggering

Abstract: Most event-triggered controllers available nowadays are based on static state-feedback controllers. As in many control applications full state measurements are not available for feedback, it is the objective of this paper to propose event-triggered dynamical output-based controllers. The fact that the controller is based on output feedback instead of state feedback does not allow for straightforward extensions of existing event-triggering mechanisms if a minimum time between two subsequent events has to be guaranteed. Furthermore, since sensor and actuator nodes can be physically distributed, centralized event-triggering mechanisms are often prohibitive and, therefore, we will propose a decentralized event-triggering mechanism. This event-triggering mechanism invokes transmission of the outputs in a node when the difference between the current values of the outputs in the node and their previously transmitted values becomes “large” compared to the current values and an additional threshold. For such event-triggering mechanisms, we will study closed-loop stability and L∞-performance and provide bounds on the minimum time between two subsequent events generated by each node, the so-called inter-event time of a node. This enables us to make tradeoffs between closed-loop performance on the one hand and communication load on the other hand, or even between the communication load of individual nodes. In addition, we will model the event-triggered control system using an impulsive model, which truly describes the behavior of the event-triggered control system. As a result, we will be able to guarantee stability and performance for event-triggered controllers with larger minimum inter-event times than the existing results in the literature. We illustrate the developed theory using three numerical examples.

On Distributed Convex Optimization Under Inequality and Equality Constraints

Abstract: We consider a general multi-agent convex optimization problem where the agents are to collectively minimize a global objective function subject to a global inequality constraint, a global equality constraint, and a global constraint set. The objective function is defined by a sum of local objective functions, while the global constraint set is produced by the intersection of local constraint sets. In particular, we study two cases: one where the equality constraint is absent, and the other where the local constraint sets are identical. We devise two distributed primal-dual subgradient algorithms based on the characterization of the primal-dual optimal solutions as the saddle points of the Lagrangian and penalty functions. These algorithms can be implemented over networks with dynamically changing topologies but satisfying a standard connectivity property, and allow the agents to asymptotically agree on optimal solutions and optimal values of the optimization problem under the Slater's condition.

Cooperative Output Regulation of Linear Multi-Agent Systems

Abstract: In this technical note, we consider the cooperative output regulation of linear multi-agent systems. The overall system consists of two groups of subsystems. While the first group of subsystems can access the exogenous signal, the second cannot. As a result, the problem cannot be solved by the decentralized approach. By devising a distributed observer, we can solve the problem by a dynamic full information distributed control scheme. The problem can also be viewed as a generalization of some results of the leader-following consensus problem of multi-agent systems.

Distributed Coordinated Tracking With Reduced Interaction via a Variable Structure Approach

Abstract: A distributed coordinated tracking problem is solved via a variable structure approach when there exists a dynamic virtual leader who is a neighbor of only a subset of a group of followers, all followers have only local interaction, and only partial measurements of the states of the virtual leader and the followers are available. In the context of coordinated tracking, we focus on both consensus tracking and swarm tracking algorithms. In the case of first-order kinematics, we propose a distributed consensus tracking algorithm without velocity measurements under both fixed and switching network topologies. In particular, we show that distributed consensus tracking can be achieved in finite time. The algorithm is then extended to achieve distributed swarm tracking without velocity measurements. In the case of second-order dynamics, we first propose two distributed consensus tracking algorithms without acceleration measurements when the velocity of the virtual leader is varying under, respectively, a fixed and switching network topology. In particular, we show that the proposed algorithms guarantee at least global exponential tracking. We then propose a distributed consensus tracking algorithm and a distributed swarm tracking algorithm when the velocity of the virtual leader is constant. When the velocity of the virtual leader is varying, distributed swarm tracking is solved by using a distributed estimator. For distributed consensus tracking, a mild connectivity requirement is proposed by adopting an adaptive connectivity maintenance mechanism in which the adjacency matrix is defined in a proper way. Similarly, a mild connectivity requirement is proposed for distributed swarm tracking by adopting a connectivity maintenance mechanism in which the potential function is defined in a proper way. Several simulation examples are presented as a proof of concept.

On Average Performance and Stability of Economic Model Predictive Control

Abstract: Control performance and cost optimization can be conflicting goals in the management of industrial processes. Even when optimal or optimization-based control synthesis tools are applied, the economic cost associated with plant operation is often only optimized according to static criteria that pick, among all feasible steady states, those with minimal cost. In mathematical terms, an economic cost functional differs from stage costs commonly adopted in model predictive control (MPC) as it need not be minimal at its best equilibrium. This note collects and illustrates some recent advances in receding horizon optimization of nonlinear systems that allow the control designer to simultaneously and dynamically optimize transient and steady-state economic performance. In particular, we show that average performance of economic MPC is never worse than the optimal steady-state operation. We introduce a dissipation inequality and supply function that extend previous sufficient conditions for asymptotic stability of economic MPC. Dissipativity is also shown to be a sufficient condition for concluding that steady-state operation is optimal. We show how to modify an economic cost function so that steady-state operation is asymptotically stable when that feature is deemed desirable. Finally, for the case when steady-state operation is not optimal, we develop two modified MPC controllers that asymptotically guarantee 1) improved performance compared to optimal periodic control and 2) satisfaction of constraints on average values of states and inputs.

Coherence in Large-Scale Networks: Dimension-Dependent Limitations of Local Feedback

Abstract: We consider distributed consensus and vehicular formation control problems. Specifically we address the question of whether local feedback is sufficient to maintain coherence in large-scale networks subject to stochastic disturbances. We define macroscopic performance measures which are global quantities that capture the notion of coherence; a notion of global order that quantifies how closely the formation resembles a solid object. We consider how these measures scale asymptotically with network size in the topologies of regular lattices in 1, 2, and higher dimensions, with vehicular platoons corresponding to the 1-D case. A common phenomenon appears where a higher spatial dimension implies a more favorable scaling of coherence measures, with a dimensions of 3 being necessary to achieve coherence in consensus and vehicular formations under certain conditions. In particular, we show that it is impossible to have large coherent 1-D vehicular platoons with only local feedback. We analyze these effects in terms of the underlying energetic modes of motion, showing that they take the form of large temporal and spatial scales resulting in an accordion-like motion of formations. A conclusion can be drawn that in low spatial dimensions, local feedback is unable to regulate large-scale disturbances, but it can in higher spatial dimensions. This phenomenon is distinct from, and unrelated to string instability issues which are commonly encountered in control problems for automated highways.

Interval State Estimation for a Class of Nonlinear Systems

Abstract: The goal of this technical note is to design interval observers for a class of nonlinear continuous-time systems. The first part of this work shows that it is usually possible to design an interval observer for linear systems by means of linear time-invariant changes of coordinates even if the system is not cooperative. This result is extended to a class of nonlinear systems using partial exact linearisations. The proposed observers guarantee to enclose the set of system states that is consistent with the model, the disturbances and the measurement noise. Moreover, it is only assumed that the measurement noise and the disturbances are bounded without any additional information such as stationarity, uncorrelation or type of distribution. The proposed observer is illustrated through numerical simulations.

Consensus Computation in Unreliable Networks: A System Theoretic Approach

Abstract: This paper addresses the problem of ensuring trustworthy computation in a linear consensus network. A solution to this problem is relevant for several tasks in multi-agent systems including motion coordination, clock synchronization, and cooperative estimation. In a linear consensus network, we allow for the presence of misbehaving agents, whose behavior deviate from the nominal consensus evolution. We model misbehaviors as unknown and unmeasurable inputs affecting the network, and we cast the misbehavior detection and identification problem into an unknown-input system theoretic framework. We consider two extreme cases of misbehaving agents, namely faulty (non-colluding) and malicious (Byzantine) agents. First, we characterize the set of inputs that allow misbehaving agents to affect the consensus network while remaining undetected and/or unidentified from certain observing agents. Second, we provide worst-case bounds for the number of concurrent faulty or malicious agents that can be detected and identified. Precisely, the consensus network needs to be 2k+1 (resp. k+1) connected for k malicious (resp. faulty) agents to be generically detectable and identifiable by every well behaving agent. Third, we quantify the effect of undetectable inputs on the final consensus value. Fourth, we design three algorithms to detect and identify misbehaving agents. The first and the second algorithm apply fault detection techniques, and affords complete detection and identification if global knowledge of the network is available to each agent, at a high computational cost. The third algorithm is designed to exploit the presence in the network of weakly interconnected subparts, and provides local detection and identification of misbehaving agents whose behavior deviates more than a threshold, which is quantified in terms of the interconnection structure.

Stability of a Class of Linear Switching Systems with Applications to Two Consensus Problems

Abstract: In this paper, we first establish a stability result for a class of linear switched systems involving Kronecker product. The problem is interesting in that the system matrix does not have to be Hurwitz at any time instant. This class of linear switched systems arises in the control of multi-agent systems under switching network topology. As applications of this stability result, we give the solvability conditions for both the leaderless consensus problem and the leader-following consensus problem for general marginally stable linear multi-agent systems under switching network topology. In contrast with some existing results, our results only assume that the dynamic graph is uniformly connected.

Distributed Receding Horizon Control of Vehicle Platoons: Stability and String Stability

Abstract: This paper considers the problem of distributed control of a platoon of vehicles with nonlinear dynamics. We present distributed receding horizon control algorithms and derive sufficient conditions that guarantee asymptotic stability, leader-follower string stability, and predecessor-follower string stability, following a step speed change in the platoon. Vehicles compute their own control in parallel, and receive communicated position and velocity error trajectories from their immediate predecessor. Leader-follower string stability requires additional communication from the lead car at each update, in the form of a position error trajectory. Predecessor-follower string stability, as we define it, implies leader-follower string stability. Predecessor-follower string stability requires stricter constraints in the local optimal control problems than the leader-follower formulation, but communication from the lead car is required only once at initialization. Provided an initially feasible solution can be found, subsequent feasibility of the algorithms are guaranteed at every update. The theory is generalized for nonlinear decoupled dynamics, and is thus applicable to fleets of planes, robots, or boats, in addition to cars. A simple seven-car simulation examines parametric tradeoffs that affect stability and string stability. Analysis on platoon formation, heterogeneity and size (length) is also considered, resulting in intuitive tradeoffs between lead car and following car control flexibility.

Distributed Adaptive Control of Synchronization in Complex Networks

Abstract: This technical note studies distributed adaptive control of synchronization in complex networks An effective distributed adaptive strategy to tune the coupling weights of a network is designed based on local information of node dynamics The analysis is then extended to the case where only a small fraction of coupling weights can be adjusted A general criterion is derived and it is found that synchronization can be reached if the subgraph consisting of the edges and nodes corresponding to the updated coupling weights is connected Finally, simulation examples are given to illustrate the theoretical analysis

Nash Equilibrium Seeking in Noncooperative Games

Abstract: We introduce a non-model based approach for locally stable convergence to Nash equilibria in static, noncooperative games with N players. In classical game theory algorithms, each player employs the knowledge of the functional form of his payoff and the knowledge of the other players' actions, whereas in the proposed algorithm, the players need to measure only their own payoff values. This strategy is based on the extremum seeking approach, which has previously been developed for standard optimization problems and employs sinusoidal perturbations to estimate the gradient. We consider static games with quadratic payoff functions before generalizing our results to games with non-quadratic payoff functions that are the output of a dynamic system. Specifically, we consider general nonlinear differential equations with N inputs and N outputs, where in the steady state, the output signals represent the payoff functions of a noncooperative game played by the steady-state values of the input signals. We employ the standard local averaging theory and obtain local convergence results for both quadratic payoffs, where the actual convergence is semi-global, and non-quadratic payoffs, where the potential existence of multiple Nash equilibria precludes semi-global convergence. Our convergence conditions coincide with conditions that arise in model-based Nash equilibrium seeking. However, in our framework the user is not meant to check these conditions because the payoff functions are presumed to be unknown. For non-quadratic payoffs, convergence to a Nash equilibrium is not perfect, but is biased in proportion to the perturbation amplitudes and the higher derivatives of the payoff functions. We quantify the size of these residual biases and confirm their existence numerically in an example noncooperative game. In this example, we present the first application of extremum seeking with projection to ensure that the players' actions remain in a given closed and bounded action set.

Variable Gain Super-Twisting Sliding Mode Control

Abstract: In this note, a novel, Lyapunov-based, variable-gain super-twisting algorithm (STA) is proposed. It ensures for linear time invariant systems the global, finite-time convergence to the desired sliding surface, when the matched perturbations/uncertainties are Lipschitz-continuous functions of time, that are bounded, together with their derivatives, by known functions. The proposed algorithm has similar properties to the variable-gain first-order sliding mode control, but it provides alleviation to the chattering phenomenon. The results are verified experimentally.

Receding Horizon Temporal Logic Planning

Abstract: We present a methodology for automatic synthesis of embedded control software that incorporates a class of linear temporal logic (LTL) specifications sufficient to describe a wide range of properties including safety, stability, progress, obligation, response and guarantee. To alleviate the associated computational complexity of LTL synthesis, we propose a receding horizon framework that effectively reduces the synthesis problem into a set of smaller problems. The proposed control structure consists of a goal generator, a trajectory planner, and a continuous controller. The goal generator reduces the trajectory generation problem into a sequence of smaller problems of short horizon while preserving the desired system-level temporal properties. Subsequently, in each iteration, the trajectory planner solves the corresponding short-horizon problem with the currently observed state as the initial state and generates a feasible trajectory to be implemented by the continuous controller. Based on the simulation property, we show that the composition of the goal generator, trajectory planner and continuous controller and the corresponding receding horizon framework guarantee the correctness of the system with respect to its specification regardless of the environment in which the system operates. In addition, we present a response mechanism to handle failures that may occur due to a mismatch between the actual system and its model. The effectiveness of the proposed technique is demonstrated through an example of an autonomous vehicle navigating an urban environment. This example also illustrates that the system is not only robust with respect to exogenous disturbances but is also capable of properly handling violation of the environment assumption that is explicitly stated as part of the system specification.

Computational Complexity Certification for Real-Time MPC With Input Constraints Based on the Fast Gradient Method

Abstract: This paper proposes to use Nesterov's fast gradient method for the solution of linear quadratic model predictive control (MPC) problems with input constraints. The main focus is on the method's a priori computational complexity certification which consists of deriving lower iteration bounds such that a solution of pre-specified suboptimality is obtained for any possible state of the system. We investigate cold- and warm-starting strategies and provide an easily computable lower iteration bound for cold-starting and an asymptotic characterization of the bounds for warm-starting. Moreover, we characterize the set of MPC problems for which small iteration bounds and thus short solution times are expected. The theoretical findings and the practical relevance of the obtained lower iteration bounds are underpinned by various numerical examples and compared to certification results for a primal-dual interior point method.

Symbolic Models for Nonlinear Control Systems Without Stability Assumptions

Abstract: Finite-state models of control systems were proposed by several researchers as a convenient mechanism to synthesize controllers enforcing complex specifications. Most techniques for the construction of such symbolic models have two main drawbacks: either they can only be applied to restrictive classes of systems, or they require the exact computation of reachable sets. In this paper, we propose a new abstraction technique that is applicable to any nonlinear sampled-data control system as long as we are only interested in its behavior in a compact set. Moreover, the exact computation of reachable sets is not required. The effectiveness of the proposed results is illustrated by synthesizing a controller to steer a vehicle.

Distributed Seeking of Nash Equilibria With Applications to Mobile Sensor Networks

Abstract: We consider the problem of distributed convergence to a Nash equilibrium in a noncooperative game where the players generate their actions based only on online measurements of their individual cost functions, corrupted with additive measurement noise. Exact analytical forms and/or parameters of the cost functions, as well as the current actions of the players may be unknown. Additionally, the players' actions are subject to linear dynamic constraints. We propose an algorithm based on discrete-time stochastic extremum seeking using sinusoidal perturbations and prove its almost sure convergence to a Nash equilibrium. We show how the proposed algorithm can be applied to solving coordination problems in mobile sensor networks, where motion dynamics of the players can be modeled as: 1) single integrators (velocity-actuated vehicles), 2) double integrators (force-actuated vehicles), and 3) unicycles (a kinematic model with nonholonomic constraints). Examples are given in which the cost functions are selected such that the problems of connectivity control, formation control, rendezvous and coverage control are solved in an adaptive and distributed way. The methodology is illustrated through simulations.

Distributed Containment Control with Multiple Dynamic Leaders for Double-Integrator Dynamics Using Only Position Measurements

Abstract: This note studies the distributed containment control problem for a group of autonomous vehicles modeled by double-integrator dynamics with multiple dynamic leaders. The objective is to drive the followers into the convex hull spanned by the dynamic leaders under the constraints that the velocities and the accelerations of both the leaders and the followers are not available, the leaders are neighbors of only a subset of the followers, and the followers have only local interaction. Two containment control algorithms via only position measurements of the agents are proposed. Theoretical analysis shows that the followers will move into the convex hull spanned by the dynamic leaders if the network topology among the followers is undirected, for each follower there exists at least one leader that has a directed path to the follower, and the parameters in the algorithm are properly chosen. Numerical results are provided to illustrate the theoretical results.

Sampled-Data Synchronization Control of Dynamical Networks With Stochastic Sampling

Abstract: This technical note is concerned with the sampled-data synchronization control problem for a class of dynamical networks. The sampling period considered here is assumed to be time-varying that switches between two different values in a random way with given probability. The addressed synchronization control problem is first formulated as an exponentially mean-square stabilization problem for a new class of dynamical networks that involve both the multiple probabilistic interval delays (MPIDs) and the sector-bounded nonlinearities (SBNs). Then, a novel Lyapunov functional is constructed to obtain sufficient conditions under which the dynamical network is exponentially mean-square stable. Both Gronwall's inequality and Jenson integral inequality are utilized to substantially simplify the derivation of the main results. Subsequently, a set of sampled-data synchronization controllers is designed in terms of the solution to certain matrix inequalities that can be solved effectively by using available software. Finally, a numerical simulation example is employed to show the effectiveness of the proposed sampled-data synchronization control scheme.

Coupled Distributed Estimation and Control for Mobile Sensor Networks

Abstract: In this paper, we introduce a theoretical framework for coupled distributed estimation and motion control of mobile sensor networks for collaborative target tracking. We use a Fisher Information theoretic metric for quality of sensed data. The mobile sensing agents seek to improve the information value of their sensed data while maintaining a safe-distance from other neighboring agents (i.e., perform information-driven flocking). We provide a formal stability analysis of continuous Kalman-Consensus filtering (KCF) algorithm on a mobile sensor network with a flocking-based mobility control model. The discrete-time counterpart of this coupled estimation and control algorithm is successfully applied to tracking of two types of targets with stochastic linear and nonlinear dynamics.

Zero-Gradient-Sum Algorithms for Distributed Convex Optimization: The Continuous-Time Case

Abstract: This technical note presents a set of continuous-time distributed algorithms that solve unconstrained, separable, convex optimization problems over undirected networks with fixed topologies. The algorithms are developed using a Lyapunov function candidate that exploits convexity, and are called Zero-Gradient-Sum (ZGS) algorithms as they yield nonlinear networked dynamical systems that evolve invariantly on a zero-gradient-sum manifold and converge asymptotically to the unknown optimizer. We also describe a systematic way to construct ZGS algorithms, show that a subset of them actually converge exponentially, and obtain lower and upper bounds on their convergence rates in terms of the network topologies, problem characteristics, and algorithm parameters, including the algebraic connectivity, Laplacian spectral radius, and function curvatures. The findings of this technical note may be regarded as a natural generalization of several well-known algorithms and results for distributed consensus, to distributed convex optimization.

Modeling and Control of Quantum Systems: An Introduction

Abstract: The scope of this work is to provide a self-contained introduction to a selection of basic theoretical aspects in the modeling and control of quantum mechanical systems, as well as a brief survey on the main approaches to control synthesis. While part of the existing theory, especially in the open-loop setting, stems directly from classical control theory (most notably geometric control and optimal control), a number of tools specifically tailored for quantum systems have been developed since the 1980s, in order to take into account their distinctive features: the probabilistic nature of atomic-scale physical systems, the effect of dissipation and the irreversible character of the measurements have all proved to be critical in feedback-design problems. The relevant dynamical models for both closed and open quantum systems are presented, along with the main results on their controllability and stability. A brief review of several currently available control design methods is meant to provide the interested reader with a roadmap for further studies.

Nonlinear Stabilization Under Sampled and Delayed Measurements, and With Inputs Subject to Delay and Zero-Order Hold

Abstract: Sampling arises simultaneously with input and output delays in networked control systems. When the delay is left uncompensated, the sampling period is generally required to be sufficiently small, the delay sufficiently short, and, for nonlinear systems, only semiglobal practical stability is generally achieved. For example, global stabilization of strict-feedforward systems under sampled measurements, sampled-data stabilization of the nonholonomic unicycle with arbitrarily sparse sampling, and sampled-data stabilization of LTI systems over networks with long delays, are open problems. In this paper, we present two general results that address these example problems as special cases. First, we present global asymptotic stabilizers for forward complete systems under arbitrarily long input and output delays, with arbitrarily long sampling periods, and with continuous application of the control input. Second, we consider systems with sampled measurements and with control applied through a zero-order hold, under the assumption that the system is stabilizable under sampled-data feedback for some sampling period, and then construct sampled-data feedback laws that achieve global asymptotic stabilization under arbitrarily long input and measurement delays. All the results employ “nominal” feedback laws designed for the continuous-time systems in the absence of delays, combined with “predictor-based” compensation of delays and the effect of sampling.

Quantized $H_{\infty }$ Control for Nonlinear Stochastic Time-Delay Systems With Missing Measurements

Abstract: In this paper, the quantized H∞ control problem is investigated for a class of nonlinear stochastic time-delay network-based systems with probabilistic data missing. A nonlinear stochastic system with state delays is employed to model the networked control systems where the measured output and the input signals are quantized by two logarithmic quantizers, respectively. Moreover, the data missing phenomena are modeled by introducing a diagonal matrix composed of Bernoulli distributed stochastic variables taking values of 1 and 0, which describes that the data from different sensors may be lost with different missing probabilities. Subsequently, a sufficient condition is first derived in virtue of the method of sector-bounded uncertainties, which guarantees that the closed-loop system is stochastically stable and the controlled output satisfies H∞ performance constraint for all nonzero exogenous disturbances under the zero-initial condition. Then, the sufficient condition is decoupled into some inequalities for the convenience of practical verification. Based on that, quantized H∞ controllers are designed successfully for some special classes of nonlinear stochastic time-delay systems by using Matlab linear matrix inequality toolbox. Finally, a numerical simulation example is exploited to show the effectiveness and applicability of the results derived.

Consensus of Multi-Agent Networks With Aperiodic Sampled Communication Via Impulsive Algorithms Using Position-Only Measurements

Abstract: In this technical note, an impulsive consensus algorithm is proposed for second-order continuous-time multi-agent networks with switching topology. The communication among agents occurs at sampling instants based on position only measurements. By using the property of stochastic matrices and algebraic graph theory, some sufficient conditions are obtained to ensure the consensus of the controlled multi-agent network if the communication graph has a spanning tree jointly. A numerical example is given to illustrate the effectiveness of the proposed algorithm.