Finite ‐gain problem for networked control systems with delays via event‐triggered control

By using the integrals of the signals to construct the triggering condition, integral‐based event‐triggered control can relax the requirement of persistent decrease on the Lyapunov function and, then, may yield better sampling performance. This paper studies the disturbance rejection problem for the integral‐based event‐triggered control systems with transmission delays and observer‐based output feedbacks. An integral‐based triggering condition is employed to generate the events. Two asynchronous models are implemented in the different sides of the networks. The model in the observer node is used to detect the events, whereas the model in the controller node is used to calculate the control signals. This structure contributes to avoiding the Zeno behavior, and then, an estimation on the lower bound of the interevent times is provided. Moreover, the criteria on the parameter in the triggering condition and on the bounds of the transmission delays are given to guarantee the desired disturbance rejection performance. Finally, a numerical example is provided to illustrate the efficiency and feasibility of the obtained results.     

‐Gain analysis of event‐triggered networked control systems: a discontinuous Lyapunov functional approach

In this paper, the problems of exponential stability and ‐gain analysis of event‐triggered networked control systems (NCSs) with network‐induced delays are studied. We first propose event‐triggering conditions in the sensor side and controller side, respectively. Because the implementation of our event‐triggering scheme only needs periodic supervision of the system state at the constant sampling instants, instead of being monitored continuously, it is expected that the scheme will improve the resource utilization. Taking the network‐induced delays into account and using delay system approach, we constructed a unified model of NCSs with hybrid event‐triggering schemes. On the basis of this model, sufficient conditions for the exponential stability and ‐gain analysis are developed in the form of LMIs by using a discontinuous Lyapunov–Krasovskii functional approach. Moreover, the corresponding results can be further extended to more general cases, where the system matrices of the considered plant contain parameter uncertainties, represented in either polytopic or norm‐bounded frameworks. In addition, as a special case, we also present the exponential stability, ‐gain analysis, and the control feedback gain design of event‐triggered NCSs without considering the effects of network‐induced delays and event‐triggering condition in the controller side. Finally, a simulation example is provided to illustrate the usefulness and effectiveness of the proposed hybrid event‐triggering schemes.Copyright © 2012 John Wiley & Sons, Ltd.     

Event‐triggered predictive control for networked control systems with network‐induced delays and packet dropouts

This paper presents an event‐triggered predictive control approach to stabilize a networked control system subject to network‐induced delays and packet dropouts, for which the states are not measurable. An observer‐based event generator is first designed according to the deviation between the state estimation at the current time and the one at the last trigger time. A predictive control scheme with a selector is then proposed to compensate the effect of network‐induced delays and packet dropouts. Sufficient conditions for stabilization of the networked control system are derived by solving linear matrix inequalities and the corresponding gains of the controller and the observer are obtained. It is shown that the event‐triggered implementation is able to realize reduction in communication and save bandwidth resources of feedback channel networks. A simulation example of an inverted pendulum model illustrates the efficacy of the proposed scheme.     

Mixed Event‐Triggered Mechanism Modeling and Controlling for Networked Control Systems with Time‐Varying Delays and Uncertainties

This paper is concerned with modeling and controlling under the mixed event‐triggered mechanism (ETM) for networked control systems (NCSs) with time‐varying delays and uncertainties. Firstly, an event‐triggered threshold is set by using both state and state‐independent informations in the mixed ETM. Then the event‐triggered NCSs with network‐induced time‐varying delays which exist in both sensor‐to‐controller and controller‐to‐actuator channels are modeled as a general time‐delay system. Based on the piecewise differentiable characteristic of the time‐varying delay and by using the approach of free weighting matrix and reciprocally convex, a less conservative criterion to be globally uniformly ultimately bounded (GUUB) stability and a controller design method are derived. Furthermore, an algorithm is proposed to obtain the desired mixed ETM and state‐feedback controller which can render the network load and control performance to reach an expected level. Compared with the relative and absolute ETMs, the proposed mechanism can effectively improve the transmission efficiency during the whole working time. Finally, a numerical example is given to show the effectiveness of the proposed approach.     

Mixed Event/Time‐Triggered Static Output Feedback L2‐Gain Control for Networked Control Systems

This paper considers the design of mixed event/time‐triggered controllers for networked control systems (NCSs) under transmission delay and possible packet dropout. Assuming that a conventional delayed static output feedback L₂‐gain controller exists, we propose an output‐based mixed event/time‐triggered communication scheme for reducing the network traffic in a NCS. Moreover, we show that a conventional delayed static output feedback L₂‐gain controller can be obtained by solving a linear matrix inequality with a matrix equality constraint. A numerical example is proposed for demonstrating the theoretical results.     

Distributed event‐triggered feedback consensus control with state‐dependent threshold for general linear multi‐agent systems

This paper considers the distributed event‐triggered consensus problem for multi‐agent systems with general linear dynamics under undirected graphs. Based on state feedback, we propose a novel distributed event‐triggered consensus controller with state‐dependent threshold for each agent to achieve consensus, without continuous communication in either controller update or triggering condition monitoring. Each agent only needs to monitor its own state continuously to determine if the event is triggered. It is proved that there is no Zeno behavior under the proposed consensus control algorithm. To relax the requirement of the state measurement of each agent, we further propose a novel distributed observer‐based event‐triggered consensus controller to solve the consensus problem in the case with output feedback and prove that there is no Zeno behavior exhibited. Finally, simulation results are given to illustrate the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust event‐triggered control of second‐order disturbed leader‐follower MASs: A nonsingular finite‐time consensus approach

This paper addresses the finite‐time and the prescribed finite‐time event‐triggered consensus tracking problems for second‐order multi‐agent systems (MASs) with uncertain disturbances. The prescribed finite‐time event‐triggered consensus of the second‐order disturbed MASs was obtained for the first time and the controller is nonsingular. Furthermore, a new self‐triggered control scheme is presented for the finite‐time consensus tracking, and the continuous communication can be avoided in the triggering condition monitoring. Hence, the finite‐time consensus tracking can be achieved with intermittent communication. Moreover, Zeno behavior is excluded for each follower. The efficiency of the proposed algorithms is verified by numerical simulations.     

Distributed edge event‐triggered consensus protocol of multi‐agent systems with communication buffer

This paper proposes a distributed edge event‐triggered (DEET) scheme of multi‐agent systems via a communication buffer to reduce unnecessary update of controllers induced by fast information transmission. This edge scheme avoids a synchronous phenomenon in node event‐triggered mechanism, in which the triggering of one agent activates information transmission of all edges linked with this agent. Hence, the node event‐triggered scheme leads to unnecessary update of control protocols while the DEET provides a new approach without constrains on synchronous phenomenon of edge information exchange. That is, the communication on each edge is independent with other edges. In addition, we investigate another case where edge information transmission is subject to quantization and a quantized edge event‐triggered control protocol is proposed. Note that such a quantized protocol guarantees asymptotical consensus instead of bounded consensus in most of the existing literature. Meanwhile, both DEET and quantized edge event‐triggered schemes have nontrivial properties of excluding Zeno behavior. Furthermore, an algorithm is provided to avoid continuous event detection; hence, the communication traffic of the whole network is reduced significantly. Copyright © 2016 John Wiley & Sons, Ltd.     

Distributed Adaptive Event‐Triggered Control for Leader‐Following Consensus of Multi‐Agent Systems

This paper studies the leader‐following consensus problem for Lipschitz nonlinear multi‐agent systems using novel event‐triggered controllers. A distributed adaptive law is introduced for the event‐based control strategy design such that the proposed controllers are independent of system parameters and only use the relative states of neighboring agents, and hence are fully distributed. Due to the introduction of an event‐triggered control scheme, the controller of the agent is only triggered at it's own event times, and thus reduces the amount of communication between controller and actuator and lowers the frequency of controller updates in practice. Based on a quadratic Lyapunov function, the event condition which uses only neighbor information and local computation at trigger instants is established. Infinite triggers within a finite time are also verified to be impossible. The effectiveness of the theoretical results are illustrated through simulation examples.     

Consensus of multi‐agent systems with time‐varying topology: An event‐based dynamic feedback scheme

The event‐based control strategy is an effective methodology for reducing the controller update and communication over the network. In this paper, the event‐based consensus of multi‐agent systems with linear dynamics and time‐varying topology is studied. For each agent, a state‐dependent threshold with an exponentially decaying bound is presented to determine the event times, and a new event‐based dynamic feedback scheme is proposed. It is shown that the controller update for each agent is only dependent on its own event times, which reduces significantly the controller update or computation for each agent. Moreover, based on the event‐based dynamic feedback scheme and the event triggering function presented in this paper, the continuous communication among neighboring agents is avoided, and the Zeno‐behavior of the closed‐loop systems is excluded. A numerical example is given to illustrate the effectiveness of theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

Event‐triggered observer‐based robust H∞ control for networked control systems with unknown disturbance

In this article, the event‐triggered robust H_∞ control is studied for a class of uncertain networked control systems (NCSs) subject to unknown state and variable disturbance. First, aiming to decrease the unnecessary transmissions of sampled data, an efficient adaptive event‐triggered scheme (AETS) is presented, which can reflect the full real‐time variation of addressed NCSs and help to reduce the conservativeness. Second, based on the triggered output signals and disturbance model, two effective observers are, respectively, exploited to estimate the state and disturbance, which are further utilized to reject the disturbance and design the controller. By using the overall closed‐loop system and selecting an augmented Lyapunov‐Krasovskii functional, two sufficient conditions on jointly designing the adaptive event scheme, observers, and controller are established via linear matrix inequality forms, which can guarantee the global exponential stability and ensure H_∞ performance. Finally, some simulations and comparisons in a numerical example are provided to demonstrate the effectiveness of the derived results.     

Event‐Based Consensus Controller for Linear Multi‐Agent Systems Over Directed Communication Topologies: A Co‐Design Approach

The paper addresses the distributed event‐triggered consensus problem in directed topologies for multi‐agent systems (MAS) with general linear dynamic agents. A co‐design approach is proposed to determine parameters of the consensus controller and its event‐triggered mechanism (ETM), simultaneously. This approach guarantees asymptotic stability along with decreasing data transmission among agents. In the proposed event‐based consensus controller, each agent broadcasts data to the neighbors only at its own triggering instants; this differs from previous studies in which continuous data streams among agents were required. Furthermore, the proposed control law is based on the piecewise constant functions of the measurement values, which are updated at triggering instants. In this case the control scheme decreases the communication network usage, energy consumption, and wear of the actuator. As a result, it facilitates distributed implementation of the proposed consensus controller for real‐world applications. A theorem is proved to outline sufficient conditions to guarantee the asymptotic stability of the closed‐loop system with the event‐based consensus controller. Another theorem is also proved to show the Zeno behavior exclusion. As a case study, the proposed event‐based controller is applied for a diving consensus problem to illustrate the effectiveness of the method.     

Event‐triggered MPC design for distributed systems toward global performance

This paper studies the coordination control problem of stabilizing large‐scale dynamically coupled systems via a novel event‐triggered distributed model predictive control (DMPC) approach. In order to achieve global performance, certain constraints relevant to the triggering instant are imposed on the DMPC optimization problem, and triggering mechanisms are designed by taking into account coupling influences. Specifically, the triggering conditions derived from the feasibility and stability analysis are based on the local subsystem state and the information received from its neighbors. Based on these triggering mechanisms, the event‐triggered DMPC algorithm is built, and a dual‐mode strategy is adopted. As a result, the controllers solve the optimization problem and coordinate with each other asynchronously, which reduces the amount of communication and lowers the frequency of controller updates while achieving global performance. The recursive feasibility of the proposed event‐triggered DMPC algorithm is proved, and sufficient parameter conditions about the prediction horizon and the triggering threshold are established. It shows that the system state can be gradually driven into the terminal set under the proposed strategy. Finally, an academic example and a realistic simulation problem to the water level of a 4‐tank system are provided to verify the effectiveness of the proposed algorithm.     

Distributed event‐triggered consensus control with fully continuous communication free for general linear multi‐agent systems under directed graph

This paper considers the distributed event‐triggered consensus problem for multi‐agent systems with general linear dynamics under a directed graph. We propose a novel distributed event‐triggered consensus controller with state‐dependent threshold for each agent to achieve consensus. In this strategy, continuous communication in both controller update and triggering condition monitoring is not required, which means the proposed strategy is fully continuous communication free. Each agent only needs to monitor its own state continuously to determine if the event is triggered. Additionally, the approach shown here provides consensus with guaranteed positive inter‐event time intervals. Therefore, there is no Zeno behavior under the proposed consensus control algorithm. Finally, numerical simulations are given to illustrate the theoretical results.     

Event‐Triggered Control for Multi‐Agent Systems with General Directed Topology and Time Delays

Recent years have witnessed a growing interest in event‐triggered strategies for coordination and cooperative control of multi‐agent systems. However, the most previous works and developments focus on the interactive network that has no communication delays. This paper deals with the consensus problem of an agent system with event‐triggered control strategy under communication time delays. We first propose a time delays system model, then present a novel event triggering function that not only avoids continuous communication but also excludes the Zeno behavior. Furthermore, we provide the consensus analysis using an inequality technique instead of the traditional linear matrix inequality method, and we demonstrate that the inter‐event times for each agent are strictly positive, which implies that the Zeno behavior can be excluded. Finally, simulation results show the effectiveness of the proposed approach and illustrate the correctness of the theoretical results.     

Trigger‐based tracking control for a class of uncertain nonlinear systems via an event‐triggered extended state observer

An event‐triggered observer‐based output feedback control issue together with triggered input is investigated for a class of uncertain nonlinear systems subject to unknown external disturbances. Two separate event‐triggered conditions are located on the measurement channel and control channel, respectively. An event‐triggered extended state observer (ETESO) is employed to estimate unmeasurable states and compensate uncertainties and disturbances in real time while it is not required for real‐time output measurement. Then, combined with backstepping method and active disturbance rejection control, an output feedback control scheme is proposed, where an event‐triggered input is developed for reducing the communication rate between the controller and the actuator. The triggered instants are determined by a time‐varying event‐triggered condition. Two simulations, including a numerical example and an permanent‐magnet motor, are illustrated to verify the effectiveness of the proposed schemes.     

Event‐triggered fault‐tolerant control and scheduling codesign for nonlinear networked control systems with medium‐access constraint and packet disordering

This paper studies an event‐triggered communication, scheduling, and fault‐tolerant control codesign method for nonlinear networked control systems with medium‐access constraint, delay, and packet disordering using an adaptive approximation method and adaptive technique. By considering nonlinear dynamics and controller reconfiguration, a novel event‐triggering scheme with an adjustable triggering condition and adaptive triggering thresholds is proposed. The stochastic event‐driven actuator scheduling is investigated without the assumption that the controller can access the current modes of the actuators. By considering the Markovian delay and focusing on the transmitter node, a new packet reordering approach is used to cope with packet disordering. This paper proposes an active fault‐tolerant control method, in which the nominal controller is redesigned for the postfault plant by using the fault information provided by an estimator. It is proven that the estimation error of the estimator is uniformly bounded, the reconfigurable controller and event‐trigger ensure the boundedness in probability of the state tracking error before and after the fault occurrence in the presence of medium‐access constraint, delay, and packet disordering while reducing communication load. The effectiveness of the proposed method is demonstrated in the numerical example.     

Adaptive event‐triggered control for nonlinear discrete‐time systems

This paper focuses on the analysis and the design of event‐triggering scheme for discrete‐time systems. Both static event‐triggering scheme (SETS) and adaptive event‐triggering scheme (AETS) are presented for discrete‐time nonlinear and linear systems. What makes AETS different from SETS is that an auxiliary dynamic variable satisfying a certain difference equation is incorporated into the event‐triggering condition. The sufficient conditions of asymptotic stability of the closed‐loop event‐triggered control systems under both two triggering schemes are given. Especially, for the linear systems case, the minimum time between two consecutive control updates is discussed. Also, the quantitative relation among the system parameters, the preselected triggering parameters in AETS, and a quadratic performance index are established. Finally, the effectiveness and respective advantage of the proposed event‐triggering schemes are illustrated on a practical example. Copyright © 2016 John Wiley & Sons, Ltd.     

Event‐based global stabilization of linear systems via a saturated linear controller

This paper investigates the problem of event‐based linear control of systems subject to input saturation. First, for discrete‐time systems with neutrally stable or double‐integrator dynamics, novel event‐triggered control algorithms with non‐quadratic event‐triggering conditions are proposed to achieve global stabilization. Compared with the quadratic event‐triggering conditions, the non‐quadratic ones can further reduce unnecessary control updates for the input‐saturated systems. Furthermore, for continuous‐time systems with neutrally stable or double‐integrator dynamics, because an inherent lower bound of the inter‐event time does not exist for systems subject to input saturation, novel event‐triggered control algorithms with an appropriately selected minimum inter‐event time are proposed to achieve global stabilization. Finally, numerical examples are provided to illustrate the theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.