Periodic event‐triggered control for distributed networked multiagents with asynchronous communication: A predictive control approach

This paper investigates the periodic event‐triggered control problem for distributed networked multiagent systems with interconnected nonlinear dynamics subject to asynchronous communication. A method of state trajectory estimation for the interconnected neighboring agents over each prediction horizon with guaranteed error bounds is addressed to handle the asynchronous communication. Based on it, a distributed robust model predictive control (MPC) is proposed with a distributed periodic event‐triggered scheme for each agent. According to this algorithm, each subsystem generates presumed state trajectories for all its upstream neighbors and computes its own control locally. By checking the designed triggering condition periodically, the optimization problem of MPC will be implemented and solved when the local error of the subsystem exceeds a specified threshold. Then, the optimized control input will be determined and applied until the next time instant when the triggering condition is invoked. Moreover, sufficient condition for ensuring feasibility of the designed algorithm is conducted, along with the analysis of asymptotic stabilization of the closed‐loop system. The illustrative example for a set of coupled Van der Pol oscillators is reported to verify the effectiveness of the proposed approach.     

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.     

自适应事件触发网络化非线性系统滤波器设计

本文针对网络化非线性控制系统设计了基于自适应事件触发方案满足H∞性能的模糊滤波器.第一,提出新的自适应事件触发方案来决定数据包是否需要传输到通信网络中,从而提高网络资源利用率;第二,运用模糊线积分的方法,构建模糊李雅普诺夫泛函,避免求解隶属函数的时间微分;第三,利用Wirtinger不等式及倒凸引理结合的技术,得到滤波...     

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.     

Model‐based event‐triggered predictive control for networked systems with communication delays compensation

This paper addresses the model‐based event‐triggered predictive control problem for networked control systems (NCSs). Firstly, we propose a discrete event‐triggered transmission scheme on the sensor node by introducing a quadratic event‐triggering function. Then, on the basis of the aforementioned scheme, a novel class of model‐based event‐triggered predictive control algorithms on the controller node is designed for compensating for the communication delays actively and achieving the desired control performance while using less network resources. Two cases, that is, the value of the communication delay of the first event‐triggered state is less or bigger than the sampling period, are considered separately for certain NCSs, regardless of the communication delays of the subsequent event‐triggered states. The codesign problems of the controller and event‐triggering parameter for the two cases are discussed by using the linear matrix inequality approach and the (switching) Lyapunov functional method. Furthermore, we extended our results to the NCSs with systems uncertainties. Finally, a practical ball and beam system is studied numerically to demonstrate the compensation effect for the communication delays with the proposed novel model‐based event‐triggered predictive control scheme. Copyright © 2014 John Wiley & Sons, Ltd.     

Decentralized control of network‐based interconnected systems: A state‐dependent triggering method

This paper investigates decentralized control for a class of interconnected system. Different from the traditional systems, the considered system has the following features: (i) its subsystems are connected through a communication network subject to transmission delays and packet losses; (ii) the subsystems' multi‐actuators are subjected to random faults; and (iii) the subsystems are subject to probabilistic nonlinear disturbances, the inner variation information of the nonlinearities, as well as their bounds information, is utilized to analyze the nonlinearities. Furthermore, in order to reduce the network bandwidth burden, a decentralized state‐dependent triggering scheme is proposed. Considering aforementioned characteristics and using the state‐dependent triggering scheme, new type of network‐based interconnected system model is built. By using the Lyapunov functional approach, sufficient conditions for the mean square stability and stabilization of the network‐based interconnected systems are obtained. Then reliable controllers, as well as the triggering matrices of the local subsystems, can be co‐designed by using a cone complementary linearization algorithm. Two simulation examples are given to illustrate the effectiveness and application of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.     

Decentralized dynamic event-triggered control for networked control systems under unreliable communication network and actuator saturation

In this paper, the stochastic stability of networked control systems (NCSs) with nonlinear perturbation and parameter uncertainties is studied. A decentralized dynamic event triggering scheme (DDETS) is introduced to reduce energy consumption and network transmission burden. Each channel can decide whether to transmit signals sampled by corresponding sensors through this mechanism. Due to the unreliability of communication network, a new mathematical model of NCSs based on multi-channel fading and hybrid cyber attacks is established, and the actuator is constrained by saturation. A sufficient condition for stochastic stability based on static controller is derived through Lyapunov stability theory, and two numerical examples are given to demonstrate the effectiveness of the method.     

Security distributed state estimation for nonlinear networked systems against DoS attacks

This paper is concerned with security distributed state estimation for nonlinear networked systems against denial‐of‐service attacks. By taking the effects of resource constraints into consideration, an event‐triggered scheme and a quantization mechanism are employed to alleviate the burden of network. A mathematical model of distributed state estimation is constructed for nonlinear networked systems against denial‐of‐service attacks. Sufficient conditions ensuring the exponential stability of the estimation error systems are obtained by utilizing the Lyapunov stability theory. The explicit expressions of the designed state estimators are acquired in terms of the linear matrix inequalities. Finally, a numerical example is used to testify the feasibility of the proposed method.     

‐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 control for networked Markovian jump systems

The problem of H_∞ control for networked Markovian jump system under event‐triggered scheme is studied in this paper. In order to reduce the utilization of limited network bandwidth, a dynamic discrete event‐triggered scheme to choose the transmitted data is designed. A Markovian jump time‐delay system model is employed to describe the event‐triggered scheme and the network related behavior, such as transmission delay, data package dropout, and disorder. Furthermore, a sufficient condition is derived to guarantee that the resulting closed‐loop system is stable and has a prescribed performance index. A co‐design method for the H_∞ controller and the event‐triggered scheme is then proposed. The effectiveness and potential of the theoretic results obtained are illustrated by a simulation example. Copyright © 2014 John Wiley & Sons, Ltd.     

Event‐triggered H∞ control for a class of nonlinear networked control systems using novel integral inequalities

This paper is concerned with event‐triggered H_∞ control for a class of nonlinear networked control systems. An event‐triggered transmission scheme is introduced to select ‘necessary’ sampled data packets to be transmitted so that precious communication resources can be saved significantly. Under the event‐triggered transmission scheme, the closed‐loop system is modeled as a system with an interval time‐varying delay. Two novel integral inequalities are established to provide a tight estimation on the derivative of the Lyapunov–Krasovskii functional. As a result, a novel sufficient condition on the existence of desired event‐triggered H_∞ controllers is derived in terms of solutions to a set of linear matrix inequalities. No parameters need to be tuned when controllers are designed. The proposed method is then applied to the robust stabilization of a class of nonlinear networked control systems, and some linear matrix inequality‐based conditions are formulated to design both event‐triggered and time‐triggered H_∞ controllers. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

An adaptive critic approach to event‐triggered robust control of nonlinear systems with unmatched uncertainties

In this paper, we develop a novel event‐triggered robust control strategy for continuous‐time nonlinear systems with unmatched uncertainties. First, we build a relationship to show that the event‐triggered robust control can be obtained by solving an event‐triggered nonlinear optimal control problem of the auxiliary system. Then, within the framework of reinforcement learning, we propose an adaptive critic approach to solve the event‐triggered nonlinear optimal control problem. Unlike typical actor‐critic dual approximators used in reinforcement learning, we employ a unique critic approximator to derive the solution of the event‐triggered Hamilton‐Jacobi‐Bellman equation arising in the nonlinear optimal control problem. The critic approximator is updated via the gradient descent method, and the persistence of excitation condition is necessary. Meanwhile, under a newly proposed event‐triggering condition, we prove that the developed critic approximator update rule guarantees all signals in the auxiliary closed‐loop system to be uniformly ultimately bounded. Moreover, we demonstrate that the obtained event‐triggered optimal control can ensure the original system to be stable in the sense of uniform ultimate boundedness. Finally, a F‐16 aircraft plant and a nonlinear system are provided to validate the present event‐triggered robust control scheme.     

H∞ stabilization for networked semi‐Markovian jump systems with randomly occurring uncertainties via improved dynamic event‐triggered scheme

This paper aims to solve the H_∞ stabilization problem for networked semi‐Markovian jump systems subject to randomly occurring uncertainties by an improved event‐triggered technique. A new measurement error that is defined as the difference value between the latest transmitted data and the mean value of both current data and latest transmitted data is introduced into the event‐triggered condition. Compared with traditional dynamic event‐triggered scheme, more unexpected data could be avoided to be transmitted, which is demonstrated in the simulation through sufficient comparison experiments. Furthermore, by employing a Lyapunov‐Krasovskii functional method and a free‐weighting matrix method, sufficient conditions are derived to guarantee the stabilization of the closed‐loop semi‐Markovian jump time‐delay system with uncertainties and a prescribed performance index. Then, a codesign method for H_∞ controller gains and event‐triggered parameters is presented. Finally, simulations are given to verify the effectiveness of our improved dynamic event‐triggered scheme.     

Global adaptive finite‐time stabilization for a class of p‐normal nonlinear systems via an event‐triggered strategy

This article addresses the problem of global adaptive finite‐time control for a class of p‐normal nonlinear systems via an event‐triggered strategy. A state feedback controller is first designed for the nominal system by adding a power integrator method. Then, by the skillful design of adaptive dynamic gain mechanism, a novel event‐triggered controller is constructed for uncertain nonlinear system without homogeneous growth condition. It is proved that the global finite‐time stabilization of p‐normal nonlinear systems is guaranteed and the Zeno phenomenon is excluded. Finally, two examples are presented to indicate the effectiveness of the proposed control scheme.     

Adaptive Control of Piecewise Linear Systems with State Feedback for Output Tracking

A piecewise linear system consists of a set of linear time‐invariant (LTI) subsystems, with a switching sequence specifying an active subsystem at each time instant. This paper studies the adaptive control problem of single‐input, single‐output (SISO) piecewise linear systems. By employing the knowledge of the time instant indicator functions of system parameter switches, a new controller structure parametrization is proposed for the development of a stable adaptive control scheme with reduced modeling error in the estimation error signal used for parameter adaptive laws. This key feature is achieved by the new control scheme's ability to avoid a major parameter swapping term in the error model, with the help of indicator functions whose knowledge is available in many applications. A direct state feedback model reference adaptive control (MRAC) scheme is presented for such systems to achieve closed‐loop signal boundedness and small output tracking error in the mean square sense, under the usual slow system parameter switching condition. Simulation results on linearized NASA GTM models are presented to demonstrate the effectiveness of the proposed scheme.     

Aperiodic Sampled-Data Control of Distributed Networked Control Systems Under Stochastic Cyber-Attacks

This paper examines the stabilization problem of a distributed networked control system under the effect of cyber-attacks by employing a hybrid aperiodic triggering mechanism. The cyber-attack considered in the paper is a stochastic deception attack at the sensor-controller end. The probability of the occurrence of attack on a subsystem is represented using a random variable. A decentralized hybrid sampled-data strategy is introduced to save energy consumption and reduce the transmission load of the network. In the proposed decentralized strategy, each subsystem can decide independently whether its state should be transmitted to the controller or not. The scheme of the hybrid triggering mechanism for each subsystem composed of two stages: In the first stage, the next sampling instant is computed using a self-triggering strategy. Subsequently, in the second stage, an event-triggering condition is checked at these sampling instants and the control signal is computed only if the event-triggering condition is violated. The self-triggering condition used in the first stage is dependent on the selection of event-triggering condition of the second stage. Finally, a comparison of the proposed approach with other triggering mechanisms existing in the literature is presented in terms of the sampling instants, transmission frequency and performance measures 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.     

Distributed adaptive integral‐type event‐triggered cooperative output regulation of switched multiagent systems by agent‐dependent switching with dwell time

This article presents a distributed adaptive integral‐type event‐triggered scheme (ETS) and an agent‐dependent switching strategy with dwell time to solve the cooperative output regulation problem for switched multiagent systems. First, by constructing an adaptive law to dynamically update the time‐varying coupling weights for all the communication links, a fully distributed ETS is designed, where only the local information of the topology is adopted. Based on the integral‐type triggering condition, the interevent interval is substantially enlarged and Zeno behavior is explicitly ruled out. Second, each agent permits all the subsystems to be unstabilizable. The switching signal for each agent is different, and any adjacent switches of each agent satisfy the preset dwell time. Under the designed switching strategy, the solvability of the regulation problem is guaranteed. Finally, the effectiveness of the designed ETS and switching strategy is substantiated by an example.     

Decentralized summation‐based triggering mechanism for Lipschitz nonlinear systems

In this paper, a decentralized event‐based triggering mechanism for a class of nonlinear control systems is studied. It is assumed that the measurement sensors are geographically distributed and so local event generator modules are employed. Then, a novel periodic triggering condition is proposed for each module, which can potentially reduce the information exchange between subsystems compared with traditional control approaches, while maintaining closed‐loop asymptotic stability. The triggering condition parameters are designed through a convex optimization problem with LMI constraints. Finally, simulations are carried out to illustrate the performance of the introduced scheme. Copyright © 2017 John Wiley & Sons, Ltd.