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 constrained control of positive systems with input saturation

This paper addresses the problem of event‐triggered stabilization for positive systems subject to input saturation, where the state variables are in the nonnegative orthant. An event‐triggered linear state feedback law is constructed. By expressing the saturated linear state feedback law on a convex hull of a group of auxiliary linear feedback laws, we establish conditions under which the closed‐loop system is asymptotically stable with a given set contained in the domain of attraction. On the basis of these conditions, the problem of designing the feedback gain and the event‐triggering strategy for attaining the largest domain of attraction is formulated and solved as an optimization problem with linear matrix inequality constraints. The problem of designing the feedback gain and the event‐triggering strategy for achieving fast transience response with a guaranteed size of the domain of attraction is also formulated and solved as an linear matrix inequality problem. The effectiveness of these results is then illustrated by numerical simulation.     

A Lyapunov‐based small‐gain approach on design of triggering conditions in event‐triggered control systems

This paper studies a Lyapunov‐based small‐gain approach on design of triggering conditions in event‐triggered control systems. The event‐triggered control closed‐loop system is formulated as a hybrid system model. Firstly, by viewing the event‐triggered control closed‐loop system as a feedback connection of two smaller hybrid subsystems, the Lyapunov‐based small‐gain theorems for hybrid systems are applied to design triggering conditions. Then, a new class of triggering condition, the safe, adjustable‐type triggering condition, is proposed to tune the parameters of triggering conditions by practical regulations. This is conducive to break the restriction of the conservation of theoretical results and improve the practicability of event‐triggered control strategy. Finally, a numerical example is given to illustrate the efficiency and the feasibility of the proposed results. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

Distributed event‐triggered containment control for dynamical multiagent networks

This paper studies the event‐triggered containment control problem for dynamical multiagent networks of general MIMO linear agents. An event‐triggered containment control strategy is provided, which consists of a control law based on a relative‐state feedback and a distributed triggering rule based on both the relative‐state information and a time‐dependent threshold function. Compared to the previous related works, our main contribution is that the triggering rule depends only on local information of communication networks. It is proved that under the proposed event‐based controller, the containment errors are uniformly ultimately bounded and the Zeno behavior can be excluded. Moreover, when the derivation constant in the threshold function is equal to zero, the containment control problem can be solved. Then, the results are extended to the event‐triggered observer‐based containment controller design.     

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.     

Event‐Triggered Consensus of Nonlinear Multi‐Agent Systems with Unknown External Disturbance

This paper addresses the consensus problem of nonlinear multi‐agent systems with unknown external disturbance. First, a distributed observer is proposed to estimate the state and unknown disturbance of each agent simultaneously. Then, a novel event‐triggered control scheme based on the agent state estimation and disturbance estimation is proposed. Unlike the existing strategies, our event‐triggered conditions depend on agent state estimation and disturbance estimation, which are more effective and practical. Under this observer and control strategy, some sufficient conditions are derived to ensure the consensus of the multi‐agent system with unknown external disturbance. Moreover, the Zeno‐behavior of triggering time sequences is also excluded. Finally, a simulation example is given to verify the theoretical analysis.     

Event‐triggered global leader‐following consensus of a group of neutrally stable linear systems subject to input saturation

This paper studies the global leader‐following consensus problem for a multiagent system using event‐triggered linear feedback control laws. The leader agent is described by a neutrally stable linear system and the follower agents are also described by a neutrally stable linear system but with saturating input. Both the state‐feedback case and the output‐feedback case are considered. In each case, an event‐triggered control law is constructed for each follower agent and an event‐triggering strategy is designed for updating these control laws. These event‐triggered control laws are shown to achieve global leader‐following consensus when the communication topology among the follower agents is strongly connected and detailed balanced and the leader is a neighbor of at least one follower agent. The Zeno behavior is excluded. The theoretical results are illustrated by simulation.     

通讯信息约束下具有全局稳定性的分布式系统预测控制

本文针对一类由状态相互耦合的子系统组成的分布式系统, 提出了一种可以处理输入约束的保证稳定性的非 迭代协调分布式预测控制方法(distributed model predictive control, DMPC). 该方法中, 每个控制器在求解控制率时只与 其它控制器通信一次来满足系统对通信负荷限制; 同时, 通过优化全局性能指标来提高优化性能. 另外, 该方法在优化 问题中加入了一致性约束来限制关联子系统的估计状态与当前时刻更新的状态之间的偏差, 进而保证各子系统优化问 题初始可行时, 后续时刻相继可行. 在此基础上, 通过加入终端约束来保证闭环系统渐进稳定. 该方法能够在使用较少 的通信和计算负荷情况下, 提高系统优化性能. 即使对于强耦合系统同样能够保证优化问题的递推可行性和闭环系统的 渐进稳定性. 仿真结果验证了本文所提出方法的有效性.     

Event‐triggered control for a class of strict‐feedback nonlinear systems

This paper is concerned with the event‐triggered control problem for a class of strict feedback nonlinear networked systems. Different from the existing design methods, a novel user‐adjustable event‐triggered mechanism is first developed to determine the sampling state instants using the negative definite property of the derivatives of Lyapunov functions. Then, an event‐triggered control strategy is devised based on the sampled state vectors and backstepping techniques. It is proved that the proposed control scheme ensures the global convergence of the closed‐loop systems via Lyapunov analyses and the correlation criteria of real variable functions. Finally, two examples are performed to illustrate the effectiveness of the provided control approaches.     

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.     

A novel event‐triggered extended state observer for networked control systems subjected to external disturbances

In this paper, the event‐triggered‐based state estimation problem is investigated for a class of nonlinear networked control systems subjected to external disturbances. A novel event‐triggered extended state observer (ESO) is utilized to estimate the so‐called total disturbance, and an output predictor is adopted for the proposed ESO between two consecutive transmission instants. It is also worth pointing out that, in the newly proposed ESO, an event‐triggered mechanism is adopted to update the measurement signal so as to save the communication resource. The sufficient conditions are provided such that the estimation error dynamics is exponentially ultimately bounded. Furthermore, it is proven that the Zeno behavior does not exist for the event‐triggering rules. A number of numerical simulations are conducted to verify the validity of the theoretical results.     

Model Based Robust Control Law for Linear Event‐Triggered System

This paper proposes a framework to design an event‐triggered based robust control law for linear uncertain system. The robust control law is realized through both static and dynamic event‐triggering approach to reduce the computation and communication usages. Proposed control strategies ensure stability in the presence of bounded matched and mismatched system uncertainties. Derivation of event‐triggering rule with a non‐zero positive inter‐event time and corresponding stability criteria for uncertain event‐triggered system are the key contributions of this paper. The efficacy of proposed algorithm is carried out through a comparative study of simulation results.     

Fixed‐time sliding mode cooperative control for multiagent networks via event‐triggered strategy

In this article, the problem of event‐triggered‐based fixed‐time sliding mode cooperative control is addressed for a class of leader‐follower multiagent networks with bounded perturbation. First, a terminal integral sliding mode manifold with fast convergent speed is designed. Then, a distributed consensus tracking control strategy based on event‐triggered and sliding mode control is developed that guarantees the multiagent networks achieve consensus within a fixed time which is independent of initial states of agents in comparison with the finite‐time convergence. Furthermore, the update frequency of control law can be considerably reduced and Zeno behavior can be removed by utilizing the proposed event‐triggered control algorithm. Simulation examples are used to show the effectiveness of the new control protocol.     

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.     

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.     

Dynamic output‐feedback fuzzy MPC for Takagi‐Sugeno fuzzy systems under event‐triggering–based try‐once‐discard protocol

The fuzzy model predictive control (FMPC) problem is studied for a class of discrete‐time Takagi‐Sugeno (T‐S) fuzzy systems with hard constraints. In order to improve the network utilization as well as reduce the transmission burden and avoid data collisions, a novel event‐triggering–based try‐once‐discard (TOD) protocol is developed for networks between sensors and the controller. Moreover, due to practical difficulties in obtaining measurements, the dynamic output‐feedback method is introduced to replace the traditional state feedback method for addressing the FMPC problem. Our aim is to design a series of controllers in the framework of dynamic output‐feedback FMPC for T‐S fuzzy systems so as to find a good balance between the system performance and the time efficiency. Considering nonlinearities in the context of the T‐S fuzzy model, a “min‐max” strategy is put forward to formulate an online optimization problem over the infinite‐time horizon. Then, in light of the Lyapunov‐like function approach that fully involves the properties of the T‐S fuzzy model and the proposed protocol, sufficient conditions are derived to guarantee the input‐to‐state stability of the underlying system. In order to handle the side effects of the proposed event‐triggering–based TOD protocol, its impacts are fully taken into consideration by virtue of the S‐procedure technique and the quadratic boundedness methodology. Furthermore, a certain upper bound of the objective is provided to construct an auxiliary online problem for the solvability, and the corresponding algorithm is given to find the desired controllers. Finally, two numerical examples are used to demonstrate the validity of proposed methods.     

Data‐driven optimal event‐triggered consensus control for unknown nonlinear multiagent systems with control constraints

This paper considers optimal consensus control problem for unknown nonlinear multiagent systems (MASs) subjected to control constraints by utilizing event‐triggered adaptive dynamic programming (ETADP) technique. To deal with the control constraints, we introduce nonquadratic energy consumption functions into performance indices and formulate the Hamilton‐Jacobi‐Bellman (HJB) equations. Then, based on the Bellman's optimality principle, constrained optimal consensus control policies are designed from the HJB equations. In order to implement the ETADP algorithm, the critic networks and action networks are developed to approximate the value functions and consensus control policies respectively based on the measurable system data. Under the event‐triggered control framework, the weights of the critic networks and action networks are only updated at the triggering instants which are decided by the designed adaptive triggered conditions. The Lyapunov method is used to prove that the local neighbor consensus errors and the weight estimation errors of the critic networks and action networks are ultimately bounded. Finally, a numerical example is provided to show the effectiveness of the proposed ETADP method.     

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.     

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.