Leader-following Consensus of Nonlinear Delayed Multi-agent Systems with Randomly Occurring Uncertainties and Stochastic Disturbances under Impulsive Control Input

This paper investigates the leader-following consensus problem for a class of nonlinear delayed multiagent systems with randomly occurring uncertainties and stochastic disturbances under impulsive control inputs. For this class of multi-agent system, we present a novel impulsive control protocol which can effectively reduce the control cost and is easy to implement. Two consensus criteria are derived for ensuring global exponential consensus of nonlinear delayed multi-agent systems under non-uniformly distributed impulsive control signals based on comparison principle and average impulsive interval. Compared with the consensus criteria which are derived by the upper bound or lower bound of the impulse intervals in existing results, the obtained criteria are proved to be easier to be satisfied. Simulation results illustrate the effectiveness of the theoretical results.     

Quantised consensus of multi-agent systems with nonlinear dynamics

This paper studies the consensus problem of first-order and second-order multi-agent systems with nonlinear dynamics and quantised interactions. Continuous-time and impulsive control inputs are designed for the multi-agent systems on the logarithmic quantised relative state measurements of agents, respectively. By using nonsmooth analysis tools, we get some sufficient conditions for the consensus of multi-agent systems under the continuous-time inputs. Compared with continuous-time control inputs, impulsive distributed control inputs just use the state variables of the systems at discrete-time instances. Based on impulsive control theory, we prove that the multi-agent systems can reach consensus by choosing proper control gains and impulsive intervals. The simulation results are given to verify the effectiveness of the theoretical results.     

Consensus of multi-agent linear dynamic systems via impulsive control protocols

In this article, we introduce impulsive control protocols for multi-agent linear dynamic systems. First, an impulsive control protocol is designed for network with fixed topology based on the local information of agents. Then sufficient conditions are given to guarantee the consensus of the multi-agent linear dynamic systems by the theory of impulsive systems. Furthermore, how to select the discrete instants and impulsive matrices is discussed. The case that the topologies of networks are switching is also considered. Numerical simulations show the effectiveness of our theoretical results.     

Consensus of second-order multi-agent systems via impulsive control using sampled hetero-information

In this paper, the consensus problem for second-order multi-agent systems using impulsive control with sampled hetero-information is investigated. Necessary and sufficient conditions for sampling interval to achieve consensus for the second-order multi-agent systems are obtained. Analysis for the upper bound of sampling interval, convergence performance, and communication cost of the proposed control protocols are also discussed. Some numerical examples are given to demonstrate the effectiveness of the proposed control protocols.     

Impulsive observer-based consensus control for multi-agent systems with time delay

The paper deals with the distributed consensus problem of a class of general linear multi-agent systems with time delay. Assuming that the state of the multi-agent system cannot be measured and the output of the multi-agent system is measured discontinuously, a novel impulsive observer is constructed. Based on the impulsive observer, a distributed consensus protocol is proposed for the multi-agent system with a directed communication topology. In view of the hybrid characteristic of the multi-agent system with the impulsive observer, a novel type of piecewise Lyapunov functional which can overcome the jump phenomena at impulsive times is introduced. Based on this, some sufficient conditions in terms of linear matrix inequalities are presented such that the consensus of the multi-agent system can be achieved with an exponential convergence rate. A numerical example under two cases is given to show the effectiveness of the theoretical results.     

具有引导者的多智能体网络系统的脉冲一致性

多智能体网络系统的协调与控制在工程领域中有着重要的作用. 本文给出了具有引导者的一阶多智能体网络系统的动力学模型. 模型中, 假设网络系统中仅有一个智能体在一系列离散时刻基于自身及引导者的信息, 以脉冲跳跃方式改变自身的状态.应用矩阵理论、数值分析理论、脉冲微分方程等理论给出了网络系统达到一致的一个充分条件. 计算机仿真实验验证了算法的正确性和有效性,展示了系统的一致收敛速度与脉冲间隔、脉冲强度之间的关系.     

Impulsive consensus seeking in directed networks of multi-agent systems with communication time delays

In this article, we consider average consensus problem in directed delayed networked multi-agent systems having impulsive effects with fixed topology and stochastic switching topology. A simple impulsive consensus protocol for such networks is proposed, and some generic criteria for solving the average consensus problem are analytically derived. It is shown that a directed delayed networked multi-agent system can achieve average consensus globally exponentially with suitable impulsive gain and impulsive interval. Subsequently, two typical illustrative examples, along with computer simulation results, are provided to visualise the effectiveness and feasibility of our theoretical results.     

脉冲式事件触发控制的时变多个体系统一致性

针对时变拓扑连接环境下的时变多个体系统的一致性问题,提出基于事件触发的脉冲控制协议。在该协议里对于每个个体,只有当相关状态误差超过阈值时才会更新控制器,同时控制输入将仅在事件触发时刻执行,且个体间不需要持续通信。该协议将大幅节约系统实现一致性的通信和控制成本。使用代数图论、李雅普诺夫稳定性和脉冲微分方程等数学理论分析和推导具有时变特性的多个体系统在事件触发脉冲控制下达到一致性的充分条件,同时理论证明事件触发的时间序列不存在芝诺行为。最后,数值仿真验证了所得到的理论结论的有效性。     

Consensus of Delayed Multi‐agent Systems via Intermittent Impulsive Control

A novel intermittent impulsive scheme is presented to realize consensus of multi‐agent systems with time‐varying delay in this paper because intermittent impulsive control may break through the limitation of upper bound of impulsive intervals in general impulsive control in our consensus scheme. Instead of activating all the time, we introduce the intermittent impulsive control approach into the delayed multi‐agent systems where the impulsive controller is only functioned in the control windows. Based on the algebraic graph theory, the Lyapunov stability theory, and Halanay inequality matrix theory, some adequate conditions are proposed to guarantee the consensus of delayed multi‐agent systems via pinning intermittent impulsive control. Simulation results are provided ultimately to verify the validity of the proposed control mechanism.     

事件触发脉冲控制多智能体系统的安全一致

对多智能体系统在欺骗攻击下的均方有界一致性问题进行研究,并在固定时间脉冲控制的基础上结合事件触发控制,设计了一种具有触发时间上界的事件触发脉冲控制方法。利用李雅普诺夫稳定性理论、图论和线性矩阵不等式技巧,得到了多智能体系统的均方有界一致的充分条件,并验证了所提出的事件触发脉冲控制方法可以自动调节脉冲时间间隔,快速达到安全一致。最后,数值仿真结果进一步验证了理论研究结果的有效性。     

Guaranteed performance consensus in second-order multi-agent systems with hybrid impulsive control

This paper studies the problem of guaranteed performance consensus in second-order multi-agent systems. Taking advantage of impulsive control, a hybrid cooperative control is presented, and an index function is introduced to assess the performance of agents. It is shown that by synthesizing the coupling weights and the average impulsive intermittence, multi-agent systems can achieve guaranteed performance consensus. A numerical example is given to illustrate the theoretical results.     

一类脉冲随机系统的有限时间有界性分析与H∞控制

本文研究一类线性脉冲随机系统的有限时间有界性及H_∞控制问题.首先,利用Lyapunov函数和平均脉冲区间条件,建立了系统有限时间均方有界定理;其次,基于H_∞控制理论,获得了保证系统有限时间有界且满足一定的H_∞性能指标的判据;再次,针对有限时间H_∞控制问题,给出了状态反馈控制器存在的充分条件.最后,用一个数值例子表明了理论结果的有效性.     

Consensus of linear conformable fractional order multi-agent systems with impulsive control protocols

In this article, we study the impulsive consensus problem of linear multi-agent systems composed of α-order conformable differential equations (α ∈ (0, 1]). Two cases of fixed and switching interaction networks are considered, respectively. Impulsive protocol of each agent is introduced based on the local information of the interaction networks. Firstly, we derive the analytic solution of the general linear conformable systems with impulses. Secondly, two sufficient criterions are presented to guarantee the convergence of the consistent state for all the agents by using matrix theory, graph theory, and impulsive control theory. Finally, three numerical simulations are provided to demonstrate the obtained theoretical results and to compare the convergence rates of the systems with distinct orders.     

Coordination of fractional-order nonlinear multi-agent systems via distributed impulsive control

The coordination of fractional-order nonlinear multi-agent systems via distributed impulsive control method is studied in this paper. Based on the theory of impulsive differential equations, algebraic graph theory, Lyapunov stability theory and Mittag-Leffler function, two novel sufficient conditions for achieving the cooperative control of a class of fractional-order nonlinear multi-agent systems are derived. Finally, two numerical simulations are verified to illustrate the effectiveness and feasibility of the proposed method.     

Second-order consensus of multi-agent systems in the cooperation–competition network with switching topologies: A time-delayed impulsive control approach

This paper investigates the consensus problem of second-order multi-agent systems with switching topologies by designing a time-delayed impulsive consensus control scheme. All the agents are governed by the same nonlinear intrinsic dynamics. In this study, agents can cooperate or compete with each other, i.e., the elements in the weight matrix of the coupling graph can be either positive or negative. By establishing a comparison system, a new comparison principle method is successfully applied to study such consensus problem. Then, several effective sufficient conditions are attained without assuming that the interaction topology is strongly connected or contains a directed spanning tree. Meanwhile, the exponential consensus rate is also obtained. Finally, simulation results are presented to validate the effectiveness of the theoretical analysis.     

Exponential Stability Analysis for Stochastic Delayed Differential Systems with Impulsive Effects: Average Impulsive Interval Approach

This paper is concerned with the exponential stability analysis of stochastic delayed systems with impulsive effects. By using the average impulsive interval approach, and together with comparison lemma and Razumikhin techniques, sufficient conditions ensuring the moment exponential stability of the systems under consideration are established. A stability criterion for non‐delayed stochastic systems with impulses is also derived as a corollary. Compared with the existing stability results in the literature, which are usually based on the supremum or infimum of impulsive intervals, the results reported in this paper are less conservative. Two illustrative examples are provided to validate the effectiveness and advantages of our theoretical results.     

Finite-time annular domain stability of Itô stochastic impulsive systems with markovian jumping under asynchronous switching

ABSTRACT

This study examines the finite time annular domain stability (FTADS) and stabilisation of a class of Itô stochastic impulsive systems with asynchronous switching controller. The asynchronous switching means that the controller switching does not accurately coincide with system switching in delayed time interval. The design of the controller depends on the observed jumping parameters, which cannot be precisely measured in real-time because of switching delay. Our results apply to cases where some subsystems of the switched systems are not necessarily stable under the influence of input delay. When the subsystem is stable in the synchronous switching interval and unstable in the asynchronous case, a compromise among the average impulsive interval, the upper bound of delay, and the decay/increasing rate of Lyapunov function in the synchronous/asynchronous switching interval respectively is given. By the mode-dependent parameter approach (MDPA) and allowing the increase of the impulses on all the switching times, the extended FTADS criteria for Itô stochastic impulsive systems in generally nonlinear setting are derived first. Then, we focus on the case when the system in both synchronous and asynchronous switching intervals are unstable. By reaching a tradeoff among average impulsive interval, the upper bound of delay, the magnitude of impulses and the difference between the increasing rate of Lyapunov function in the synchronous and asynchronous switching interval, new sufficient conditions for existence of the state feedback controller are also developed by MDPA. In addition, we consider the effect of different impulsive strengths (harmful and beneficial impulses) and obtained less conservative results because the Lyapunov function may be non-decreasing during switching interval. Moreover, we extend the conclusion from nonlinear stochastic impulsive switching systems to linear case. Finally, we present two examples to illustrate the effectiveness of the results obtained in this study.     

A new unified input‐to‐state stability criterion for impulsive stochastic delay systems with Markovian switching

In this paper, the problems of the input‐to‐state stability (ISS), the integral input‐to‐state stability (iISS), the stochastic input‐to‐state stability (SISS) and the e^λt(λ>0)‐weighted input‐to‐state stability (e^λt‐ISS) are investigated for nonlinear time‐varying impulsive stochastic delay systems with Markovian switching. We propose one unified criterion for the stabilizing impulse and the destabilizing impulse to guarantee the ISS, iISS, SISS and e^λt‐ISS for such systems. We verify that when the upper bound of the average impulsive interval is given, the stabilizing impulsive effect can stabilize the systems without ISS. We also show that the destabilizing impulsive signal with a given lower bound of the average impulsive interval can preserve the ISS of the systems. In addition, one criterion for guaranteeing the ISS of nonlinear time‐varying stochastic hybrid systems under no impulsive effect is derived. Two examples including one coupled dynamic systems model subject to external random perturbation of the continuous input and impulsive input disturbances are provided to illustrate the effectiveness of the theoretic results developed.     

Leaderless and leader‐following fixed‐time consensus for multiagent systems via impulsive control

This article addresses the leaderless fixed‐time consensus (LLFTC) and leader‐following fixed‐time consensus (LFFTC) problems for multiagent systems (MASs) via impulsive control. First, a novel fixed‐time stability for impulsive dynamical system is developed. Then the novel fixed‐time impulsive control protocols are designed to achieve leaderless and leader‐following consensus for MASs. Based on the impulsive control theory, fixed‐time stability theory and algebraic graph theory, some sufficient conditions are derived for each agent to achieve LLFTC and LFFTC under the proposed control protocols. Finally, numerical simulations are put forward to validate the theoretical results.     

Synchronizing chaotic systems with parametric uncertainty via a novel adaptive impulsive observer

This paper proposes a new class of observers, called adaptive impulsive observers. These observers are capable of estimating the states and unknown parameters of an uncertain system using the output of the system at discrete jump times only. Through a proposed theorem, the stability of the states estimation error system is proved and an upper bound on the maximum possible impulses (jumps) interval is given. Due to these advantages, the proposed adaptive impulsive observer is used in a chaotic systems synchronization scheme. The presented simulation results show the effectiveness of the proposed observer even when the coupling signal is scalar. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society