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.     

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.     

The consensus of multi-agent systems with uncertainties and randomly occurring nonlinearities via impulsive control

In many real-world multi-agent systems, the intrinsic dynamics of the agents are usually dynamic rather than static as the environmental uncertainty and the additive exogenous disturbance input. This paper aims at investigating the consensus problem of multi-agent systems with uncertainties and randomly occurring nonlinearities (RONs). Consider the robust and lost-cost, an effective impulsive control protocol is designed. Based on the Lyapunov stability theory and hybrid control theory, sufficient conditions are obtained to ensure consensus of multi-agent systems. Furthermore, both mathematical investigations and numerical simulations are presented to demonstrate the effectiveness of the proposed approaches.     

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.     

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.     

Leader-following consensus of nonlinear multi-agent systems with randomly occurring uncertainties and stochastic disturbances under impulsive control input

This paper focuses on the leader-following consensus problem of nonlinear multi-agent systems with randomly occurring uncertainties and stochastic disturbances under impulsive control input. Based on the average impulsive interval, a unified consensus criterion is derived for multi-agent systems. On the other hand, our consensus criterion is applicable to impulsive control sequences in which the lower bound of impulsive interval is allowed to be arbitrarily small and the upper bound of impulsive interval is allowed to be big enough. The proposed consensus criterion is theoretically and numerically proved to be less conservative than existing results. Two numerical simulations illustrate the effectiveness of theoretical results.     

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.     

网络攻击下多智能体系统动态事件触发一致性

研究网络攻击下一般线性多智能体系统的动态事件触发一致性问题.考虑多智能体系统在受到网络攻击后,被攻击节点的状态会改变,导致与其相应的连接无法工作,设计修复策略恢复被攻击节点及其相应的连接,给出网络攻击下分布式事件触发控制协议.在静态事件触发机制基础上,通过引入动态阈值参数,提出动态事件触发机制.进一步,利用图论、线性矩阵不等式和李雅普诺夫函数方法,给出网络攻击下实现多智能体系统一致性的充分条件,并证明在所提出的动态事件触发条件下,能够有效避免芝诺行为.最后,通过仿真例子来验证理论结果的有效性.     

Containment control of switched multi-agent systems

In this paper, we consider the containment control problem for the switched multi-agent system which is composed of continuous-time and discrete-time subsystems. Continuous-time protocol based on the relative state measurements of agents are designed for the switched multi-agent system with multiple stationary and dynamic leaders, respectively. By using graph theory and matrix theory, some necessary and sufficient conditions are obtained for solving the containment control problem under arbitrary switching. When the leaders are dynamic, impulsive protocol are also proposed for the switched multi-agent system. The simulation results are given to verify the effectiveness of the 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.     

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.     

Cooperative output regulation of multi-agent systems with switched leader dynamics

In this paper, the cooperative output regulation problem for heterogeneous multi-agent systems is addressed by considering a switched leader dynamics. The switched leader dynamics consists of multiple linear models and a switching rule governing the switches among them. A switched leader is capable of generating various sophisticated reference signals for more complicated multi-agent coordination tasks. A novel distributed hybrid impulsive switching control scheme is proposed to achieve cooperative output regulation. Distributed switching stability is established using the average dwell-time technique with multiple Lyapunov functions. Moreover, the associated distributed control synthesis conditions are formulated in terms of linear matrix inequalities plus linear matrix equations. As a result, both switching rules for the leader and distributed switching protocols for the followers can be jointly synthesised via efficient semi-definite programming. An example has been used to demonstrate the effectiveness of the proposed approach.     

Cooperative output regulation with application to multi-agent consensus under switching network

In this paper, we consider the cooperative output regulation of linear multi-agent systems under switching network. The problem can be viewed as a generalization of the leader-following consensus problem of multi-agent systems. Due to the limited information exchanges of different subsystems, the problem cannot be solved by the decentralized approach and is not allowed to be solved by the centralized control. By devising a distributed observer network, we can solve the problem by both dynamic state feedback control and dynamic measurement output feedback control. As an application of our main result, we show that a special case of our results leads to the solution of the leader-following consensus problem of linear multi-agent systems.     

Composite nonlinear feedback control for cooperative output regulation of linear multi-agent systems by a distributed dynamic compensator

This paper investigates the cooperative output regulation problem of linear multi-agent systems with a linear exogenous system (exo-system). The network topology is described by a directed graph which contains a directed spanning tree with the exo-system as the root. Aiming at improving the transient performance of the multi-agent systems, a dynamic control law is developed by the composite nonlinear feedback (CNF) control technique. In particular, a distributed dynamic compensator independent of the interaction on the compensator states of agents among the network, is adopted. The solvability condition for the cooperative output regulation problem is obtained using the small-gain theory, which will not be destroyed by adding the nonlinear feedback part of the CNF control law. It is also shown that in the case with the exo-system not diverging exponentially, the small-gain condition can be guaranteed using the low-gain design. Finally, simulation results illustrate that the proposed CNF control law improves the transient performance for the cooperative output regulation of linear multi-agent systems.     

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.     

脉冲切换系统的鲁棒H∞动态输出反馈控制

考虑了脉冲切换系统的鲁棒H∞控制问题.该系统的状态矩阵和控制矩阵都有不确定性和扰动.利用线性矩阵不等式(LMI)、H∞控制理论、Lyapunov函数和变量替换方法,对这类系统给出了鲁棒稳定且具有γ鲁棒性能的充分条件.然后,使用MATLAB软件设计出H∞鲁棒动态输出反馈控制器和脉冲控制矩阵.最后通过一个仿真算例验证了文中结论的有效性.     

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。     

Distributed event-triggered output regulation of multi-agent systems

Motivated by the future use of embedded microprocessors with limited resources and limited computational resources, the distributed output regulation with event-driven strategies problem of linear multi-agent systems is considered in this paper. The main task is to design distributed feedback by employing event-triggered technique for multi-agent systems such that all agents can track an active leader, and/or distributed disturbance rejection. Both leader and disturbance are generated by some external system (exosystem). Both distributed static and dynamic feedback with event-triggered strategy are constructed here. Then, the input-to-state stability of the closed-loop multi-agent system is analysed. Finally, a numerical example is given to validate the proposed control.     

Distributed output regulation for linear multi-agent systems with communication delays

In this paper, a distributed output regulation approach is presented for the cooperative control of linear multi-agent systems in the presence of communication delays. Both dynamic state and output feedback control laws are designed for achieving the property of output regulation. Sufficient conditions for the existence of these control laws are provided in terms of linear matrix inequalities. Simulation results are given to support the efficiency of the proposed distributed output regulation approach.     

On controllability and observability for a class of impulsive systems

Many dynamic systems in physics, chemistry, biology, engineering, and information science have impulsive dynamical behaviors due to abrupt jumps at certain instants during the dynamical processes. These complex dynamic behaviors can be modeled by impulsive differential systems. This paper studies the controllability and observability for a class of time-varying impulsive control systems. Several sufficient and necessary conditions for state controllability and state observability of such systems are established and the corresponding criteria for time-invariant impulsive control systems are also obtained. Meanwhile, several new results associated with variation of parameters for time-varying impulsive control systems are derived.