基于分布式PID控制的时变时延多智能体系统的一致性

研究普通阶多智能体系统存在时变时延条件下的一致性问题.首先,针对系统存在时变时延的情况,结合状态反馈与PID控制提出一种一致性协议;然后,将系统状态空间分解为一致子空间和一致补子空间,采用状态空间分解法将一致性问题转化为渐近稳定问题,给出系统实现一致的充分必要条件;并确定系统的一致性函数的显示表达式;最后,构造Lyapunov-Krasovskii泛函,基于线性矩阵不等式(LMI)给出控制参数的计算方法,采用可扩充性方法降低线性矩阵不等式的计算数量.仿真结果表明,系统的结构拓扑图存在全局可达节点时,系统在所提出的协议作用下通过计算合适的PID参数和控制参数可实现一致性,通过与纯比例控制的结果对比表明,所提出的协议能够消除系统稳态误差,使系统趋于一致.     

事件触发控制多智能体网络点对点一致性

针对具有领导层与跟随者层的多智能体网络点对点的一致性问题进行了研究。为了有效降低多智能体一致性控制协议的更新频率,同时为避免芝诺现象的产生,采用了周期采样与事件触发控制相结合的方案,实现了多智能体网络的点对点一致性。进一步,根据李雅普诺夫稳定性理论,通过建立线性矩阵不等式,给出了领导层与跟随者层网络达到点对点一致性的充分条件。最后,数值仿真进一步验证了理论结果的有效性。     

切换拓扑结构下多智能体系统的一致性研究

针对一类多智能体系统,研究了系统在切换拓扑结构下的一致性控制问题。假定系统拓扑结构的变化符合马尔可夫过程,设计与切换拓扑结构相关的一致性协议,利用线性矩阵不等式和随机稳定性理论,给出了多智能体系统满足一致性的充分条件,并通过数值仿真验证了所提控制方案的可行性和有效性。     

高阶时滞多智能体系统一致性控制

本文讨论了多输入网络化时滞多智能体系统的一致性问题.应用无向或有向图描述网络化系统的拓扑结构.多智能体的一致性收敛问题可以转化为线性时滞系统的稳定性问题.通过双线性矩阵不等式可以得到高阶多智能体系统时滞相依以及时滞独立的一致性准则.最后,举例一个无向拓扑结构的时滞多智能体来说明本文方法的有效性.     

2阶多智能体网络在切换拓扑下的群一致性

针对2阶多智能体网络的群一致性问题,提出了基于牵引控制方法的群一致性协议.考虑到网络模型具有切换拓扑结构,在模型中引入相应的虚拟领导者.对于网络中的每一个智能体,其一致性协议依赖于智能体邻居的状态及速度信息,并受到虚拟领导者的牵引控制;进一步地,来自虚拟领导者的牵引控制可以随时间发生变换.利用代数图论、线性矩阵不等式和李亚普诺夫稳定性理论,对网络进行群一致性分析,给出了切换拓扑下2阶多智能体网络达到群一致性的充分条件.最后,数值仿真验证了理论结果的有效性.     

一类多时变时延异质多智能体系统的组一致性

研究了一类由一阶和二阶智能体组成的异质多智能体系统的组一致性问题．首先,在多时变时延异质系统中设计了实现静态组一致的控制算法;其次,运用稳定性理论和线性矩阵不等式,分别给出了无时延、同时具有通信与输入时延的异质多智能体系统实现组一致性的充分条件;再次,通过求解一组可行的线性矩阵不等式,得到了输入时延的容许上界,并得出了通信时延与异质多智能体系统的组一致性无关的结论;最后,仿真结果验证了理论结果的有效性．     

网络攻击下双层结构多智能体系统一致性

研究了遭受网络攻击的双层结构多智能体系统的一致性问题。针对包含领导层和跟随者层的双层网络结构的多智能体系统,考虑了如下情况：领导层相邻智能体之间为友好合作关系,跟随者层相邻智能体之间既包含友好合作也包含对抗竞争关系,同时领导层与跟随者层中部分对应智能体之间存在牵制关系。分析了受网络攻击的领导层多智能体系统、跟随者层多智能体系统和双层网络结构多智能体系统的节点之间的一致性关系。基于线性矩阵不等式（LMI）、李雅普诺夫稳定性理论和图论等相关知识给出了领导层多智能体系统节点间实现一致,跟随者层多智能体系统节点间实现二分一致,以及双层结构的多智能体系统之间实现点对点二分一致的充分性判据。最后,给出了具体的数值仿真例子,实现了遭受网络攻击的双层结构多智能体系统的一致性,验证了所给出的判据的有效性。     

一类多时延异质多智能体系统的一致性

针对一类具有多变时延的一阶与二阶异构多智能体系统,研究了一致性问题。首先在异质系统中设计了一致性控制算法,通过将一阶、二阶系统重排和模型变换,使原系统分解成多个简单子系统;其次,利用李雅普洛夫稳定理论,分别在固定有向拓扑结构和切换有向拓扑结构下,以线性矩阵不等式的形式给出了系统达到平均一致的充分条件;再次,通过求解一组可行的线性矩阵不等式,得到了多时延的一个容许上界;然后讨论了时延导数和控制增益对时延容许上界的影响,得出了时延上界与时延导数和控制增益分别成正相关及反相关,时延导数未知时的时延上界相对较小的结论;最后的仿真结果表明了理论结果的有效性。     

基于观测器的线性时变时滞多智能体系统一致性

针对系统状态不可测和具有通信时延的线性多智能体系统,提出一种基于观测器的一致性控制算法.设计观测器用于解决智能体状态不可测的问题,在观测器的基础上,提出一种控制协议来实现带时变时延的线性多智能体系统一致性.利用模型转换的方式将原系统转换为新的模型系统,在此基础上,构造Lyapunov-Krasovskii函数并分析系统稳定性,通过求解线性矩阵不等式获取控制器系数矩阵.最后通过Matlab数值仿真验证所提出方法的有效性.     

重放攻击下多智能体系统H∞一致性PID控制

本文针对一类带有加性噪声和乘性噪声的离散多智能体系统,研究重放攻击下多智能体系统的H∞一致性比例–积分–微分(PID)控制问题.首先,根据智能体的测量输出设计状态观测器,对智能体的状态进行有效估计,观测器设计过程中考虑了系统测量输出从传感器传输到观测器过程中受到重放网络攻击的影响.然后,利用智能体与其邻居智能体的估计状态差设计PID控制器.利用李雅普诺夫稳定性理论和代数图论,证明在该控制策略下,多智能体系统在重放攻击存在的情况下达到预期的H∞性能指标.最后,利用线性矩阵不等式(LMI)方法求解观测器和控制器增益,利用数值仿真验证了所设计的观测器和PID控制器的有效性.     

Integral-based event-triggered control for multi-agent systems with general linear dynamics

ABSTRACT

This paper proposes an integral-based event-triggered control strategy to solve the consensus problem of multi-agent systems with general linear dynamics. We first consider the leader-following consensus problem where the communication topology has a directed spanning tree with the leader as the root. It is proved that under the proposed strategy leader-following consensus is guaranteed and the inter-event intervals are lower bounded by positive constants. Then, the leaderless consensus problem of multi-agent systems is investigated under directed topology. We show that consensus is achieved and no Zeno behaviour occurs. Simulation results verify the effectiveness of the obtained results.     

Consensus of multi-agent systems based on sampled-data control

This article studies the consensus problem in directed networks, assuming that each agent is with double-integrator dynamics and only obtains the measurements of its positions relative to its neighbours at sampling instants. We propose a protocol based on sampled-data control and derive an equivalent characterisation of the solvability of the consensus problem under this protocol. In virtue of this equivalent characterisation, we further consider two cases: fixed topology and switching topology. For the first case, we present a set of sampling periods and feedback coefficients which ensure that the protocol can solve a consensus problem. For the second case, we derive sufficient conditions for the protocol to solve a consensus problem under arbitrary switching signals and under a class of switching signals, respectively. Finally, simulations are provided to illustrate the effectiveness of the theoretical results.     

Consensus control of leader-following nonlinear multi-agent systems with distributed adaptive iterative learning control

This paper addresses the consensus problem of leader-following nonlinear multi-agent systems with iterative learning control. The assumption that only a small portion of following agents can receive the information of leader agent is considered. To approximate the nonlinear dynamics of a given system, the radial basis function neural network is introduced. Then, a distributed adaptive iterative learning control protocol with an auxiliary control term is designed, where the estimates of nonlinear dynamics are applied in control protocol design and three adaptive laws are presented. Furthermore, the convergence of the proposed control protocol is analysed by Lyapunov stability theory. Finally, a simulation example is provided to demonstrate the validity of theoretical results.     

Containment control of continuous-time multi-agent systems with general linear dynamics under time-varying communication topologies

This paper devotes itself to the containment tracking problem of general linear high-order multiagent systems (MASs) under time-varying communications. For general linear MASs with time-varying weightunbalanced digraph, the containment control problem is difficult and challenging, because the Lyapunov method is not an effective approach in this case. Under the assumption that the graph topology uniformly and jointly has a directed spanning forest, we show that when the exponentially unstable mode associated with each agent’s self-dynamics is weak enough, the followers can asymptotically tend to the dynamical convex hull spanned by the leaders, i.e. the containment can be achieved. Moreover, the least convergence rate is explicitly specified. Simulations are also provided to demonstrate the effectiveness of our result.

     

非连续混合自时延多智能体系统的饱和分布式控制

研究一类非连续混合自时延多智能体系统的全局指数一致性问题.首先,利用具有时变控制增益的分布式负反馈控制器实现智能体之间状态信息交互.考虑到实际系统运行环境与节省控制成本,增设外部饱和环节将控制信号幅值限制在一个合理的范围内,从而提出利用高斯误差函数以及微分中值定理来近似模拟饱和效应,以此降低控制信号的不平滑度.随后,利用Filippov微分包含理论和测度选择定理将多智能体系统的非线性动力学函数映射为Filippov集值函数,再通过广义Halanay不等式和Lyapunov稳定性定理给出该多智能体系统的指数一致性判定条件及其最大容许时延.最后,通过数值仿真验证所提出控制策略的有效性.     

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 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.     

分数阶非线性多智能体系统的一致性研究

研究固定拓扑结构下的分数阶非线性多智能体系统协调控制的动力学模型问题。由于实际多智能体系统中,系统的状态变量难以全部测量,为了克服这一困难,利用状态观测器对系统状态进行重构并基于重构状态进行状态反馈。利用分数阶Lyapunov稳定性理论,证明了当反馈增益矩阵满足一定的线性矩阵不等式（LMI）条件时,系统中的智能体最终趋于所给定的目标状态。最后利用分数阶微积分的预估-校正算法进行数值仿真验证了理论分析的有效性和可行性。     

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。