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.

Consensus of multi-agent systems with time-varying delays based on distributed PID control

This paper investigates the consensus problem of a general linear multi-agent systems(MAS) with variable time delays. Firstly, a protocol based on the combination of the state feedback and the distributed PID control law is proposed. Then, the state space of the system is decomposed into a consensus subspace and a consensus complement subspace, on this basis, the sufficient and necessary condition of the consensus of the MAS is given by using the state space decomposition approach. The explicit form of the consensus functioin is given. Finally, a new Lyapunov-Krasovskii functional is constructed, and the parameters of the control system are given based on the linear matrix inequations(LMIs). An extented method is introduced to decrease the computation of the LMIs. The simulation results show that, under the condition that the topology has a global reachable node, through calculating proper PID parameters and control parameters, the proposed protocol can overcome the delay to some extent, so that the MAS can achieve consensus and have strong robustness. Through comparing with the pure propotional control, the proposed protocol can eliminate the steady-state error finally and make the system achieve consensus.