模型不确定多智能体系统的鲁棒一致性控制

Robust consensus control of multi-agent systems with model uncertainties

针对模型不确定性多智能体系统的分布式鲁棒一致问题,提出了鲁棒部分变元稳定性方法,将连续时间多智能体不确定系统的状态一致性问题转化为相应线性系统的鲁棒部分变元渐近稳定性问题.首先根据有向图生成树建立关联矩阵,对原来的不确定系统进行线性变换,实现结构分解.其次根据得到的降阶系统设计鲁棒二次镇定控制器,推导出所有智能体状态达到渐近一致的充分条件,将控制协议的设计最终转化成求解线性矩阵不等式可行解的问题,使得所有的智能体能够在所设计的控制协议下不仅能保证不确定性闭环系统是渐进稳定的,而且实现了多智能体系统状态的一致性.最后通过数值仿真验证了所提出的一致性协议的可行性和有效性.

To solve the distributed robust consensus problem for the continuous time linear multi-agent systems(MASs)with model uncertainties,an approach of robust partial stability was proposed,which transformed the problem of state consensus of uncertain multi-agent systems into the problem of robust partial asymptotic stability of corresponding linear systems.Firstly,an incidence matrix was established based on a spanning tree of directed graph,which can make the structural decomposition of the original uncertain system.Secondly,based on the reduced-order system,a robust controller of quadratic stabilization was designed,and a sufficient condition guaranteeing multi-agent systems states achieve uniformly asymptotically stable was derived.Eventually,the problem of control protocol design was converted into finding the feasible solution of linear matrix inequality.It enables all agents to not only ensure that the uncertainty closed-loop system is progressively stable under the designed control protocol,but also realize the consistency of the state of the multi-agent system.Finally,the effectiveness and feasibility of the proposed approach was verified by simulation examples.