不确定通信拓扑下多智能体系统鲁棒一致性

Robust consensus of multi-agent systems with uncertain communication topology

本文研究一类具有通信不确定的多智能体系统鲁棒一致性问题.本文提出基于标称通信拓扑有向生成树的线性变换方法,将线性多智能体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.首先采用基于有向生成树关联矩阵的线性变换,将多智能体系统网络的全局状态方程转化为一个降阶子系统;其次,将拉普拉斯矩阵的摄动部分进行分解,利用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.在此基础上将控制协议的参数设计转化为求解线性矩阵不等式的可行解.最后,通过数值仿真验证了所提出的一致性协议分析与设计方法的可行性和有效性.

Distributed robust consensus problem for a class of multi-agent systems(MASs)with uncertain communication topology is investigated.We propose a state linear transformation by constructing the incidence matrix of a directed spanning tree in the nominal communication topology,and transform the problem of state consensus of uncertain multiagent systems into the problem of robust partial asymptotic stability of corresponding linear systems.Firstly,we use the linear transformation constructed from a directed spanning tree to transform the closed uncertain MAS into a reduced-order system.Secondly,by using decomposition of perturbation Laplacian matrix,we design a quadratic stabilization robust controller for the reduced-order system,and derive a sufficient condition guaranteeing all agents’s states to achieve asymptotic consensus.Based on the condition,the design problem of protocol parameters is converted into finding the feasible solution of linear matrix inequalities.Finally,the effectiveness and feasibility of the proposed approach is verified by simulation examples.