具有马尔可夫切换的不确定离散多智能体系统的鲁棒最优一致性

Robust Optimal Consensus of Uncertain Discrete-time Multi-agent Systems under Markovian swicthing topology

针对不确定二阶离散多智能体系统,研究了其在马尔可夫切换拓扑结构下的鲁棒最优一致性问题.基于智能体的邻居信息设计了控制协议,使得多智能体系统在满足保代价性能指标下最终趋于一致.利用线性矩阵不等式理论以及Lyapunov方法,得到了系统实现均方一致所需要的条件,并且证明了所有智能体的状态最终收敛到其初始状态平均值.进一步,设计了一个保代价性能指标,研究了系统在满足该性能指标下的一致性问题,得到了系统实现均方一致的条件.最后,通过数值仿真实例验证了所得结论的有效性.

This paper deals with robust optimal consensus problem of uncertain second- order discrete-time multi-agent systems under Markovian switching topologies. A control protocol is designed based on the information of agent and its neighbors, which makes the systems realize consensus. By using the methods of linear matrix inequalities and Lyapunov function, we obtained a sufficient condition of the mean square consensus and proved that the states of all agents converge to the initial states average. Further, a guaranteed cost performance index is designed to study a condition of the mean square consensus under it. Finally, numerical simulations are given to illustrate the effectiveness of results.