有向切换拓扑条件下考虑暂态响应的多智能体H_∞一致性控制

H_∞ Consensus Control of Multi-agent Systems with Transient Response under Directed Switching Topology

针对有向切换拓扑多智能体系统带领导者的一致性追踪问题,研究了H∞一致性控制方法。通过带有领导者的Laplacian矩阵,将带领导者的一致性追踪问题转化成低维系统的稳定性问题,并给出满足暂态性能指标的充分条件;利用Lyapunov函数法并结合线性矩阵不等式方法,对系统进行了稳定性分析,得到了分布式控制器的设计方法和平均驻留时间条件。该设计方法能够使系统受到随机外部扰动时,系统状态以较小的振荡快速趋于一致,满足暂态响应性能指标。分别在考虑暂态响应、不考虑暂态响应和不受外部扰动3种条件下,对多无人机系统进行了仿真。结果表明,考虑暂态响应的H∞一致性控制器能够使系统达成一致,比不考虑暂态响应所设计的控制器能更快地、更平稳地趋于一致,满足暂态性能指标。

The H∞ consensus control method is studied for consensus tracking of leader in multi-agent system under directed switching topology.The consensus tracking problem of leader is transformed into the stability problem of low-dimensional system by using Laplacian matrix with leader.The sufficient conditions satisfying the transient response index are given.Lyapunov function and linear matrix inequality are used to analyze the stability of the system,and the design method of distributed controller and the average dwell time condition are obtained.The proposed method can be used to make the states of the system tend to be identical rapidly with smaller oscillation when the system is affected by random external disturbance.The multi-UAV system was simulated with considering the transient response,and without considering the transient response and external disturbance.The results show that the H∞consensus controller considering the transient response can attain the consensus faster and more smoothly than the controller without considering the transient response,which meets the transient response performance index.