Time-Varying Trajectory Tracking Formation H∞ Control for Multiagent Systems With Communication Delays and External Disturbances
研究了有向通信拓扑下，存在通信时延和外部干扰时，多智能体系统实现时变编队并跟踪给定编队中心轨迹的H∞控制问题，提出了分布式控制协议并给出了线性矩阵不等式形式的充分条件。
Time-varying formation (TVF) and trajectory tracking <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> control problem of multiagent systems (MASs) subject to communication delays and external disturbances under the directed communication topology is studied. This article’s objective is for all agents to attain the desired TVF and track the pregiven formation center trajectory simultaneously. First, a distributed TVF and trajectory tracking control protocol employing neighborhood interaction information is developed in the presence of communication delays. Second, since the Laplacian matrix of a graph can be decomposed into the product of two specific matrices, the TVF and trajectory tracking <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> control problem is converted into the lower dimension asymptotic stability problem of a closed-loop system by applying an appropriate variable conversion. Third, a Lyapunov–Krasovskii functional is constructed to analyze the stability of MASs. Sufficient conditions are obtained in the form of linear matrix inequalities (LMIs) to ensure the completion of the TVF and formation center trajectory tracking of MASs. In the meantime, the maximum allowable communication delay can be calculated by the LMIs. Finally, the results of numerical simulations are presented to verify the validity of the approach this article proposes.