Time-Varying Formation <i>H</i>∞ Tracking Control and Optimization for Delayed Multi-Agent Systems With Exogenous Disturbances
Xiao‐Jie Peng, Yong He, Zhouzhou Liu, Le You, Hongyi Li
Abstract
This paper presents a novel time-varying formation (TVF) <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> tracking controller for multi-agent systems (MASs) under exogenous disturbances and time-varying delays. In order to address the issue that most of the existing formation controllers are designed under the predetermined small time delay, a formation controller which can tolerate a large delay upper bound is designed. This is achieved by employing the Lyapunov functional method. At the same time, in order to suppress the influence of exogenous disturbances on the formation process, the robustness of the formation controller is improved through optimizing the <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> performance index. To derive the gain matrix of the formation protocol, a mere two linear matrix inequalities (LMIs) need to be resolved. On this basis, differential evolution (DE) algorithm is employed to further adjust and optimize the parameters of the formation controller. Finally, it is proved that the obtained results can be directly applied to resolving the leader-follower consensus problem. Two simulation experiments are carried out to verify the superiority and effectiveness of the proposed scheme, where four followers achieve the <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> formation tracking following the leader. Note to Practitioners—The motivation of this article is to address the TVF <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> tracking control problem for MAS under limited network communication resources. The TVF model is extensively applied in the flocking control domain, such as robot formation control, spacecrafts formation flight and so on. In the engineering application scenarios, the communication between agents usually has the following problems: 1) The information interaction among the agents is often influenced by exogenous disturbances and time delays; 2) The existing formation tracking controllers are only suitable for handling predetermined small time delay. Thus, this paper presents a TVF <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> tracking controller with excellent robustness to deal with these problems, and this controller is optimized based on a DE algorithm.