PDE‐based event‐triggered containment control of multi‐agent systems with input delay under spatial boundary communication
Hao Zhang, Jiachen Li, Tong Wang, Qingshuang Zeng, Huaicheng Yan · International Journal of Robust and Nonlinear Control · 2022
Abstract This article studies the containment control problem for multi‐agent systems with input delay under spatial boundary communication by employing an event‐based approach. Firstly, the collective dynamics of multi‐agent systems are described as parabolic partial differential equations (PDEs). Applying the integral transformation method developed in PDEs, the delayed parabolic PDEs are transformed into a series of new coupled PDE‐PDE systems. Then, by taking the spatial boundary communication scheme into account and using the local boundary information, two boundary containment control protocols together with a dynamic event‐triggered scheme (DETS) are designed, such that the states of all followers converge to a convex hull formed by multiple leader agents with and without input delay. The optimal protocols are given by minimizing the 2‐norm of the designed control gain matrix, and the exclusion of the Zeno behavior is analyzed. Finally, a numerical simulation example is provided to support the main results.