Self-Triggered Min-Max DMPC for Asynchronous Multiagent Systems With Communication Delays

This article studies the formation stabilization problem of asynchronous nonlinear multiagent systems (MAS) subject to parametric uncertainties, external disturbances, and bounded time-varying communication delays. A self-triggered min-max distributed model predictive control (DMPC) approach is proposed to address this problem. At triggering instants, each agent solves a local min-max optimization problem based on local system states and predicted states of neighbors, determines its next triggering instant, and broadcasts its predicted state trajectory to the neighbors. As a result, the communication load is greatly alleviated while retaining robustness and comparable control performance compared to periodic DMPC algorithms. In order to handle time-varying delays, a novel consistency constraint is incorporated into each local optimization problem to restrict the deviation between the newest predicted states and previously broadcasted predicted states. Consequently, each agent can utilize previously predicted states of its neighbors to achieve cooperation in the presence of the asynchronous communication and time-varying delays. The proposed algorithm's recursive feasibility and MAS's closed-loop stability at triggering instants are proven. Finally, numerical simulations are conducted to verify the theoretical results.