Virtual leader-follower synchronization controller design for distributed parameter multi-agent systems with time-varying disturbances

This paper addresses the virtual leader-follower synchronization control problem for a class of distributed parameter multi-agent systems, and all agents are governed by the heat equations with structured time-varying perturbations and time-varying disturbances, communicating through an undirected and connected static topology. A stable heat equation is designed as the virtual leader, and all agents as followers need to track the leader, such that the multi-agent systems can achieve a consensus. The design of the controller is split into two parts: one is design infinite dimension observers to estimate the total disturbances online by using the estimation/cancellation strategy in active disturbance rejection control (ADRC), the other is that the adaptive proportional differential (PD) synchronous controller determined by the Lyapunov functional is proposed to ensure all agent's states and the leader's state reach a consensus. The linear local interaction protocol realizes the synchronization of multi agent system, and the adaptive PD control accelerates the subsystem to follow the virtual leader. The well-posedness of the closed-loop system is analyzed and proved. Simulation results illustrate the effectiveness of the proposed method. (c) 2021 Elsevier B.V. All rights reserved.