Robust Optimal Consensus Control for Multi-Agent Systems with Disturbances

The purpose of this article is to develop optimal control strategies for discrete-time multi-agent systems (DT-MASs) with unknown disturbances, with the goal of enhancing their consensus performance and disturbance rejection capabilities. Complex flight conditions, such as the scenario of multi-unmanned aerial vehicle (multi-UAV) maintaining consensus under strong wind gusts, pose significant challenges for MAS control. To address these challenges, this article develops an optimal controller for UAV-based MASs with unknown disturbances to reach consensus. First, a novel improved nonlinear extended state observer (INESO) is designed to estimate disturbances in real time, accompanied by a corresponding disturbance compensation scheme. Subsequently, the consensus error systems and cost functions are established based on the disturbance-free DT-MASs. Building on this, a policy iterative algorithm based on a momentum-accelerated Actor–Critic network is proposed for the disturbance-free DT-MASs to synthesize an optimal consensus controller, whose integration with the disturbance compensation scheme yields an optimal disturbance rejection controller for the disturbance-affected DT-MASs to achieve consensus control. Comparative quantitative analysis demonstrates significant performance improvements over a standard gradient Actor–Critic network: the proposed approach reduces convergence time by 12.8%, improves steady-state position accuracy by 22.7%, enhances orientation accuracy by 42.1%, and reduces overshoot by 22.7%. Finally, numerical simulations confirm the efficacy and superiority of the method.