Optimal Consensus Control for Multi-Agent Systems With Unknown Dynamics and States of Leader: A Distributed KREM Learning Method

This brief addresses the optimal consensus control problem of a class of nonlinear leader-follower multi-agent systems (MASs), where the dynamics and states of the leader are unknown. A distributed Kreisselmeiers Regressor Extension and Mixing (KREM)-based control scheme is developed. Specifically, a distributed parameter estimation-based observer is first proposed, which can estimate not only the dynamic parameters but also the states of the leader for each agent. This allows to transform the optimal consensus control problem into an optimal tracking control problem of the leader's state. To solve the optimization problem, an only-critic learning structure is proposed, incorporating a novel adaptive tuning rule for the critic networks using the KREM technique to learn the unknown network weights. The system stability of the closed-loop MASs and the fast convergence of the distributed parameter estimation-based observer are conducted based on the Lyapunov stability theory. The effectiveness of the proposed control method is validated via a numerical simulation.