An Adaptive Distributed Optimal Control Design for Nonlinear Continuous Leader–Follower Systems With Unknown Dynamics

ABSTRACT This paper investigates an adaptive distributed optimal control problem for a class of nonlinear continuous‐time leader–follower multi‐agent systems. A distributed performance index is first constructed by incorporating the leader–follower tracking error dynamics. Based on this formulation, the Hamilton–Jacobi–Bellman (HJB) equation associated with the distributed optimal control problem is derived, and the corresponding optimal control law is obtained. Then, by employing basis function approximation, an adaptive distributed optimal control algorithm is developed, which enables online adjustment of the control policy while ensuring the stability of the error system. The convergence properties of the proposed algorithm, along with the stability of the closed‐loop error dynamics, are rigorously analyzed using Lyapunov stability theory. Two numerical examples are then presented to verify the effectiveness and feasibility of the proposed approach.