Optimal consensus control for input-delay nonlinear multi-agent systems with input saturation utilizing synchronous integral reinforcement learning

This paper addresses the optimal consensus control (OCC) problem for nonlinear multi-agent systems (MASs) with input saturation and input delay based on synchronous integral reinforcement learning (IRL). First, the model reduction method is employed to convert the original system into a delay-free model, subsequently, the new performance index functions are introduced, based on which an equivalence relationship is established between the performance indices of two MASs. Through this equivalence, the challenging problem of OCC for MAS with input delays can be successfully transformed into that of delay-free MAS. Second, the Hamilton–Jacobi–Bellman (HJB) equations with non-quadratic functions are established. It is further demonstrated that the solutions to these coupled HJB equations not only are optimal control policies but also constitute Nash equilibrium. Third, the online synchronized IRL algorithm is utilized to design the optimal controllers, constructing actor–critic (A–C) neural networks (NNs) structure to approximate the control policies and value function, respectively. The weights of both NNs are updated synchronously. Finally, the simulation example shows the effectiveness of the method.