Neural networks-based optimal tracking control for nonzero-sum games of multi-player continuous-time nonlinear systems via reinforcement learning

Abstract

In this paper, optimal tracking control for nonzero-sum games of multi-player continuous-time nonlinear systems is investigated by using a novel reinforcement learning scheme. Based on the multi-player nonlinear systems and reference signal, we firstly formulate the tracking problem by constructing an augmented multi-player nonlinear systems. The optimal tracking control problem for nonzero-sum games of original multi-player nonlinear systems is thus transformed into solving the coupled Hamilton–Jacobi equations of the augmented multi-player nonlinear systems. The novel neural networks (NNs) – based online reinforcement learning (RL) method can learn the solution to coupled Hamilton–Jacobi equations in a forward-in-time manner without requiring any value, policy iterations. In order to relax the dependence of the traditional reinforcement learning method on Persistence of Excitation (PE) conditions, historical data from a period of time has been collected to design NNs tuning laws. The drift dynamic of the augmented system is not required in our scheme. The Uniformly Ultimately Boundedness (UUB) of NNs weight errors and closed-loop augmented system states are rigorous proved. Numerical simulation examples are given to demonstrate the effectiveness of our proposed scheme.