Online event-based adaptive critic design with experience replay to solve partially unknown multi-player nonzero-sum games

Abstract

This paper designs a novel online event-based near-optimal control scheme for multi-player nonzero-sum (NZS) games with partially unknown system dynamics. With the introduction of event-triggered mechanism (ETM), the repetitive computing burdens and communication loads of the signals are largely alleviated. Under the event-triggered mechanism, the framework of identifier-critic is structured to solve the coupled Hamilton–Jacobi equations (CHJEs) for NZS games. A feedforward neural network (FNN) is employed to construct an identifier to learn the unknown dynamics of the nonlinear system. The critic network for each player utilizes a modified tuning law, which is composed of three terms, to seek for the approximated optimal control schemes. Besides the conventional term derived from the gradient descent method, the second term derived from the experience replay (ER) technique utilizes the historical state data to update the critic network weight vector so as to remove the persistence of excitation (PE) condition. In addition, a novel term is added to stabilize the closed-loop systems. Owing to the stabilizing term, there is no need for the initial stabilizing control. In theory, the uniform ultimate boundedness (UUB) properties of the system states and the critic network weight errors are proved by utilizing Lyapunov theorem. Furthermore, the minimal intersample time is proved to be lower bounded with a positive constant which means that the Zeno behavior is excluded during the learning phases. Finally, we show the validity of the designed algorithm via simulating two examples.