Online Dual-Network-Based Adaptive Dynamic Programming for Solving Partially Unknown Multi-Player Non-Zero-Sum Games With Control Constraints

Abstract

In this article, a novel online method for multi-player non-zero-sum (NZS) differential games of nonlinear partially unknown continuous time (CT) systems with control constraints is developed based on neural networks (NN). The issue of multi-player NZS games with saturated actuator is elaborately analyzed and the unknown dynamics model is learned by applying identifier NN. Different from using the standard identifier-actor-critic framework of adaptive dynamic programming (ADP), the proposed method uses only identifier networks and critic networks for all the players to solve the coupled Hamilton-Jacobi (HJ) equations for multi-player NZS games, which could effectively simplify the algorithm and save computing resources. Moreover, a tuning law which utilizes the gradient descent method is designed for each critic network. Meanwhile, to remove the requirement for the initial stabilizing control, a novel stability term is designed to ensure the system stability during the training phase of the critic NN. By the means of Lyapunov approach, it is proven that the system states, the critic network weight estimation errors and the obtained control are all uniformly ultimately bounded (UUB). Finally, two numerical examples are simulated to illustrate the validity of the developed method for multi-player NZS games with control constraints.

Keywords

• Adaptive critic designs
• adaptive dynamic programming
• control constraints
• multi-player
• non-zero-sum games