Data-Driven Robust Tracking Control for Multi-Player Nonzero-Sum Games with Constrained Inputs

In this paper, the robust tracking control for unknown multi-player nonlinear systems with constrained inputs and uncertainties is studied by data-driven reinforcement learning scheme. In this study, the dependence on system dynamics is relaxed through the use of system input and state data. First of all, an augmented multi-player uncertain system is built by integrating the multi-player uncertain nonlinear systems and the given reference signal system. Afterwards, a non-quadratic cost function including the bounded functions, system states and all players control inputs is designed to handle the input constraints and uncertainties, and the robust tracking control problem is therefore converted into a constrained optimal control problem of the nominal system corresponding to the augmented multi-player uncertain system. Further, we rigorously analyze the equivalence of this conversion under specific conditions. The solution of the constrained optimal control problem can be obtained by solving a coupled Hamilton-Jacobi (HJ) equations. Then, on the basis of a given policy iteration scheme, a data-driven reinforcement learning scheme utilizing actor-critic neural networks is designed to solve the coupled HJ equation under the restriction of unavailable system dynamics. The weights of the neural network are learned using the least squares method from the input and state data collected from the system. Finally, a two-player uncertain nonlinear system and an induction heater circuit system are simulated to support the theoretical analysis.