Adaptive optimal tracking controls of unknown multi-input systems based on nonzero-sum game theory

This paper focuses on the optimal tracking control problem (OTCP) for the unknown multi-input system by using a reinforcement learning (RL) scheme and nonzero-sum (NZS) game theory. First, a generic method for the OTCP of multi-input systems is formulated with steady-state controls and optimal feedback controls based on the NZS game theory. Then a three-layer neural network (NN) identifier is introduced to approximate the unknown system, and the input dynamics are obtained by using the derivative of the identifier. To transform the OTCP into a regulation optimal problem, an augmentation of the multi-input system is constructed by using the tracking error and the commanded trajectory. Moreover, we use an NN-based RL method to online learn the optimal value functions of all the inputs, which are then directly used to calculate the optimal tracking controls. All the NN weights are tuned synchronously online with a newly introduced adaptation based on the estimation error. The convergence of the NN weights and the stability of the closed-loop system are analyzed. Finally, a two-motor driven servo system and another nonlinear system are presented to illustrate the feasibility of the algorithm for both linear and nonlinear multi-input systems.