Online Nash-optimization tracking control of multi-motor driven load system with simplified RL scheme

Although the optimal tracking control problem (OTCP) has been addressed recently, only the single-input system is considered in the recent literature. In this paper, the OTCP of unknown multi-motor driven load systems (MMDLS) is addressed based on a simplified reinforcement learning (RL) structure, where all the motor inputs with different dynamics will be obtained as a Nash equilibrium. Thus, the performance indexes associated with each input can be optimized as an outcome of a Nash equilibrium. Firstly, we use an identifier to reconstruct MMDLS dynamics, such that the accurate model required in the general control design is avoided. We use the identified dynamics to drive Nash-optimization inputs, which include the steady-state controls and the RL-based controls. The steady-state controls are designed with the identified system model. The RL-based controls are designed using the optimization method with the simplified RL-based critic NN schemes. We use the simplified RL structures to approximate the cost function of each motor input in the optimal control design. The NN weights of both the identified algorithm and simplified RL-based structure are approximated by using a novel adaptation algorithm, where the learning gains can be optimized adaptively. The weight convergences and the Nash-optimization MMDLS stability are all proved. Finally, numerical MMDLS simulations are implemented to show the correctness and the improved performance of the proposed methods.