MRAC for unknown discrete-time nonlinear systems based on supervised neural dynamic programming

This paper investigates the model reference adaptive control (MRAC) problem for unknown nonlinear discrete-time systems, which is how to guarantee adaptation to the variable reference input and robustness to perturbation. A supervised neural dynamic programming (SNDP) approach is developed to solve this MRAC problem, which includes a learning mode and a control mode. In the learning mode, a data-based adaptive critic learning algorithm is proposed, which guarantees that the controlled objective adaptively tracks the reference model on behavior. Such an algorithm also ensures flexible switching from the learning mode to the control mode under which the robustness of the closed-loop control systems is further improved. By employing a newly defined mode scheduler that regulates the learning mode and the control mode, the adaptation and the robustness of the systems are both achieved by the developed SNDP approach. Its uniformly ultimately bounded property is proved by using Lyapunov method. Simulation results verify that the developed SNDP approach ensures the adaptation to the variable reference input, and has superiority over some traditional MRAC methods in improving the robustness. (C) 2019 Elsevier B.V. All rights reserved.