IJCAS

This paper proposes a novel scheme to investigate the adaptive optimal tracking control problem of a class of strict-feedback nonlinear system via adaptive dynamic programming (ADP). First of all, by employing backstepping technique, a tracking error system is established. Then, the solution to adaptive optimal tracking control problem of strict-feedback nonlinear system is shown to be obtainable by solving the optimal regulation problem of established tracking error system. The solution of optimal regulation problem can be found by solving the corresponding Hamilton-Jacobi-Bellman (HJB) equation. In order to solve the HJB equation, a neural network (NN)-based online ADP algorithm is provided. To relax traditional Persistence of Excitation (PE) conditions, the historical and instantaneous state data are used to deign the NN weights tuning law simultaneously. In the provided ADP algorithm, the optimal control input is calculated in a forward-in-time manner without requiring any value or policy iterations. Based on the Lyapunov theory, we demonstrate that uniform ultimate boundedness (UUB) of all the signals in the closed-loop system are guaranteed. Application to the adaptive optimal tracking control of a nonholonomic mobile robot system demonstrates the efficacy of the provided ADP scheme. The designed ADP scheme achieves good tracking performance under different reference signals.

Keywords: Adaptive dynamic programming, nonholonomic mobile robot, nonlinear systems, strict-feedback, tracking control.