Observer-based adaptive optimal control for unknown singularly perturbed nonlinear systems with input constraints

This paper introduces an observer-based adaptive optimal control method for unknown singularly perturbed nonlinear systems with input constraints. First, a multi-time scales dynamic neural network U+0028 MTSDNN U+0029 observer with a novel updating law derived from a properly designed Lyapunov function is proposed to estimate the system states. Then, an adaptive learning rule driven by the critic NN weight error is presented for the critic NN, which is used to approximate the optimal cost function. Finally, the optimal control action is calculated by online solving the Hamilton-Jacobi-Bellman U+0028 HJB U+0029 equation associated with the MTSDNN observer and critic NN. The stability of the overall closed-loop system consisting of the MTSDNN observer, the critic NN and the optimal control action is proved. The proposed observer-based optimal control approach has an essential advantage that the system dynamics are not needed for implementation, and only the measured input U+002F output data is needed. Moreover, the proposed optimal control design takes the input constraints into consideration and thus can overcome the restriction of actuator saturation. Simulation results are presented to confirm the validity of the investigated approach.