Disturbance observer based inverse optimal control for a class of nonlinear systems

Abstract

In this paper, we propose an inverse optimal composite control (IOCC) method to solve the optimization problem for a class of high-dimensional nonlinear strict-feedback systems with disturbances. Initially, we give these systems an inverse optimal control framework that avoids solving Hamilton–Jacobi-Bellman equations. Then, a nonlinear disturbance observer is designed to estimate the disturbances in the systems. We incorporate these disturbance estimates into the virtual control law design through a backstepping method that gives us a control Lyapunov function. In the end, this control Lyapunov function is utilized to obtain a composite controller that achieves optimality and disturbance rejection. We provide rigorous proofs for the convergence of the proposed composite controller. Simulation studies and comparative results from a real-life application to single-link robots show that the proposed composite controller achieves more robustness and effectiveness than the popular control methods in high-dimensional nonlinear systems.