Optimal Sliding Mode Control for Nonlinear Systems with Matched and Mismatched Uncertainties Based on ENDOB

Abstract

This paper proposes a novel result on optimal sliding mode control (OSMC) approach for general nth order nonlinear systems with matched and mismatched uncertainties based on extended nonlinear disturbance observer (ENDOB). The combination of the control Lyapunov function (CLF) method with the ISMC based on disturbance observer guarantee the robustness, maintain the nearly optimal performance of the sliding-mode dynamics. In the first step, the nonlinear optimal control strategy based on the CLF is proposed for the known part of nonlinear system. As the optimal controller is highly sensitive to the system uncertainty, a ENDOB is designed to approximate matched and mismatched uncertainties. Then by designing a novel sliding mode manifold integrated with a disturbance estimation technique, a ENDOB-based OSMC method is designed for these systems. A rigorous stability analysis of the composite closed-loop system is provided using Lyapunov theory. The final two simulation results are provided to verify the effectiveness of the proposed control method.