A Barrier-Function-Based Second-Order Sliding Mode Control With Optimal Reaching for Full-State and Input-Constrained Nonlinear Systems

Abstract

This paper considers the design of a minimum-time Second Order Sliding Mode Control (SOSMC) method for a class of full state and input constrained nonlinear systems. In this study, to enable the handling of the state and input constraints, a barrier function-based state transformation method is employed to convert the original control problem to an unconstrained control problem. Using the new representation of the system dynamics and the input-state linearization technique, a novel sliding manifold is proposed. Relying on the proposed sliding manifold on the concept of the Robust Fuller's Problem, a second order sliding mode controller is developed to achieve optimal reaching time in the presence of the considered constraints. Furthermore, as a tool for computing the reaching time of the proposed minimum-time SOSMC, a new computational method is developed. To quantify the effects of the constraints on the optimal reaching time, the reaching time of the proposed SOSMC and the unconstrained minimum-time SOSMC methods are compared. Numerical simulations verify the efficacy of the proposed control method making reference, as an illustrative example, to the Duffing oscillator.