The Design of Quasi-Optimal Higher Order Sliding Mode Control via Disturbance Observer and Switching-Gain Adaptation

In this paper, a quasi-optimal higher order sliding mode control (HOSMC) scheme is designed using disturbance observer (DOB) and adaptive techniques. The overall HOSMC scheme is constituted by three portions: 1) a switch-based quasi-optimal control law that ensures rapid finite-time stabilization of the origin, producing a nominally uncertainty-free system, based on a perturbed chain of integrators; 2) a DOB which estimates the lumped uncertainties with lower frequencies; and 3) an adaptive controller designed to deal with the fast-varying terms of these lumped uncertainties over the pass-band of the DOB. Since the adaptive controller and the DOB work in a cooperative manner, the only requirement is that the switching gain be greater than the bound of the DOB estimation error, instead of the bound of the lumped uncertainties. As a consequence, overestimation in the adaptive controller can be avoided by resorting to the equivalent control. Simulation results confirm the capabilities of the proposed control strategy.