Gain-scheduled continuous higher-order sliding mode control for uncertain nonlinear system

This paper proposes a gain-scheduled continuous higher-order sliding mode control scheme for a class of minimum phase uncertain nonlinear system. Higher-order sliding mode control is equivalently represented as finite time stabilization of all-dimension integrator chains with bounded uncertainties. After carried out state feedback control, the control law is composed of two parts. One part achieves finite time convergence of pure integrator chains. The other part, gain-scheduled super-twisting control algorithm, is employed to overcome the uncertainties without obtaining the upper bounds in advance. This control approach features that the whole control input is continuous, control chattering is puny, and over-estimated gain is not existent. Finite time convergence of the closed-loop control system is formally proved based on quadratic form Lyapunov function. Simulation results for an academic example and the ship heading control verify the effectiveness and applicability of the proposed approach.