A Continuous First-Order Sliding Mode Control Law

Abstract

Sliding mode control is a technique to design robust feedback control laws. In its classical formulation, this approach involves discontinuous controls that arise several theoretical and practical challenges, such as the existence of non-unique solutions of nonlinear differential equations and chattering. Numerous variations of the sliding mode control architecture, such as the higher-order sliding mode method, have been presented to overcome these issues. In this paper, we present an alternative sliding mode control architecture that involves Hölder continuous feedback control laws, is simpler to implement than other non-classical nonlinear robust control techniques, guarantees robustness and uniform asymptotic stability of the closed-loop system, and ensures both existence and uniqueness of the closed-loop system’s trajectory. Our results are applied to design a robust nonlinear observer in the same form as the Walcott and Żak observer. Moreover, a numerical example illustrates our theoretical results and compares the proposed control law to the classical sliding mode control, the second order sliding mode control, and the super-twisting control.