Hybrid-Impulsive Higher Order Sliding Mode Control

Abstract

A hybrid-impulsive second order/higher order sliding mode (2-SMC/HOSM) control is explored in order to reduce dramatically the convergence time practically to zero, achieving instantaneous (or short time) convergence and uniformity. For systems of relative degree 2, the impulsive portion of the control function drives the system’s output (the sliding variable) and it’s derivative to zero instantaneously (or in short time) achieving a uniform convergence. Then the discontinuous state or output feedback stabilizes system’s trajectory at the origin (or its close vicinity), while achieving the ideal or real second order sliding mode (2-SM). The Lyapunov analysis of the considered hybrid-impulsive-discontinuous systems is performed. Hybrid-impulsive continuous HOSM (CHOSM) control is studied in systems of arbitrary relative degree with impulsive action that achieves almost instantaneous convergence and uniformity. This approach allows reducing the CHOSM amplitude, since the task of compensating the initial conditions is addressed by the impulsive action. Two hybrid-impulsive 2-SMCs are studied in systems of arbitrary relative degree in a reduced information environment. Only “snap” knowledge of the all states is required to facilitate the impulsive action. The efficacy of studied hybrid-impulsive control algorithms is illustrated via simulations.