Suboptimal variable structure control of uncertain nonlinear slowly varying systems

Abstract

ABSTRACTIn this paper, a new robust suboptimal controller is designed to stabilize a class of uncertain nonlinear time-varying systems with slowly varying parameters. In the design procedure of the proposed controller, first a suboptimal control law is designed for the nominal system based on considering a given cost function and an appropriate Slowly Varying Control Lyapunov Function (SVCLF). After that, a robustifying term is added to the nominal controller in order to vanish the effects of model uncertainties and/or external disturbances in a finite time. For this purpose, a special sliding surface, which is a combination of terminal and integral sliding surfaces, is used. This surface has the advantages of both of terminal and integral surfaces. Due to the structure of this surface, the actual trajectories track the desired one in the finite time. The other innovation of the proposed approach is accessing a chattering-free Controller. Finally, in order to confirm the applicability of the proposed controller and verify the theoretical results, it is applied on a practical benchmark system (a time-varying inertia pendulum). Computer simulations show the efficiency of the proposed controller.