On Quasi-optimal Variable Structure Control Approaches

Abstract

In this paper, variable structure control (VSC) approaches are integrated with nonlinear optimal control approaches. VSC design consists of two phases: sliding mode design and switching control design. For the first phase, we propose a nonlinear sliding mode design methodology incorporating optimality for a class of nonlinear MIMO systems. Two issues are addressed in detail: 1) how to construct a sliding mode for cascaded nonlinear dynamics where the linear-type sliding mode design is not applicable; 2) how to achieve a nonlinear sliding mode with optimality. As for the second phase, a kind of nonlinear suboptimal control according to the system nominal part is integrated with VSC mechanism with the predesigned nonlinear sliding mode. By integration, we achieve a quasi-optimal controller in which the suboptimal control part and VSC part are made to function in a complementary manner. In particular when the system nominal part is predominant, the nonlinear optimal control part will govern the system response as well as drive the system to approach the equilibrium in an optimal fashion. On the contrary, when the system perturbation becomes the main factor, the VSC will take over the control task to warrant the desired control precision by its robustness property.