Composite control for singularly perturbed bilinear systems with successive Galerkin approximation

Abstract

This paper presents the closed-loop composite control of singularly perturbed bilinear systems with a quadratic performance criterion, using the successive Galerkin approximation (SGA). The singularly perturbed bilinear system is decomposed into two subsystems of a slow-time and fast-time scale by the singular perturbation theory, and we obtain feedback control laws from each subsystem using the SGA. We design the composite control law that consists of two optimal control laws for each subsystem. This paper attempts to design the closed-loop composite controller of singularly perturbed bilinear systems with the SGA method, and to reduce the disadvantages of the SGA method.