Composite control for singularly perturbed bilinear systems via successive Galerkin approximation

The authors present algorithms for the finite-time and infinite-time closed-loop composite control of singularly perturbed bilinear systems with respect to performance criteria, using the successive Galerkin approximation (SGA) method. The singularly perturbed bilinear system is decomposed into two subsystems of a slow-time scale and a fast-time scale via singular perturbation theory, and two optimal control laws are obtained for each subsystem by using the SGA method. Then the composite control law that consists of two optimal control laws for each subsystem is designed. The authors aim to design closed-loop composite control laws for the singularly perturbed bilinear systems via the SGA method. They also aim to reduce the computational complexity when the SGA method is applied to high-order systems.