H∞ Control for Singularly Perturbed Bilinear Systems with Parameter Uncertainties Using Successive Galerkin Approximation

Abstract

This paper presents a new algorithm for the closed-loop H∞ composite control of singularly perturbed bilinear systems with time-varying parameter uncertainties and exogenous disturbance using the successive Galerkin approximation (SGA). 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 then two H∞ control laws are obtained for each subsystem. H∞ control theory guarantees robust closed-loop performance but the resulting problem is difficult to solve for bilinear systems. In order to overcome the difficulties inherent in the H∞ control problem, the suitable robust H∞ feedback control law can be constructed in term of the approximated solution to a Hamilton-Jacobi-Isaac equation using SGA. The composite control law consists of H∞ control laws for each subsystem.