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

摘要

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.