Parallel Robust H∞ Control for Weakly Coupled Bilinear Systems with Parameter Uncertainties Using Successive Galerkin Approximation

Abstract: This paper presents a new algorithm for the closed-loop H∞ composite control of weakly coupled bilinear systems with time-varying parameter uncertainties and exogenous disturbance using the successive Galerkin approximation (SGA). By using weak coupling theory, the robust H∞ control can be obtained from two reduced-order robust H∞ control problems in parallel. The H∞ control theory guarantees robust closed-loop performance but the resulting problem is difficult to solve for uncertain bilinear systems. In order to overcome the difficulties inherent in the H∞ control problem, two H∞ control laws are constructed in terms of the approximated solution to two independent Hamilton-Jacobi-Isaac equations using the SGA method. One of the purposes of this paper is to design a closed-loop parallel robust H∞ control law for the weakly coupled bilinear systems with parameter uncertainties using the SGA method. The other is to reduce the computational complexity when the SGA method is applied to the high order systems.