Parallel optimal control for weakly coupled bilinear systems using successive Galerkin approximation

A new algorithm for the closed-loop parallel optimal control of weakly coupled bilinear systems with respect to performance criteria using the successive Galerkin approximation (SGA) is presented. From the spirit of the general weak coupling theory, the Hamilton- Jacobi-Bellman equation (HJB: which is related to optimal control problems) is decomposed into three independent HJB equations. The optimal control law consists of the solutions to sub-equations using the SGA method in parallel. The main contributions are as follows: (i) design of a closed-loop optimal control law for weakly coupled bilinear systems using the SGA method and (ii) reduction of the computational complexity when the SGA method is applied to the high-order systems.