Successive-approximation approach of optimal control for bilinear discrete-time systems

A successive-approximation approach designing optimal controllers is developed for bilinear discrete-time systems with a quadratic performance index. By using the successive-approximation approach, the original optimal control problem is transformed into a sequence of nonhomogeneous linear two-point boundary-value problems. The optimal control law consists of an accurate linear term and a nonlinear compensating term that is the limit of the adjoint vector sequence. Through a finite-step iteration process of a nonlinear compensating sequence a suboptimal control law is obtained. Simulation results show that the algorithm is easily implemented and has a fast convergence rate.