Optimal control for discrete time bilinear system with persistent disturbances

For discrete time bilinear systems with persistent disturbances, optimal control problem is considered. The paper discusses optimal control law in terms of two cases that time is finite and infinite. By the feedforward and feedback terms, the disturbances are damped in optimal fashion. The algorithm is based on a new SAA (successive approximation approach). Original optimal control problem is transformed into a sequence of nonhomogeneous linear two-point boundary value (TPBV) problems. By using of the disturbance observer, the paper constructs a physically realizable optimal controller. Simulation shows that the algorithm is easily implemented and can damp the external persistent disturbance efficiently.