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

A successive approximation approach designing optimal controller is developed for affine nonlinear discrete- time systems with a quadratic performance index. By using this approach the original optimal control problem is transformed into a sequence of nonhomogeneous linear two- point boundary value ( TPBV) problems. The optimal control law consists of an accurate linear term and a nonlinear compensating term which is the limit of a sequence of adjoint vectors. By taking a finite- time iteration instead of the limit of the sequence of adjoint vectors, we obtain a suboptimal control law. Simulation examples are employed to verify the validity of the proposed algorithm.