Optimal control for nonlinear discrete-time systems: a successive approximation approach

A new successive approximation algorithm is developed for the optimal control of nonlinear discrete-time systems with quadratic cost functional. By using the proposed algorithm the original nonlinear optimal problem is transformed into a sequence of linear two-point boundary value (TPBV) problems. The optimal control law obtained consists of an accurate linear feedback term and a nonlinear compensation term, which is the limit of the solution sequence of the adjoint vector differential equations. Through the finite-step iterations of nonlinear compensation term of optimal solution sequence, we can obtain a suboptimal control law. Simulation examples are employed to verify the validity of the successive approximation approach.