Improved successive approximation procedure for optimal control of nonlinear systems

Optimal control for a class of Lipschitz nonlinear systems with respect to linear quadratic cost functional is considered. An improved successive approximation procedure is proposed to enhance the performance of the closed loop system and accelerate the iteration steps. By introducing the Successive Approximation Approach (SAA) of the nonlinear differential equation theory, together with a modeling technique, a linear two-point boundary value (TPBV) problem sequence is constructed to approximate the nonlinear TPBV problem, which is the necessary condition of the nonlinear optimal control problem. By iteratively solving this approximating linear sequence, a linear feedback optimal control law with a nonlinear compensation term is designed.