Feedforward feedback nearly optimal compensatory control for a class of nonlinear systems

This paper considers an optimal control for a class of nonlinear systems with respect to linear quadratic functional. A nearly feedforward feedback optimal compensatory control strategy is proposed. By introducing the successive approximation approach of the nonlinear differential equation theory, a linear two-point boundary value problem sequence is constructed to approximate the nonlinear two-point boundary value problem, which is the necessary condition of the nonlinear control problem. By iteratively solving this approximating linear sequence, optimal control law composed of a linear feedback compensatory term and a feedforward compensatory term is designed. An algorithm is presented to design certain qualified nearly optimal control law by truncating the infinite iteration. An illustrative example shows the validity of the algorithm.