Optimal control for nonlinear similar composite systems: an improved successive approximation approach

This paper investigates the optimal control problem for a class of nonlinear composite systems. A decomposition method is first employed to transform the nonlinear composite system into certain affine nonlinear system. And then by introducing an improved successive approximation approach, approximating sequence of linear homogeneous two-point boundary value problems is constructed to approximate the nonlinear two-point boundary value problem that is the necessary condition of the optimal control problem. Solving the approximating sequence iteratively, an optimal control law of closed-loop linear feedback form is obtained. And the convergence is proved. An algorithm designing nearly optimal control law for practical applications is proposed. And Simulation example shows its validity.