Approximate optimal control of nonlinear systems with quadratic performance criteria

A method is presented that approximates the solution to a nonlinear optimal control problem with quadratic cost function. We assume that the nonlinear system is accurately represented by a high-fidelity (hf) model which can be of high complexity or even of “black-box” type. The hf-model is oftentimes unsuitable for solving the optimal control problem. The proposed solution method is based on an Iterative Model and Trajectory Refinement (IMTR) strategy that uses a low-fidelity (lf) model to solve the optimal control problem. The lf-model is obtained through linearization of the hf-model, where the linearization point is variable by the optimization algorithm. The method is demonstrated for two problems of orbital transfer and of underactuated spacecraft attitude control with two reaction wheels. In both examples the solutions are shown to be in good agreement with the optimal solutions obtained by solving the respective nonlinear two-point-boundary value problem.