Nonlinear Optimal Control Synthesis Using Basis Functions: Algorithms and Examples

The ability to quickly synthesize an optimal control signal for a nonlinear system is critical for practical implementations. In previous work, we have introduced a computational procedure to iteratively synthesize an optimal control signal for a very broad class of nonlinear control systems. This paper presents an extension of the approach to allow for different parameterizations of control inputs, resulting in a substantial reduction in the number of decision variables and thus computation time. The highlighted efficiency and effectiveness of the proposed approach are illustrated and compared against other methods using various control examples.