Optimal closed loop control for nonlinear systems using Chebyshev polynomials

A method is proposed to construct the optimal feedback control law of a nonlinear optimal control problem. The method is based on two steps: the first step is to determine the open loop optimal control and trajectories, by using the quasilinearization and the state variables parameterization via Chebyshev polynomials of the first type; the second step is to use the results of the last quasilinearization iteration, when acceptable convergence error is achieved, to obtain the optimal feedback control law. To show the effectiveness of the proposed method, the simulation results of a nonlinear optimal control problem are shown.