CONSTRUCTION OF OPTIMAL FEEDBACK-CONTROL FOR NONLINEAR-SYSTEMS VIA CHEBYSHEV POLYNOMIALS

A method is proposed to determine the optimal feedback control law of a class of nonlinear optimal control problems. The method is based on two steps. The first step is to determine the open-loop optimal contro l and trajectories, by using the quasilinearization and the state vari ables parameterization via Chebyshev polynomials of the first type. Th erefore the nonlinear optimal control problem is replaced by a sequenc e of small quadratic programming problems which can easily be solved T he second step is to use the results of the last quasilinearization it eration, when an acceptable convergence en or is achieved, to obtain t he optimal feedback control law. To this end, the matrix Riccati equat ion and another n linear differential equations are solved using the C hebyshev polynomials of the fir st type. Moreover, the differentiation operational matrix of Chebyshev polynomials is introduced. To show th e effectiveness of the proposed method, the simulation results of a no nlinear optimal control problem are shown.