A Chebyshev expansion method for solving nonlinear optimal control problems

摘要

This paper presents a numerical technique for solving the controlled Duffing oscillator. The control and state variables are approximated by Chebyshev series. A technique is provided for approximating the system dynamics, boundary conditions, and performance index. This technique is based on using an explicit formula for the Chebyshev polynomials in terms of arbitrary order of their derivatives. The system dynamics and the performance index are converted into some algebraic equations. Then the optimal control problem is reduced to constrained optimization problem. Results and comparisons are given at the end of this paper.