A Chebyshev approximation for solving optimal control problems

This paper presents a numerical solution for solving optimal control problems, and the controlled Duffing oscillator. A new Chebyshev spectral procedure is introduced. Control variables and state variables are approximated by Chebyshev series. Then the system dynamics is transformed into systems of algebraic equations. The optimal control problem is reduced to a constrained optimization problem. Results and comparisons are given at the end of the paper.