Application of Chebyshev polynomials to derive efficient algorithms for the solution of optimal control problems

In this paper, new and efficient algorithms for solving optimal control problems and the controlled Duffing oscillator are presented. The solution is based on state parameterization, such that the state variable can be considered as a linear combination of Chebyshev polynomials with unknown coefficients. First, an optimization problem in (n+1)-dimensional space is changed into a one-dimensional optimization problem, which can then be solved easily. By these algorithms, the control and state variables can be approximated as a function of time. Convergence of the algorithms is proved and some illustrative examples are presented to show the efficiency and reliability of the presented method.