An Efficient Numerical Scheme for Solving Fractional Optimal Control Problems

This paper presents an accurate numerical method for solving a class of fractional optimal control problems (FOCPs). The fractional derivative in these problems is in the Caputo sense. In this technique, we approximate FOCPs and end up with a finite dimensional problem. The method is based on the combination of the useful properties of Chebyshev polynomials approximation and finite difference method. The fractional derivative approximated using the proposed formula here, along with Clenshaw and Curtis procedure for the numerical integration of a non-singular functions and the Rayleigh-Ritz method for the constrained extremum are considered. By the proposed method the given FOCP is reduced to a problem for solving a system of algebraic equations and by solving it, we obtain the solution of FOCP. The error upper bound of the obtained approximate formula is proved. Illustrative examples are included to demonstrate the validity and applicability of the proposed technique. A comparison with another method is given.

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