SOLVING FRACTIONAL OPTIMAL CONTROL PROBLEMS BY HERMITE POLYNOMIALS

In this paper a numerical method for solving a class of frac-tional optimal control problems is presented which is based on Hermitepolynomials approximation. Using known formulas sush as Caputo andRiemann Liouville operators for computing fractional derivatives and inte-graion of polynomials, Operational matrices of integration, differentiationare introduced and are utilized to reduce the problem of solving a systemof algebraic equations. The method in general is easy to implement andyields good results. Illustrative examples are included to demonstrate thevalidity and applicability of the new technique.

Keywords:

Fractional Optimal Control Problem , left Riemann-Liouville fractional integration , Caputo derivative , Hermite Polynomials , polynomials basis , Operational matrix