A SPECTRAL METHOD BASED ON THE SECONDKIND CHEBYSHEV POLYNOMIALS FOR SOLVING ACLASS OF FRACTIONAL OPTIMAL CONTROLPROBLEMS

In this paper, we consider the second-kind Chebyshevpolynomials (SKCPs) for the numerical solution of the fractionaloptimal control problems (FOCPs). Firstly, an introduction of thefractional calculus and properties of the shifted SKCPs are givenand then operational matrix of fractional integration is introduced.Next, these properties are used together with the Legendre-Gaussquadrature formula to reduce the fractional optimal control problem to solving a system of nonlinear algebraic equations that greatlysimplifies the problem. Finally, some examples are included to confirm the efficiency and accuracy of the proposed method.

Keywords:

Fractional optimal control problems , Caputo fractionalderivative , Riemann-Liouville fractional integral , Second-kind Chebyshev polynomials , Operational matrix