Numerical Solution of Delay Fractional Optimal Control Problems using Modification of Hat Functions

Abstract

In this paper, we consider the numerical solution of a class of delay fractional optimal control problems using modification of hat functions. First, we introduce the fractional calculus and modification of hat functions. Fractional integral is considered in the sense of Riemann-Liouville and fractional derivative is considered in the sense of Caputo. Then, operational matrix of fractional integration, product and delay operational matrix of the basis functions vector are introduced. For solving the optimal control problem, all functions in the problem are approximated using the basis functions. A system of nonlinear algebraic equations are obtained using the properties of modification of hat functions and the introduced operational matrices. By solving the obtained system, the unknown coefficients of the state and control input functions are determined and by substituting these values an approximation of the solution of the problem is given. Finally, some examples of different kinds of delay fractional optimal control problems are considered to confirm the accuracy and applicability of the suggested method../files/site1/files/42/9Abstract.pdf

Keywords

• delay fractional optimal control problem
• modification of hat functions
• riemann-liouville integral
• caputo derivative
• operational matrix of integration
• product operational matrix
• delay operational matrix