Efficient radial basis functions approaches for solving a class of fractional optimal control problems

Abstract

The method of radial basis functions (RBFs) is a method of scattered data interpolation that has many applications in different fields. Based on the RBFs approach, two simple and accurate methods are presented in this paper to favor the solution of fractional optimal control problems (FOCPs) which are nominated as indirect and direct methods. In the first one, the considered FOCP is converted into a system of fractional differential equations (FDEs) that is called two-point boundary value problem (TPBVP) of fractional order. Then, both the context of minimization the total error and a joint application of Volterra integral equation will be used to rewrite this problems as as an unconstrained optimization problem that can be solved by using RBFs approximation. In direct one, we rewrite the FOCP as a classical static optimization problem that can be easily solved using known formulas for computing fractional derivatives of RBFs. Numerical example are given to prove the accuracy, effectiveness and feasibility of these methods.