Modified Adomian decomposition method for solving fractional optimal control problems

Abstract

In this study, we use the modified Adomian decomposition method to solve a class of fractional optimal control problems. The performance index of a<br><br>fractional optimal control problem is considered as a function of both the state and the control variables, and the dynamical system is expressed in<br><br>terms of a Caputo type fractional derivative. Some properties of fractional derivatives and integrals are used to obtain Euler–Lagrange equations for a<br><br>linear tracking fractional control problem and then, the modified Adomian decomposition method is used to solve the resulting fractional differential<br><br>equations. This technique rapidly provides convergent successive approximations of the exact solution to a linear tracking fractional optimal control<br><br>problem. We compare the proposed technique with some numerical methods to demonstrate the accuracy and efficiency of the modified Adomian<br><br>decomposition method by examining several illustrative test problems.