An application of a fuzzy system for solving time delay fractional optimal control problems with Atangana–Baleanu derivative

Abstract

In this article, a new approach based on fuzzy systems is used for solving time delay fractional order optimal control problems. The fractional derivatives are considered in the Atangana–Baleanu sense that is a new derivative with the nonsingular and nonlocal kernel. By means of the calculus of variations and the formula for fractional integration by parts, the necessary optimality conditions associated to the time delay problem is derived. In order to solve the obtained optimality system, the solution of the system is first approximated by fuzzy solutions with adjustable parameters. The optimality system is then reduced to an unconstrained optimization problem by using appropriate error function. A learning algorithm is also presented to achieve the parameters of these fuzzy solutions. The efficiency and accuracy of the proposed approach are assessed through some illustrative examples of the time delay fractional optimal control problems.