AN ANALYTICAL APPROCH FOR SOLVING FRACTIONAL FUZZY OPTIMAL CONTROL PROBLEM WITH FUZZY INITIAL CONDITIONS
DOI:
https://doi.org/10.32461/2226-3209.3.2018.176880Abstract
Abstract. A fractional – fuzzy optimal control problem is an optimal control problem in which it is governed
by a fuzzy system of fractional differential equation. The aim of this paper is to introduce an analytically solution for such Bolza problems when the initial state is also fuzzy. For this purpose, first the problem is turned to two fractional optimal control problems by concept of 훽-cut and complex numbers. Then, we apply a new method to solve these ractional optimal control problems, analytically by applying a new Riccati differential equation determined from PMP. Indeed this Riccati equation transfer each mentioned fractional optimal control problem to a fractional differential system. We show that if the new system has close solution, one is able to obtain the analytical solution of the fractional – fuzzy optimal control problems. A numerical simulation based on the new method is presented for different values of 훽 and fractional order and the results are compered. In the last section, a numerical example of fractional-fuzzy optima control problem is solved by the new method for different 훽 and 훾; and compared with the exact state; also, they are shown in figures for each cases.
Key words: Fractional differential equation, optimal control, fuzzy.
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