A Numerical Technique for Solving Fuzzy Fractional Optimal Control Problems

Abstract

In this paper, the fuzzy fractional optimal control problem with both fixed and free final state conditions has been considered. Our problem is defined in the sense of Riemann-Liouville fractional derivative based on Hukuhara difference, and the dynamic constraint is described by a fractional differential equation of order less than 1. Using fuzzy variational approach, a necessary conditions of our problem has been derived. A numerical technique based on Gr¨unwald-Letnikov definition of fractional derivative and the relation between right Riemann-Liouville fractional derivative and right Caputo fractional derivative is proposed. Finally, some numerical examples are given to illustrate our main results