Abstract
We prove necessary optimality conditions of Pontryagin type for a class of fuzzy fractional optimal control problems with the fuzzy fractional derivative described in the Caputo sense. The new results are illustrated by computing the extremals of three fuzzy optimal control systems, which improve recent results of Najariyan and Farahi.
Highlights
Optimal control problems are usually solved with the help of the famous Pontryagin Maximum Principle (PMP), which provides a generalization of the classical Euler–Lagrange and Weierstrass necessary optimality conditions of the calculus of variations and is one of the central results of the mathematics of the XX century [30, 32]
The notion of fuzzy set has been widely spread to various research areas, such as linear programming, optimization, differential equations and even fractional differential equations [34]
The study of a fuzzy optimal control theory forms a suitable setting for the mathematical modelling of real world problems in which uncertainties or vagueness pervade [14]
Summary
Optimal control problems are usually solved with the help of the famous Pontryagin Maximum Principle (PMP), which provides a generalization of the classical Euler–Lagrange and Weierstrass necessary optimality conditions of the calculus of variations and is one of the central results of the mathematics of the XX century [30, 32]. The authors of [26, 27] study the following fuzzy optimal control problem subject to a time-invariant linear control system: b If the order of the derivatives appearing in the formulation of our problems approach integer values, one obtains via our results the extremals of fuzzy optimal control problems investigated in [12, 26, 27].
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