Expressing the concept of confidence level on quadratic problems of fuzzy fractional optimal control

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Karimyar Jahromi Mojtaba

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Journal Paper

Paper Information

Journal: سیستم های فازی و کاربردها Year:2024 | Volume:7 | Issue:2 Page(s): 181-200

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Information Journal Paper

Title

Expressing the concept of confidence level on quadratic problems of fuzzy fractional optimal control

Author(s)

Karimyar Jahromi Mojtaba | Issue Writer Certificate

Keywords

Optimal control

Fuzzy

Fractional order derivatives

confidence level

Abstract

The Fuzzy fractional Optimal control problem can be transformed into two fractional Optimal control problems using the concept of α-cut. Then, by applying the Pontryagin’s minimum principle for the fractional Optimal control problem, one can obtain the optimal trajectory and Optimal control. Based on this, by expressing the concept of degree of confidence for this category of problems, the decision-maker can compute the optimal trajectory and Optimal control of the given problem as an interval by choosing a confidence level α. It should be noted that as the value of α approaches one, the upper and lower bounds of the obtained intervals for the optimal trajectory and Optimal control get closer to the optimal trajectory and control of the exact (non-fuzzy) case of the problem. At the end of this paper, we will solve a numerical example using the method presented in this paper with different α-cuts, as well as fractional derivatives of various orders β, and show that the Optimal control and optimal trajectory obtained for the case of α=β=1 correspond with the optimal solutions obtained in the non-fuzzy case and with first-order derivatives.

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