Dear A. M. Abdallah

Look the link, maybe helpful.

https://pdfs.semanticscholar.org/3ed0/943a8f71bf08fe52bc3c190f2d0ca370d278.pdf

Article Fuzzy Optimal Control Problem with Non-linear Functional

https://www.academia.edu/1954526/Fuzzy_Optimal_Control_under_Generalized_Differentiability_of_Fuzzy-number-valued_Functions

Regards, Shafagat

Dear A. M. Abdallah,

The fuzzy optimal control will be relative to decision making in a fuzzy environment. According to whether we consider a fuzzy objective and a fuzzy constraint according to the decision-making mechanism of Bellman and Zadeh. The resulting fuzzy decision D is given by the intersection of the objective G and the constraint C. In the fuzzy decision-making mechanism, an optimal decision refers to the decision with the highest degree of belonging (better decision ). This optimal decision is also called maximizing the decision.

For more information about this subject i suggest you to see links and attached file in topic.

- Fuzzy optimal control of linear quadratic models - ScienceDirect

https://www.sciencedirect.com/science/article/pii/S0898122110003019

- A Fuzzy Optimal Control Model - Semantic Scholar

https://pdfs.semanticscholar.org/.../943a8f71bf08fe52bc3c190f2d0...

- Fuzzy optimal control problem with non-linear functional | SpringerLink

https://link.springer.com/article/10.1007/s12543-011-0085-6

- Fuzzy optimal control of a poisoning-pest model by using 𝜶-cuts

jert.iugaza.edu.ps/Portals/130/pdf-files/issue31.pdf

Best regards

According YanjuanZhao and YuanguoZhu :

"" Fuzzy optimal control is to choose the best decision such that an objective function related to a fuzzy process provided by a fuzzy differential equation is optimized. Because the objective function is a fuzzy variable for any decision, we cannot optimize it as a real function. A question is how to compare two different fuzzy variables, or how to decide which is large. In fact, there are many methods to do so but there is no any method to be best. These methods are established due to some criteria including, for example, expected value, optimistic value, and credibility "".

For more details see :

- YanjuanZhao and YuanguoZhu , Fuzzy optimal control of linear quadratic models, Computers & Mathematics with Applications, Volume 60, Issue 1, July 2010, Pages 67-73 .

- Yuanguo Zhu , A Fuzzy Optimal Control Model , Journal of Uncertain Systems Volume 3, Issue 4, 2009, pages.270-279.

- Hua Wang , Jing Li , David Niemann , Fuzzy Optimal Control and Its Application to Nonlinear Benchmark Problem.

- Pavel Steinbauer, Michael Valasek , Fuzzy Optimal Control of Mechanical Systems

A control can be optimal only in a sense of the assumed multi-criterion (consisting of many component criteria) of the control. Which component criteria should be taken into aacount when a concrete plant is controlled depends on the plant specificity and on individual views of a control engineer. Generally the problem is very complicated. For practical aims I advice you to see papers on control of the plant type of your interest and assume a multi-criterion that is mostly used by engineers in the case of this plant.

Thanks Prof for the knowledge shared

Please check this link for your reference

http://elib.mi.sanu.ac.rs/files/journals/yjor/3/yujorn3p33-43.pdf