Fuzzy optimal control with application to discounted profit advertising problem

Authors:
Md. Azizul Baten;Anton Abdulbasah Kamil
Affiliations:
Department of Decision Science, School of Quantitative Sciences, Universiti Utara Malaysia, Kedah, Malaysia;Mathematics Program, School of Distance Education, Universiti Sains Malaysia, Pulau Pinang, Malaysia
Venue:
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
Year:
2012

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Abstract

A fuzzy optimal control model was formulated maximizing the expected discounted objective function subject to fuzzy differential equation for fuzzy control system. We proved that the value function of fuzzy optimal control problem satisfied the dynamic programming principle. The optimality equation in fuzzy optimal control was derived and an example was carried out to obtain the optimality conditions by using the optimality equation. As an application, we used the Bellman's principle of optimality to solve the fuzzy advertising model.