Abstract
The purpose of this paper is to establish the necessary conditions for a fuzzy optimal control problem of several variables. Also, we define fuzzy optimal control problems involving isoperimetric constraints and higher order differential equations. Then, we convert these problems to fuzzy optimal control problems of several variables in order to solve these problems using the same solution method. The main results of this paper are illustrated throughout three examples, more specifically, a discussion on the strong solutions (fuzzy solutions) of our problems.
Highlights
Optimal control theory is considered as a modern extension of the classical calculus of variations; it differs from calculus of variations in that it uses control variables to optimize the function
The main aim of this paper is to derive the necessary conditions of the fuzzy optimal control problem of several variables based on the concepts of differentiability and integrability of a fuzzy valued function parameterized by the left- and Advances in Mathematical Physics right-hand functions of its α-level set and variational approaches, in order to provide the solutions of this problem
This section is aimed at deriving the necessary conditions for the fuzzy optimal control problem of several variables
Summary
Optimal control theory is considered as a modern extension of the classical calculus of variations; it differs from calculus of variations in that it uses control variables to optimize the function. A lot of works done in the field of the fuzzy optimal control problem have only examined problems with one control and one dependent state variable; many times, we will wish to examine fuzzy optimal control problems which arise in a wide variety of scientific and engineering applications such as physics, chemical engineering, and economy, with more variables (more controls and more states). The main aim of this paper is to derive the necessary conditions of the fuzzy optimal control problem of several variables based on the concepts of differentiability and integrability of a fuzzy valued function parameterized by the left- and Advances in Mathematical Physics right-hand functions of its α-level set and variational approaches, in order to provide the solutions of this problem.
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