Abstract
The paper is devoted to the study of an approximation process of time optimal control for fractional evolution systems in Banach spaces. We firstly convert time optimal control problem into Meyer problem. By virtue of the properties of the family of solution operators given by us, the existence of optimal controls for Meyer problem is proved. Secondly, we construct a sequence of Meyer problems to successive approximation of the original time optimal control problem. Finally, a new approximation process is established to find the solution of time optimal control problem. Our method is different from the standard method.
Highlights
It has been shown that the accurate modelling in dynamics of many engineering, physics, and economy systems can be obtained by using fractional differential equations
There has been a great deal of interest in the solutions of fractional differential equations in analytical and numerical sense
When the fractional differential equations describe the performance index and system dynamics, a classical optimal control problem reduces to a fractional optimal control problem
Summary
It has been shown that the accurate modelling in dynamics of many engineering, physics, and economy systems can be obtained by using fractional differential equations. When the fractional differential equations describe the performance index and system dynamics, a classical optimal control problem reduces to a fractional optimal control problem. There has been very little work in the area of fractional optimal control problems 18, 22 , especially the time optimal control for fractional evolution equations 19. We will construct a sequences of Meyer problems Pεn to successive approximation time optimal control problem P. We show that there exists a subsequence of Meyer problems Pεn whose corresponding sequence of optimal controls {wεn} ∈ W converges to a time optimal control of problem P in some sense. The existence of time optimal controls for problem P is proved by this constructive approach which provides a new method to solve the time optimal control. We display the Meyer approximation process of time optimal control and derive the main result of this paper
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