Abstract
In this article, the linear quadratic optimization problem subject to fractional order differential algebraic systems of Riemann-Liouville type is studied. The goal of this article is to find the optimal control-state pairs satisfying the dynamic constraint of the form a fractional order differential algebraic systems such that the linear quadratic objective functional is minimized. The transformation method is used to find the optimal controlstate pairs for this problem. The optimal control-state pairs is stated in terms of Mittag-Leffler function.
Highlights
Many issues in the physical field have used the optimal control theory for problem solving
As reported in [Frank et all, 2016], the optimal control theory is applied for a complex atomic quantum system
It can be proved that the solution of fractional differential algebraic system (2) exists if det = 0 for some s ∈ C [Batiha et all, 2018]
Summary
Many issues in the physical field have used the optimal control theory for problem solving. To the best of the author’s knowledge, little work has been done with the optimization problem (1) subject to the fractional dynamic system (2) This issue was discussed in [Chiranjeevi and Biswas, 2020] recently, for which Dtα is the fractional derivative operator in terms of the Caputo. In this paper we discuss the linear quadratic optimization problem of infinite horizon subject to differential algebraic system of fractional order of the following form:. The results of this paper constitute a new contribution in the field of optimization subject for fractional differential algebraic dynamic system This result can be used to extent the results in [Muller, 1999] on the linear mechanical descriptor systems for fractional derivative of order α, with α ∈ (0, 1).
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