Fractional linear control systems with Caputo derivative and their optimization

Fractional linear control systems with Caputo derivative and their optimization

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Article ID: iaor2016246
Volume: 36
Issue: 6
Start Page Number: 953
End Page Number: 967
Publication Date: Nov 2015
Journal: Optimal Control Applications and Methods
Authors: ,
Keywords: optimization, programming: fractional
Abstract:

In this paper, a fractional linear control system, containing Caputo derivative, with an integral performance index is studied. First, the existence and uniqueness of a solution to the mentioned control system is obtained. The main result is a theorem on the existence of optimal solutions to considered optimal control problems. Moreover, in order to find these solutions, the necessary optimality conditions (Pontryagin maximum principle) are derived. Our considerations consist of two parts: first, we consider starting a problem with zero initial condition and, next, with nonzero initial condition. All results are obtained by using results of such a type for equivalent fractional optimal control problem containing a Riemann–Liouville derivative.

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