Fractional linear control systems with Caputo derivative and their optimization. (6th November 2014)

• Record Type: Journal Article
• Authors: Kamocki, Rafał; Majewski, Marek
• Is Part Of: Optimal control applications and methods. Volume 36:Number 6(2015)
• Page Start: 953
• Page End: 967
• Publication Date: 2014-11-06
• Subjects: fractional derivatives and integrals -- fractional optimal control -- fractional ordinary Cauchy problem -- maximum principle -- existence of optimal solutions; Control theory -- Periodicals; Mathematical optimization -- Periodicals; 629.8312
• DOI: 10.1002/oca.2150
• Languages: English
• ISSNs: 0143-2087

Abstract

SUMMARY: 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. Copyright © 2014 John Wiley & Sons, Ltd.