Premium
Fractional linear control systems with Caputo derivative and their optimization
Author(s) -
Kamocki Rafał,
Majewski Marek
Publication year - 2014
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2150
Subject(s) - mathematics , uniqueness , optimal control , fractional calculus , pontryagin's minimum principle , derivative (finance) , zero (linguistics) , maximum principle , type (biology) , mathematical analysis , control (management) , control theory (sociology) , mathematical optimization , computer science , artificial intelligence , financial economics , economics , linguistics , philosophy , ecology , biology
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.