Open AccessOptimization of a fractional Mayer problem - existence of solutions, maximum principle, gradient methods
Author(s) -
Dariusz Idczak,
S. Walczak
Publication year - 2014
Publication title -
rocznik akademii górniczo-hutniczej im. stanisława staszica. opuscula mathematica/opuscula mathematica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 16
eISSN - 2300-6919
pISSN - 1232-9274
DOI - 10.7494/opmath.2014.34.4.763
Subject(s) - mathematics , maximum principle , optimization problem , mathematical optimization , mathematical analysis , combinatorics , optimal control
In the paper, we study a linear-quadratic optimal control problem of Mayer type given by a fractional control system. First, we prove a theorem on the existence of a solution to such a problem. Next, using the local implicit function theorem, we derive a formula for the gradient of a cost functional under constraints given by a control system and prove a maximum principle in the case of a control constraint set. The formula for the gradient is used to implement the gradient methods for the problem under consideration