TY  - JOUR
ID  - Idczak2016
LB  - Idczak2016
AU  - Idczak, Dariusz
AU  - Walczak, Stanislaw
TI  - On a linear-quadratic problem with Caputo derivative
ST  - On a linear-quadratic problem with Caputo derivative
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2016
VL  - 36
IS  - 1
SP  - 49
EP  - 68
DO  - http://dx.doi.org/10.7494/OpMath.2016.36.1.49
UR  - http://dx.doi.org/10.7494/OpMath.2016.36.1.49
AB  - In this paper, we study a linear-quadratic optimal control problem with a fractional control system containing a Caputo derivative of unknown function. First, we derive the formulas for the differential and gradient of the cost functional under given constraints. Next, we prove an existence result and derive a maximum principle. Finally, we describe the gradient and projection of the gradient methods for the problem under consideration.
KW  - fractional Caputo derivative
KW  - linear-quadratic problem
KW  - existence and uniqueness of a solution
KW  - maximum principle
KW  - gradient method
KW  - projection of the gradient method
SN  - 1232-9274
ER  -