TY - JOUR
T1 - Necessary optimality conditions for quasi-singular controls for systems with Caputo fractional derivatives
AU - Yusubov, Shakir Sh
AU - Mahmudov, Elimhan N.
N1 - Publisher Copyright:
Copyright © 2023. The Author(s).
PY - 2023
Y1 - 2023
N2 - In this paper, we consider an optimal control problem in which a dynamical system is controlled by a nonlinear Caputo fractional state equation. First we get the linearized maximum principle. Further, the concept of a quasi-singular control is introduced and, on this basis, an analogue of the Legendre-Clebsch conditions is obtained. When the analogue of Legendre-Clebsch condition degenerates, a necessary high-order optimality condition is derived. An illustrative example is considered.
AB - In this paper, we consider an optimal control problem in which a dynamical system is controlled by a nonlinear Caputo fractional state equation. First we get the linearized maximum principle. Further, the concept of a quasi-singular control is introduced and, on this basis, an analogue of the Legendre-Clebsch conditions is obtained. When the analogue of Legendre-Clebsch condition degenerates, a necessary high-order optimality condition is derived. An illustrative example is considered.
KW - fractional derivative
KW - fractional optimal control
KW - necessary optimality condition
UR - http://www.scopus.com/inward/record.url?scp=85172418172&partnerID=8YFLogxK
U2 - 10.24425/acs.2023.146955
DO - 10.24425/acs.2023.146955
M3 - Article
AN - SCOPUS:85172418172
SN - 1230-2384
VL - 33
SP - 463
EP - 496
JO - Archives of Control Sciences
JF - Archives of Control Sciences
IS - 3
ER -