| HILSCHER, Roman and Vera ZEIDAN. Legendre, Jacobi, and Riccati type conditions for time scale variational problem with application. Dynamic Systems and Applications. Atlanta, USA: Dynamic Publishers,Inc., 2007, vol. 16, No 3, p. 451-480. ISSN 1056-2176. |
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@article{720907,
author = {Hilscher, Roman and Zeidan, Vera},
article_location = {Atlanta, USA},
article_number = {3},
keywords = {Time scale quadratic functional; Nonnegativity; Positivity; Jacobi equation; Linear Hamiltonian system; Conjugate point; Conjoined basis; Riccati matrix equation; Strengthened Legendre condition; Time-dependent impulsive dynamical system},
language = {eng},
issn = {1056-2176},
journal = {Dynamic Systems and Applications},
title = {Legendre, Jacobi, and Riccati type conditions for time scale variational problem with application},
volume = {16},
year = {2007}
}
TY - JOUR
ID - 720907
AU - Hilscher, Roman - Zeidan, Vera
PY - 2007
TI - Legendre, Jacobi, and Riccati type conditions for time scale variational problem with application
JF - Dynamic Systems and Applications
VL - 16
IS - 3
SP - 451-480
EP - 451-480
PB - Dynamic Publishers,Inc.
SN - 10562176
KW - Time scale quadratic functional
KW - Nonnegativity
KW - Positivity
KW - Jacobi equation
KW - Linear Hamiltonian system
KW - Conjugate point
KW - Conjoined basis
KW - Riccati matrix equation
KW - Strengthened Legendre condition
KW - Time-dependent impulsive dynamical system
N2 - A time scale quadratic problem J with piecewise right-dense continuous coefficients and one varying endpoint is considered. Such problems are ``hybrid'', since they include mixing of continuous- and discrete-time problems. A new notion of a generalized conjugate point involving ``dynamic'' (hybrid) systems and comprising as special cases those known for the continuous- and discrete-time settings is introduced. A type of a strengthened Legendre condition is identified and used to establish characterizations of the nonnegativity and positivity of J in terms of (i) the nonexistence of such conjugate points, (ii) the natural conjoined basis of the associated time scale Jacobi equation, and (iii) a solution of the corresponding time scale Riccati equation. These results furnish second order necessary optimality conditions for a nonlinear time scale variational problem.
ER -
HILSCHER, Roman and Vera ZEIDAN. Legendre, Jacobi, and Riccati type conditions for time scale variational problem with application. \textit{Dynamic Systems and Applications}. Atlanta, USA: Dynamic Publishers,Inc., 2007, vol.~16, No~3, p.~451-480. ISSN~1056-2176.
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