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@article{490556,
author = {Hilscher, Roman and Zeidan, Vera},
article_number = {2},
keywords = {Discrete quadratic functional; Nonnegativity; Positivity; Linear Hamiltonian difference system; Coupled interval; Conjugate interval; Conjoined basis; Riccati difference equation},
language = {eng},
issn = {1023-6198},
journal = {Journal of Difference Equations and Applications},
title = {Coupled intervals in the discrete optimal control},
volume = {10},
year = {2004}
}
TY - JOUR
ID - 490556
AU - Hilscher, Roman - Zeidan, Vera
PY - 2004
TI - Coupled intervals in the discrete optimal control
JF - Journal of Difference Equations and Applications
VL - 10
IS - 2
SP - 151-186
EP - 151-186
PB - Taylor and Francis
SN - 10236198
KW - Discrete quadratic functional
KW - Nonnegativity
KW - Positivity
KW - Linear Hamiltonian difference system
KW - Coupled interval
KW - Conjugate interval
KW - Conjoined basis
KW - Riccati difference equation
N2 - In this paper, we investigate the nonnegativity and positivity of a quadratic functional I with variable (i.e., separable and jointly varying) endpoints in the discrete optimal control setting. We introduce a coupled interval notion, which generalizes (i) the conjugate interval notion known for the fixed right endpoint case, and (ii) the coupled interval notion known in the discrete calculus of variations . We prove necessary and sufficient conditions for the nonnegativity and positivity of I in terms of the nonexistence of such coupled intervals. Furthermore, we characterize the nonnegativity of I in terms of the (previously known notions of) conjugate intervals, a conjoined basis of the associated linear Hamiltonian system, and the solvability of an implicit Riccati equation. This completes the results for the nonnegativity that are parallel to the known ones on the positivity of I .
ER -
HILSCHER, Roman a Vera ZEIDAN. Coupled intervals in the discrete optimal control. \textit{Journal of Difference Equations and Applications}. Taylor and Francis, 2004, roč.~10, č.~2, s.~151-186. ISSN~1023-6198.
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