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@article{488396,
author = {Hilscher, Roman and Zeidan, Vera},
article_number = {10},
keywords = {discrete maximum principle; linear Hamiltonian difference system; discrete quadratic functional; accessory problem; optimality conditions; conjugate interval; Riccati difference equation},
language = {eng},
issn = {1023-6198},
journal = {Journal of Difference Equations and Applications},
title = {Discrete optimal control: second order optimality conditions},
volume = {8},
year = {2002}
}
TY - JOUR
ID - 488396
AU - Hilscher, Roman - Zeidan, Vera
PY - 2002
TI - Discrete optimal control: second order optimality conditions
JF - Journal of Difference Equations and Applications
VL - 8
IS - 10
SP - 875-896
EP - 875-896
PB - Taylor and Francis
SN - 10236198
KW - discrete maximum principle
KW - linear Hamiltonian difference system
KW - discrete quadratic functional
KW - accessory problem
KW - optimality conditions
KW - conjugate interval
KW - Riccati difference equation
N2 - In this paper we present a survey and refinement of our recent results in the discrete optimal control theory. For a general nonlinear discrete optimal control problem (P), second order necessary and sufficient optimality conditions are derived via the nonnegativity and positivity of the discrete quadratic functional I corresponding to its second variation. Thus, we fill the gap in the discrete-time theory by connecting the discrete control problems with the theory of conjugate intervals, Hamiltonian systems, and Riccati equations.
ER -
HILSCHER, Roman a Vera ZEIDAN. Discrete optimal control: second order optimality conditions. \textit{Journal of Difference Equations and Applications}. Taylor and Francis, 2002, roč.~8, č.~10, s.~875-896. ISSN~1023-6198.
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