Global stabilization in nonlinear discrete systems with time-delay

Anatoli F. Ivanov; Musa A. Mammadov; Sergei I. Trofimchuk

doi:10.1007/s10898-012-9862-y

Global stabilization in nonlinear discrete systems with time-delay

Anatoli F. Ivanov, Musa A. Mammadov, Sergei I. Trofimchuk

Penn State Wilkes-Barre

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

A class of scalar nonlinear difference equations with delay is considered. Sufficient conditions for the global asymptotic stability of a unique equilibrium are given. Applications in economics and other fields lead to consideration of associated optimal control problems. An optimal control problem of maximizing a consumption functional is stated. The existence of optimal solutions is established and their stability (the turnpike property) is proved.

Original language	English (US)
Pages (from-to)	251-263
Number of pages	13
Journal	Journal of Global Optimization
Volume	56
Issue number	2
DOIs	https://doi.org/10.1007/s10898-012-9862-y
State	Published - Jun 2013

All Science Journal Classification (ASJC) codes

Computer Science Applications
Management Science and Operations Research
Control and Optimization
Applied Mathematics

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title = "Global stabilization in nonlinear discrete systems with time-delay",

abstract = "A class of scalar nonlinear difference equations with delay is considered. Sufficient conditions for the global asymptotic stability of a unique equilibrium are given. Applications in economics and other fields lead to consideration of associated optimal control problems. An optimal control problem of maximizing a consumption functional is stated. The existence of optimal solutions is established and their stability (the turnpike property) is proved.",

author = "Ivanov, {Anatoli F.} and Mammadov, {Musa A.} and Trofimchuk, {Sergei I.}",

note = "Funding Information: Anatoli Ivanov was supported in part by CONICYT (Chile), project MEC 801100006. S. Trofimchuk was partially supported by FONDECYT (Chile), project 1110309.",

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AU - Ivanov, Anatoli F.

AU - Mammadov, Musa A.

AU - Trofimchuk, Sergei I.

N1 - Funding Information: Anatoli Ivanov was supported in part by CONICYT (Chile), project MEC 801100006. S. Trofimchuk was partially supported by FONDECYT (Chile), project 1110309.

PY - 2013/6

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N2 - A class of scalar nonlinear difference equations with delay is considered. Sufficient conditions for the global asymptotic stability of a unique equilibrium are given. Applications in economics and other fields lead to consideration of associated optimal control problems. An optimal control problem of maximizing a consumption functional is stated. The existence of optimal solutions is established and their stability (the turnpike property) is proved.

AB - A class of scalar nonlinear difference equations with delay is considered. Sufficient conditions for the global asymptotic stability of a unique equilibrium are given. Applications in economics and other fields lead to consideration of associated optimal control problems. An optimal control problem of maximizing a consumption functional is stated. The existence of optimal solutions is established and their stability (the turnpike property) is proved.

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SN - 0925-5001

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ER -

Global stabilization in nonlinear discrete systems with time-delay

Abstract

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