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Deterministic time-inconsistent optimal control problems — an essentially cooperative approach

Deterministic time-inconsistent optimal control problems — an essentially cooperative approach A general deterministic time-inconsistent optimal control problem is formulated for ordinary differential equations. To find a time-consistent equilibrium value function and the corresponding time-consistent equilibrium control, a non-cooperative N-person differential game (but essentially cooperative in some sense) is introduced. Under certain conditions, it is proved that the open-loop Nash equilibrium value function of the N-person differential game converges to a time-consistent equilibrium value function of the original problem, which is the value function of a time-consistent optimal control problem. Moreover, it is proved that any optimal control of the time-consistent limit problem is a time-consistent equilibrium control of the original problem. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Deterministic time-inconsistent optimal control problems — an essentially cooperative approach

Yong, Jiong-min
Acta Mathematicae Applicatae Sinica , Volume 28 (1) – Dec 13, 2011
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References (26)

Publisher
Springer Journals
Copyright
Copyright © 2012 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics; Applications of Mathematics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-012-0120-3
Publisher site
See Article on Publisher Site

Abstract

A general deterministic time-inconsistent optimal control problem is formulated for ordinary differential equations. To find a time-consistent equilibrium value function and the corresponding time-consistent equilibrium control, a non-cooperative N-person differential game (but essentially cooperative in some sense) is introduced. Under certain conditions, it is proved that the open-loop Nash equilibrium value function of the N-person differential game converges to a time-consistent equilibrium value function of the original problem, which is the value function of a time-consistent optimal control problem. Moreover, it is proved that any optimal control of the time-consistent limit problem is a time-consistent equilibrium control of the original problem.

Journal

Acta Mathematicae Applicatae Sinica – Springer Journals

Published: Dec 13, 2011

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