Title

Deterministic Time-Inconsistent Optimal Control Problems - An Essentially Cooperative Approach

Keywords

multi-level hierarchical differential games; pre-committed optimal control; time-consistent equilibrium control; time-inconsistency

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. © 2012 The Editorial Office of AMAS & Springer-Verlag Berlin Heidelberg.

Publication Date

1-1-2012

Publication Title

Acta Mathematicae Applicatae Sinica

Volume

28

Issue

1

Number of Pages

1-30

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s10255-012-0120-3

Socpus ID

83355170525 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/83355170525

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