Optimal control problems with time inconsistency

Wei Ji; Wei Ji

doi:10.3934/era.2023024

Electronic Research Archive

2023, Volume 31, Issue 1: 492-508. doi: 10.3934/era.2023024

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Research article

Optimal control problems with time inconsistency

Wei Ji ^{1,2
,
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1.
Department of Mathematics, Guizhou University, Guiyang 55025, Guizhou, China
2.
School of Information and Management, Guizhou Polytechnic of Construction, Guiyang 551400, Guizhou, China

Received: 15 September 2022 Revised: 04 November 2022 Accepted: 10 November 2022 Published: 11 November 2022

In the present study, the necessary and sufficient conditions of equilibrium control for general optimal control problems with time inconsistency are established in sense of open-loop. As an application, the linear quadratic optimal control problems with time inconsistency were also explored and an explicit equilibrium control is constructed.
- time inconsistency,
- two-point boundary value problem,
- open-loop,
- equilibrium control,
- quasi-variational problem
Citation: Wei Ji. Optimal control problems with time inconsistency[J]. Electronic Research Archive, 2023, 31(1): 492-508. doi: 10.3934/era.2023024

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Abstract

In the present study, the necessary and sufficient conditions of equilibrium control for general optimal control problems with time inconsistency are established in sense of open-loop. As an application, the linear quadratic optimal control problems with time inconsistency were also explored and an explicit equilibrium control is constructed.

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