A deterministic linear quadratic time-inconsistentoptimal control problem

Jiongmin Yong

doi:10.3934/mcrf.2011.1.83

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2011, Volume 1, Issue 1: 83-118. Doi: 10.3934/mcrf.2011.1.83

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A deterministic linear quadratic time-inconsistent optimal control problem

Jiongmin Yong^1,

1.
Department of Mathematics, University of Central Florida, Orlando, FL 32816

Received: September 30, 2010

Revised: October 31, 2010

Published: February 2011

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Abstract

A time-inconsistent optimal control problem is formulated and studied for a controlled linear ordinary differential equation with a quadratic cost functional. A notion of time-consistent equilibrium strategy is introduced for the original time-inconsistent problem. Under certain conditions, we construct an equilibrium strategy which can be represented via a Riccati--Volterra integral equation system. Our approach is based on a study of multi-person hierarchical differential games.

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Mathematics Subject Classification: Primary: 49L20, 49N10, 49N70; Secondary: 91A23, 91A65.

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