Mathematical Control and Related Fields (MCRF)

A deterministic linear quadratic time-inconsistent optimal control problem

Pages: 83 - 118, Volume 1, Issue 1, March 2011      doi:10.3934/mcrf.2011.1.83

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Jiongmin Yong - Department of Mathematics, University of Central Florida, Orlando, FL 32816, United States (email)

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.

Keywords:  Time-inconsistency, linear-quadratic optimal control problem, time-consistent equilibrium strategy, multi-person hierarchical differential games, Riccati--Volterra integral equation system.
Mathematics Subject Classification:  Primary: 49L20, 49N10, 49N70; Secondary: 91A23, 91A65.

Received: October 2010;      Revised: November 2010;      Available Online: March 2011.