A deterministic linear quadratic time-inconsistent
optimal control problem
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
Received: October 2010; Revised: November 2010; Available Online: March 2011.
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