A Deterministic Linear Quadratic Time-Inconsistent Optimal Control Problem

Details A Deterministic Linear Quadratic Time-Inconsistent Optimal Control Problem A Deterministic Linear Quadratic Time-Inconsistent Optimal Control Problem

2012-04-09

arxiv.org/abs/1204.1856v1

Mathematical Control and Related Fields, 1 (2011), 83-118

Mathematics

Optimization and Control

24 pages

Scientific paper

10.3934/mcrf.2011.1.83

A time-inconsistent optimal control problem is formulated and studied for a controlled linear ordinary differential equation with quadratic cost functional. A notion of equilibrium control is introduced, which can be regarded as a time-consistent solution to the original time-inconsistent problem. Under certain conditions, we constructively prove the existence of such an equilibrium control which is represented via a forward ordinary differential equation coupled with a backward Riccati--Volterra integral equation. Our constructive approach is based on the introduction of a family of $N$-person non-cooperative differential games.

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