A Deterministic Linear Quadratic Time-Inconsistent Optimal Control Problem

Abstract

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.

24 pages

References in corpus (1)

• Being serious about non-commitment: subgame perfect equilibrium in continuous time

Cited by in corpus (3)

• On Time-Consistent Solution to Time-Inconsistent Linear-Quadratic Optimal Control of Discrete-Time Stochastic Systems
• The Maximum Principle in Time-Inconsistent LQ Optimal Control Problem for Jump Diffusions
• Time-Inconsistent Mean-Field Stochastic LQ Problem: Open-Loop Time-Consistent Control