On the Time-Inconsistent Deterministic Linear-Quadratic Control

Hongyan Cai, Danhong Chen, Yunfei Peng, Wei Wei

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Abstract

A fundamental theory of deterministic linear-quadratic (LQ) control is the equivalent relationship between control problems, two-point boundary value problems, and Riccati equations. In this paper, we extend the equivalence to a general time-inconsistent deterministic LQ problem, where the inconsistency arises from nonexponential discount functions. By studying the solvability of the Riccati equation, we show the existence and uniqueness of the linear equilibrium for the time-inconsistent LQ problem.

Original languageEnglish
Pages (from-to)968-991
Number of pages24
JournalSIAM Journal on Control and Optimization
Volume60
Issue number2
DOIs
Publication statusPublished - 18 Apr 2022

Keywords

  • equilibrium control
  • intrapersonal game
  • linear-quadratic control
  • Riccati equation
  • time inconsistency
  • two-point boundary value problem

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

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