On the Time-Inconsistent Deterministic Linear-Quadratic Control

Hongyan Cai; Danhong Chen; Yunfei Peng; Wei Wei

doi:10.1137/21M1419611

On the Time-Inconsistent Deterministic Linear-Quadratic Control

Hongyan Cai, Danhong Chen, Yunfei Peng, Wei Wei

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

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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 language	English
Pages (from-to)	968-991
Number of pages	24
Journal	SIAM Journal on Control and Optimization
Volume	60
Issue number	2
DOIs	https://doi.org/10.1137/21M1419611
Publication status	Published - 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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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.",

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author = "Hongyan Cai and Danhong Chen and Yunfei Peng and Wei Wei",

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AU - Peng, Yunfei

AU - Wei, Wei

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Y1 - 2022/4/18

N2 - 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.

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KW - equilibrium control

KW - intrapersonal game

KW - linear-quadratic control

KW - Riccati equation

KW - time inconsistency

KW - two-point boundary value problem

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On the Time-Inconsistent Deterministic Linear-Quadratic Control

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