On the Time-Inconsistent Deterministic Linear-Quadratic Control
Hongyan Cai, Danhong Chen, Yunfei Peng, Wei Wei
TL;DR
This paper extends classical deterministic linear-quadratic control theory to time-inconsistent problems caused by non-exponential discounting, establishing conditions for the existence and uniqueness of solutions.
Contribution
It generalizes the equivalence between control problems, boundary value problems, and Riccati equations to time-inconsistent LQ problems with non-exponential discount functions.
Findings
Established the equivalence between control problems and Riccati equations for time-inconsistent LQ problems.
Proved the existence and uniqueness of linear equilibrium solutions.
Analyzed the solvability conditions of the Riccati equation in this context.
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 non-exponential 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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Taxonomy
TopicsStability and Control of Uncertain Systems · Optimization and Variational Analysis