An equivalence result in linear-quadratic theory

W.A. van den Broek; J.C. Engwerda; J.M. Schumacher

doi:10.1016/S0005-1098(02)00228-5

An equivalence result in linear-quadratic theory

W.A. van den Broek, J.C. Engwerda, J.M. Schumacher

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

6 Citations (Scopus)

Abstract

We consider the zero-endpoint infinite-horizon LQ problem. We show that the existence of an optimal policy in the class of feedback controls is a sufficient condition for the existence of a stabilizing solution to the algebraic Riccati equation. This result is shown without assuming positive definiteness of the state weighting matrix. The feedback formulation of the optimization problem is natural in the context of differential games and we provide a characterization of feedback Nash equilibria both in a deterministic and stochastic context.

Original language	English
Pages (from-to)	355-359
Number of pages	5
Journal	Automatica
Volume	39
Issue number	2
DOIs	https://doi.org/10.1016/S0005-1098(02)00228-5
Publication status	Published - Feb 2003

Keywords

LQG theory
LQ theory
Differential games
Algebraic Riccati equations

Access to Document

10.1016/S0005-1098(02)00228-5

Cite this

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title = "An equivalence result in linear-quadratic theory",

abstract = "We consider the zero-endpoint infinite-horizon LQ problem. We show that the existence of an optimal policy in the class of feedback controls is a sufficient condition for the existence of a stabilizing solution to the algebraic Riccati equation. This result is shown without assuming positive definiteness of the state weighting matrix. The feedback formulation of the optimization problem is natural in the context of differential games and we provide a characterization of feedback Nash equilibria both in a deterministic and stochastic context.",

keywords = "LQG theory, LQ theory, Differential games, Algebraic Riccati equations",

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AU - van den Broek, W.A.

AU - Engwerda, J.C.

AU - Schumacher, J.M.

PY - 2003/2

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N2 - We consider the zero-endpoint infinite-horizon LQ problem. We show that the existence of an optimal policy in the class of feedback controls is a sufficient condition for the existence of a stabilizing solution to the algebraic Riccati equation. This result is shown without assuming positive definiteness of the state weighting matrix. The feedback formulation of the optimization problem is natural in the context of differential games and we provide a characterization of feedback Nash equilibria both in a deterministic and stochastic context.

AB - We consider the zero-endpoint infinite-horizon LQ problem. We show that the existence of an optimal policy in the class of feedback controls is a sufficient condition for the existence of a stabilizing solution to the algebraic Riccati equation. This result is shown without assuming positive definiteness of the state weighting matrix. The feedback formulation of the optimization problem is natural in the context of differential games and we provide a characterization of feedback Nash equilibria both in a deterministic and stochastic context.

KW - LQG theory

KW - LQ theory

KW - Differential games

KW - Algebraic Riccati equations

U2 - 10.1016/S0005-1098(02)00228-5

DO - 10.1016/S0005-1098(02)00228-5

M3 - Article

SN - 0005-1098

VL - 39

SP - 355

EP - 359

JO - Automatica

JF - Automatica

IS - 2

ER -