Linear-quadratic control of discrete-time stochastic systems with indefinite weight matrices and mean-field Terms

Yuan Hua Ni; Xun Li; Ji Feng Zhang

Linear-quadratic control of discrete-time stochastic systems with indefinite weight matrices and mean-field Terms

Yuan Hua Ni, Xun Li, Ji Feng Zhang

The Hong Kong Polytechnic University

Research output: Chapter in book / Conference proceeding › Conference article published in proceeding or book › Academic research › peer-review

4 Citations (Scopus)

Abstract

In this paper, the linear-quadratic optimal control problem is considered for discrete-time stochastic systems with indefinite weight matrices in the cost function and mean-field terms in both the cost function and system dynamics. A set of generalized difference Riccati equations (GDREs) is introduced in terms of algebraic equality constraints and matrix pseudo-inverse. It is shown that the solvability of the GDRE is not only sufficient but also necessary for the well-posedness of the indefinite mean-field linear-quadratic optimal control problem and the existence of optimal feedback as well as open-loop controls.

Original language	English
Title of host publication	19th IFAC World Congress IFAC 2014, Proceedings
Publisher	IFAC Secretariat
Pages	9750-9755
Number of pages	6
Volume	19
ISBN (Electronic)	9783902823625
Publication status	Published - 1 Jan 2014
Event	19th IFAC World Congress on International Federation of Automatic Control, IFAC 2014 - Cape Town, South Africa Duration: 24 Aug 2014 → 29 Aug 2014

Conference

Conference	19th IFAC World Congress on International Federation of Automatic Control, IFAC 2014
Country/Territory	South Africa
City	Cape Town
Period	24/08/14 → 29/08/14

Keywords

Indefinite linear-quadratic control
Mean-field theory
Stochastic system

ASJC Scopus subject areas

Control and Systems Engineering

Cite this

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title = "Linear-quadratic control of discrete-time stochastic systems with indefinite weight matrices and mean-field Terms",

abstract = "In this paper, the linear-quadratic optimal control problem is considered for discrete-time stochastic systems with indefinite weight matrices in the cost function and mean-field terms in both the cost function and system dynamics. A set of generalized difference Riccati equations (GDREs) is introduced in terms of algebraic equality constraints and matrix pseudo-inverse. It is shown that the solvability of the GDRE is not only sufficient but also necessary for the well-posedness of the indefinite mean-field linear-quadratic optimal control problem and the existence of optimal feedback as well as open-loop controls.",

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Linear-quadratic control of discrete-time stochastic systems with indefinite weight matrices and mean-field Terms. / Ni, Yuan Hua; Li, Xun; Zhang, Ji Feng.
19th IFAC World Congress IFAC 2014, Proceedings. Vol. 19 IFAC Secretariat, 2014. p. 9750-9755.

Research output: Chapter in book / Conference proceeding › Conference article published in proceeding or book › Academic research › peer-review

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N2 - In this paper, the linear-quadratic optimal control problem is considered for discrete-time stochastic systems with indefinite weight matrices in the cost function and mean-field terms in both the cost function and system dynamics. A set of generalized difference Riccati equations (GDREs) is introduced in terms of algebraic equality constraints and matrix pseudo-inverse. It is shown that the solvability of the GDRE is not only sufficient but also necessary for the well-posedness of the indefinite mean-field linear-quadratic optimal control problem and the existence of optimal feedback as well as open-loop controls.

AB - In this paper, the linear-quadratic optimal control problem is considered for discrete-time stochastic systems with indefinite weight matrices in the cost function and mean-field terms in both the cost function and system dynamics. A set of generalized difference Riccati equations (GDREs) is introduced in terms of algebraic equality constraints and matrix pseudo-inverse. It is shown that the solvability of the GDRE is not only sufficient but also necessary for the well-posedness of the indefinite mean-field linear-quadratic optimal control problem and the existence of optimal feedback as well as open-loop controls.

KW - Indefinite linear-quadratic control

KW - Mean-field theory

KW - Stochastic system

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M3 - Conference article published in proceeding or book

VL - 19

SP - 9750

EP - 9755

BT - 19th IFAC World Congress IFAC 2014, Proceedings

PB - IFAC Secretariat

T2 - 19th IFAC World Congress on International Federation of Automatic Control, IFAC 2014

Y2 - 24 August 2014 through 29 August 2014

ER -

Linear-quadratic control of discrete-time stochastic systems with indefinite weight matrices and mean-field Terms

Abstract

Conference

Keywords

ASJC Scopus subject areas

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