Solvability and asymptotic behavior of generalized Riccati equations arising in indefinite stochastic LQ controls

Mustapha Ait Rami; Xi Chen; John B. Moore; Xun Yu Zhou

doi:10.1109/9.911419

Solvability and asymptotic behavior of generalized Riccati equations arising in indefinite stochastic LQ controls

Mustapha Ait Rami^*, Xi Chen, John B. Moore, Xun Yu Zhou

^*Corresponding author for this work

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

142 Citations (Scopus)

Abstract

The optimal control problem in a finite time horizon with an indefinite quadratic cost function for a linear system subject to multiplicative noise on both the state and control can be solved via a constrained matrix differential Riccati equation. In this paper, we provide general necessary and sufficient conditions for the solvability of this generalized differential Riccati equation. Furthermore, its asymptotic behavior is investigated along with its connection to the generalized algebraic Riccati equation associated with the linear quadratic control problem in infinite time horizon. Examples area presented to illustrate the results established.

Original language	English
Pages (from-to)	428-440
Number of pages	13
Journal	IEEE Transactions on Automatic Control
Volume	46
Issue number	3
DOIs	https://doi.org/10.1109/9.911419
Publication status	Published - Mar 2001

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10.1109/9.911419

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@article{60a572de54a84f3f8065afc075eb2138,

title = "Solvability and asymptotic behavior of generalized Riccati equations arising in indefinite stochastic LQ controls",

abstract = "The optimal control problem in a finite time horizon with an indefinite quadratic cost function for a linear system subject to multiplicative noise on both the state and control can be solved via a constrained matrix differential Riccati equation. In this paper, we provide general necessary and sufficient conditions for the solvability of this generalized differential Riccati equation. Furthermore, its asymptotic behavior is investigated along with its connection to the generalized algebraic Riccati equation associated with the linear quadratic control problem in infinite time horizon. Examples area presented to illustrate the results established.",

keywords = "Asymptotic analysis, Generalized Riccati equation, Indefinite stochastic linear quadratic (LQ) control, Linear matrix inequality, Solvability",

author = "Rami, {Mustapha Ait} and Xi Chen and Moore, {John B.} and Zhou, {Xun Yu}",

year = "2001",

month = mar,

doi = "10.1109/9.911419",

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journal = "IEEE Transactions on Automatic Control",

issn = "0018-9286",

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T1 - Solvability and asymptotic behavior of generalized Riccati equations arising in indefinite stochastic LQ controls

AU - Rami, Mustapha Ait

AU - Chen, Xi

AU - Moore, John B.

AU - Zhou, Xun Yu

PY - 2001/3

Y1 - 2001/3

N2 - The optimal control problem in a finite time horizon with an indefinite quadratic cost function for a linear system subject to multiplicative noise on both the state and control can be solved via a constrained matrix differential Riccati equation. In this paper, we provide general necessary and sufficient conditions for the solvability of this generalized differential Riccati equation. Furthermore, its asymptotic behavior is investigated along with its connection to the generalized algebraic Riccati equation associated with the linear quadratic control problem in infinite time horizon. Examples area presented to illustrate the results established.

AB - The optimal control problem in a finite time horizon with an indefinite quadratic cost function for a linear system subject to multiplicative noise on both the state and control can be solved via a constrained matrix differential Riccati equation. In this paper, we provide general necessary and sufficient conditions for the solvability of this generalized differential Riccati equation. Furthermore, its asymptotic behavior is investigated along with its connection to the generalized algebraic Riccati equation associated with the linear quadratic control problem in infinite time horizon. Examples area presented to illustrate the results established.

KW - Asymptotic analysis

KW - Generalized Riccati equation

KW - Indefinite stochastic linear quadratic (LQ) control

KW - Linear matrix inequality

KW - Solvability

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U2 - 10.1109/9.911419

DO - 10.1109/9.911419

M3 - Article

SN - 0018-9286

VL - 46

SP - 428

EP - 440

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 3

ER -

Solvability and asymptotic behavior of generalized Riccati equations arising in indefinite stochastic LQ controls

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