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

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 suff...

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 46; no. 3; pp. 428 - 440
Main Authors Rami, M.A., Xi Chen, Moore, J.B., Xun Yu Zhou
Format Journal Article
LanguageEnglish
Published New York IEEE 01.03.2001
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Asymptotic properties
Control equipment
Control systems
Cost function
Differential equations
Horizon
Linear quadratic
Linear systems
Mathematical analysis
Nonlinear equations
Optimal control
Riccati equation
Riccati equations
Stochastic processes
Stochastic resonance
Stochastic systems
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ISSN0018-9286
1558-2523
DOI10.1109/9.911419

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Summary: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 finite time horizon. Examples are presented to illustrate the results established.
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ISSN:0018-9286
1558-2523
DOI:10.1109/9.911419