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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| Published in | IEEE transactions on automatic control Vol. 46; no. 3; pp. 428 - 440 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
IEEE
01.03.2001
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0018-9286 1558-2523 |
| DOI | 10.1109/9.911419 |
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| 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 finite time horizon. Examples are presented to illustrate the results established. |
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| AbstractList | 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 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 are presented to illustrate the results established. (Author) 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. |
| Author | Xi Chen Rami, M.A. Xun Yu Zhou Moore, J.B. |
| Author_xml | – sequence: 1 givenname: M.A. surname: Rami fullname: Rami, M.A. organization: Dept. of Syst. Eng. & Eng. Manage., Chinese Univ. of Hong Kong, Shatin, China – sequence: 2 surname: Xi Chen fullname: Xi Chen – sequence: 3 givenname: J.B. surname: Moore fullname: Moore, J.B. – sequence: 4 surname: Xun Yu Zhou fullname: Xun Yu Zhou |
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| SubjectTerms | 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 |
| Title | Solvability and asymptotic behavior of generalized Riccati equations arising in indefinite stochastic LQ controls |
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