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The Linear Quadratic Regulator Problem for a Class of Controlled Systems Modeled by Singularly Perturbed Ito Differential Equations
https://hiroshima.repo.nii.ac.jp/records/2008777
https://hiroshima.repo.nii.ac.jp/records/2008777bd00da7f-1c11-4203-8f37-98f17c4c9b52
| Item type | デフォルトアイテムタイプ_（フル）(1) | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 公開日 | 2023-03-18 | |||||||||||
| タイトル | ||||||||||||
| タイトル | The Linear Quadratic Regulator Problem for a Class of Controlled Systems Modeled by Singularly Perturbed Ito Differential Equations | |||||||||||
| 言語 | en | |||||||||||
| 作成者 |
Dragan, Vasile
× Dragan, Vasile
× Mukaidani, Hiroaki
× Shi, Peng
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| アクセス権 | ||||||||||||
| アクセス権 | open access | |||||||||||
| アクセス権URI | http://purl.org/coar/access_right/c_abf2 | |||||||||||
| 権利情報 | ||||||||||||
| 権利情報 | (c) 2012 Society for Industrial and Applied Mathematics | |||||||||||
| 主題 | ||||||||||||
| 主題Scheme | Other | |||||||||||
| 主題 | singularly perturbed control systems | |||||||||||
| 主題 | ||||||||||||
| 主題Scheme | Other | |||||||||||
| 主題 | asymptotic behavior | |||||||||||
| 主題 | ||||||||||||
| 主題Scheme | Other | |||||||||||
| 主題 | stabilizing solution | |||||||||||
| 主題 | ||||||||||||
| 主題Scheme | NDC | |||||||||||
| 主題 | 007 | |||||||||||
| 内容記述 | ||||||||||||
| 内容記述 | This paper discusses an infinite-horizon linear quadratic (LQ) optimal control problem involving state-and control-dependent noise in singularly perturbed stochastic systems. First, an asymptotic structure along with a stabilizing solution for the stochastic algebraic Riccati equation (ARE) are newly established. It is shown that the dominant part of this solution can be obtained by solving a parameter-independent system of coupled Riccati-type equations. Moreover, sufficient conditions for the existence of the stabilizing solution to the problem are given. A new sequential numerical algorithm for solving the reduced-order AREs is also described. Based on the asymptotic behavior of the ARE, a class of O(root epsilon) approximate controller that stabilizes the system is obtained. Unlike the existing results in singularly perturbed deterministic systems, it is noteworthy that the resulting controller achieves an O(epsilon) approximation to the optimal cost of the original LQ optimal control problem. As a result, the proposed control methodology can be applied to practical applications even if the value of the small parameter epsilon is not precisely known. | |||||||||||
| 言語 | en | |||||||||||
| 出版者 | ||||||||||||
| 出版者 | Siam Publications | |||||||||||
| 言語 | ||||||||||||
| 言語 | eng | |||||||||||
| 資源タイプ | ||||||||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||||||||
| 資源タイプ | journal article | |||||||||||
| 出版タイプ | ||||||||||||
| 出版タイプ | VoR | |||||||||||
| 出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |||||||||||
| 関連情報 | ||||||||||||
| 識別子タイプ | DOI | |||||||||||
| 関連識別子 | 10.1137/100798661 | |||||||||||
| 関連情報 | ||||||||||||
| 識別子タイプ | DOI | |||||||||||
| 関連識別子 | http://dx.doi.org/10.1137/100798661 | |||||||||||
| 収録物識別子 | ||||||||||||
| 収録物識別子タイプ | ISSN | |||||||||||
| 収録物識別子 | 0363-0129 | |||||||||||
| 収録物識別子 | ||||||||||||
| 収録物識別子タイプ | NCID | |||||||||||
| 収録物識別子 | AA00831265 | |||||||||||
| 開始ページ | ||||||||||||
| 開始ページ | 448 | |||||||||||
| 書誌情報 |
SIAM Journal on Control and Optimization SIAM Journal on Control and Optimization 巻 50, 号 1, p. 448-470, 発行日 2012 |
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| 旧ID | 34755 | |||||||||||
