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Admissible Controllability for Linear Time-delay Systems in Banach Spaces : A problem in game theory
https://doi.org/10.15083/00040991
https://doi.org/10.15083/00040991157b2605-5c8c-4e4e-9933-02fda5dac14e
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
scp039002.pdf (732.7 kB)
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| Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
|---|---|---|---|---|---|---|
| 公開日 | 2008-11-19 | |||||
| タイトル | ||||||
| タイトル | Admissible Controllability for Linear Time-delay Systems in Banach Spaces : A problem in game theory | |||||
| 言語 | ||||||
| 言語 | eng | |||||
| 資源タイプ | ||||||
| 資源 | http://purl.org/coar/resource_type/c_6501 | |||||
| タイプ | departmental bulletin paper | |||||
| ID登録 | ||||||
| ID登録 | 10.15083/00040991 | |||||
| ID登録タイプ | JaLC | |||||
| 著者 |
Park, Jong Yeoul
× Park, Jong Yeoul× Nakagiri, Shin-Ichi× Yamamoto, Masahiro |
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| 著者所属 | ||||||
| 著者所属 | Department of Mathematics, Pusan National University|Department of Applied Mathematics, Faculty of Engineering, Kobe University|Department of Mathematics, College of Arts and Sciences, University of Tokyo | |||||
| 抄録 | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | We consider a linear control system with time-delays in a reflexive Banach space X : $dx(t)/dt=A_0x(t)+\int_(-n)^0 d\eta (s)x(t+s)+B(t)u(t) a.e. t>0.$ $x(0)=g^0, x(s)=g^1(s) a.e. s\in [-h,0],$ where $where (g^0,g^1)\in X\times L_p([-h,0] ; X), u\in L_q^(loc) (R^+ ; U),$ U is a reflexive Banach space, $p,q\in (1,\infty ),B(t)$ is a family of bounded linear operators on U to X and A$F_0$ generates a C$F_0$-semigroup, η is a Stieltjes measure. Moreover g$F^1$ and u are assumed to be restricted in ${g^1 ; \parallel g^1\parallel L_(p([-h,0]); X)) \leqq \rho $ and ${u ; \parallel u\parallel_ L_(p([0,T]);U)) \leqq \delta } (\rho \delta >0 ).$ For given $x^0,g^0\in X $ and a given time T>0, we discuss admissible controllability problems : (1) to determine independently g$F^1$ (･) and u (･) such that x(0)=g$F^0$ and $x(T)=x^0 or \parallel x(T)-x^0\parallel \leqq \epsilon $ (\epsilon : a given error). (the cooperative type) (2) to determine u (･) for a given g$F^1$ (･) such that x(0)=g$F^0$ and $\parallel x(T)-x^0\parallel \leqq \epsilon $(the noncooperative type) In this paper, for the both types, we establish necessary and sufficient conditions involving ρ and δ, in order that we can find such g$F^1$ and u. These conditions are expressed in terms of the fundamental solution of the homogeneous system with time-delays. | |||||
| 書誌情報 |
Scientific papers of the College of Arts and Sciences, the University of Tokyo 巻 39, p. 45-55, 発行日 1989 |
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| ISSN | ||||||
| 収録物識別子タイプ | ISSN | |||||
| 収録物識別子 | 02897520 | |||||
| 書誌レコードID | ||||||
| 収録物識別子タイプ | NCID | |||||
| 収録物識別子 | AA10538733 | |||||
| フォーマット | ||||||
| 内容記述タイプ | Other | |||||
| 内容記述 | application/pdf | |||||
| 日本十進分類法 | ||||||
| 主題Scheme | NDC | |||||
| 主題 | 410 | |||||
| 出版者 | ||||||
| 出版者 | The University of Tokyo | |||||
