Ball, J. M. and Marsden, J. E. and Slemrod, M. (1982) Controllability for Distributed Bilinear Systems. SIAM Journal on Control and Optimization, 20 (4). pp. 575-597. ISSN 0363-0129. doi:10.1137/0320042. https://resolver.caltech.edu/CaltechAUTHORS:BALsiamjco82
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Abstract
This paper studies controllability of systems of the form ${{dw} / {dt}} = \mathcal {A}w + p(t)\mathcal {B}w$ where $\mathcal{A}$ is the infinitesimal generator of a $C^0$ semigroup of bounded linear operators $e^{\mathcal{A}t} $ on a Banach space $X$, $\mathcal{B}:X \to X$ is a $C^1$ map, and $p \in L^1 ([0,T];\mathbb{R})$ is a control. The paper (i) gives conditions for elements of $X$ to be accessible from a given initial state $w_0$ and (ii) shows that controllability to a full neighborhood in $X$ of $w_0$ is impossible for $\dim X = \infty $. Examples of hyperbolic partial differential equations are provided.
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Additional Information: | ©1982 Society for Industrial and Applied Mathematics Received by the editors March 24, 1981, and in revised form September 25, 1981. The research of this author [J.M.B.] was supported in part by the U.S. Army Research Office under contract DAAG29-79-C-0086, the National Science Foundation under grant MCS-78-06718 and a United Kingdom Science Research Council Fellowship. The research of this author [J.E.M.] was supported in part by the U.S. Army Research Office under contract DAAG29-79-C-0086 and the National Science Foundation under grant MCS-78-06718. The research of this author [M.S.] was supported in part by the National Science Foundation under grant MCS-79-02773 and by the Air Force Office of Scientific Research, Air Force Systems Command, United States Air Force under contract/grant AFOSR-81-0172. | ||||||
Issue or Number: | 4 | ||||||
DOI: | 10.1137/0320042 | ||||||
Record Number: | CaltechAUTHORS:BALsiamjco82 | ||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:BALsiamjco82 | ||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
ID Code: | 4635 | ||||||
Collection: | CaltechAUTHORS | ||||||
Deposited By: | Archive Administrator | ||||||
Deposited On: | 30 Aug 2006 | ||||||
Last Modified: | 08 Nov 2021 20:18 |
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