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Controllability for Distributed Bilinear Systems

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. http://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.


Item Type:Article
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.
Record Number:CaltechAUTHORS:BALsiamjco82
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:BALsiamjco82
Alternative URL:http://dx.doi.org/10.1137/0320042
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:26 Dec 2012 09:00

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