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RESEARCH PAPERS

A Basic Theorem on Distributed Control and Point Control

[+] Author and Article Information
M. Vidyasagar

Department of Electrical Engineering, Sir George Williams University, Montreal, Canada

T. J. Higgins

Department of Electrical Engineering, University of Wisconsin, Madison, Wisc.

J. Dyn. Sys., Meas., Control 95(1), 64-67 (Mar 01, 1973) (4 pages) doi:10.1115/1.3426651 History: Received December 19, 1972; Online July 13, 2010

Abstract

This paper is concerned with linear distributed parameter systems whose input-output operators are representable in integral form. Two types of control are considered: (i) distributed control which is a function of both a spatial variable x (lying in a compact set Ω) and a time variable t, and (ii) “point” control which is applied at a specific point in Ω and is a function only of t. For such systems, a basic theorem is stated and proved, namely, that there exists a countable subset E of Ω with the following property: any state which can be attained by applying a distributed control can also be attained arbitrarily closely by applying a finite number of point controls applied at points in the set E. The theorem is applied to some specific systems, and further possible applications of the theorem are discussed.

Copyright © 1973 by ASME
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