# Pointwise and Internal Controllability for the Wave Equation

Pointwise and Internal Controllability for the Wave Equation Abstract. Problems of internal and pointwise observation and control for the one-dimensional wave equation arise in the simulation of control and identification processes in electrical engineering, flaw detection, and medical tomography. The generally accepted way of modelling sensors and actuators as pointlike objects leads to results which may make no apparent physical sense: they may depend, for instance, on the rationality or irrationality of the location for a point sensor or actuator. We propose a new formulation of sensor (actuator) action, expressed mathematically by using somewhat unconventional spaces for data presentation and processing. For interaction restricted to an interval of length ε , the limit system of observation (or control) now makes sense when ε tends to zero without a sensitive dependence on the precise location of the limiting point. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

# Pointwise and Internal Controllability for the Wave Equation

, Volume 46 (3) – Dec 19, 2002
18 pages

/lp/springer_journal/pointwise-and-internal-controllability-for-the-wave-equation-y00QvAJd8i
Publisher
Springer-Verlag
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-002-0747-1
Publisher site
See Article on Publisher Site

### Abstract

Abstract. Problems of internal and pointwise observation and control for the one-dimensional wave equation arise in the simulation of control and identification processes in electrical engineering, flaw detection, and medical tomography. The generally accepted way of modelling sensors and actuators as pointlike objects leads to results which may make no apparent physical sense: they may depend, for instance, on the rationality or irrationality of the location for a point sensor or actuator. We propose a new formulation of sensor (actuator) action, expressed mathematically by using somewhat unconventional spaces for data presentation and processing. For interaction restricted to an interval of length ε , the limit system of observation (or control) now makes sense when ε tends to zero without a sensitive dependence on the precise location of the limiting point.

### Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Dec 19, 2002

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