TY - JOUR

T1 - From exact observability to identification of singular sources

AU - Tucsnak, Marius

AU - Weiss, George

N1 - Publisher Copyright:
© 2014, Springer-Verlag London.

PY - 2014/3

Y1 - 2014/3

N2 - We give general results about the identifiability of source terms for infinite-dimensional linear systems that are exactly observable. We allow the source term to be unbounded, i.e., not contained in the state space, but in one of a sequence of extended spaces. We show that the operator from the source term to the output function is bounded from below, in suitable norms. We apply the main result to a system described by the wave equation in a bounded (Formula presented.)-dimensional domain. We derive results of independent interest concerning the range of the input map of an exactly controllable system, when restricted to various spaces of smooth input functions.

AB - We give general results about the identifiability of source terms for infinite-dimensional linear systems that are exactly observable. We allow the source term to be unbounded, i.e., not contained in the state space, but in one of a sequence of extended spaces. We show that the operator from the source term to the output function is bounded from below, in suitable norms. We apply the main result to a system described by the wave equation in a bounded (Formula presented.)-dimensional domain. We derive results of independent interest concerning the range of the input map of an exactly controllable system, when restricted to various spaces of smooth input functions.

KW - Exact controllability

KW - Exact observability

KW - Inverse problems

KW - Point sources

KW - Wave equation

UR - http://www.scopus.com/inward/record.url?scp=84922836138&partnerID=8YFLogxK

U2 - 10.1007/s00498-014-0132-z

DO - 10.1007/s00498-014-0132-z

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AN - SCOPUS:84922836138

SN - 0932-4194

VL - 27

SP - 1

EP - 21

JO - Mathematics of Control, Signals, and Systems

JF - Mathematics of Control, Signals, and Systems

IS - 1

ER -