The Consistency of Partial Observability for PDEs

Details The Consistency of Partial Observability for PDEs The Consistency of Partial Observability for PDEs

2011-11-24

arxiv.org/abs/1111.5846v1

Mathematics

Dynamical Systems

28 pages, 3 figures

Scientific paper

In this paper, a new definition of observability is introduced for PDEs. It is a quantitative measure of partial observability. The quantity is proved to be consistent if approximated using well posed approximation schemes. A first order approximation of an unobservability index using empirical gramian is introduced. For linear systems with full state observability, the empirical gramian is equivalent to the observability gramian in control theory. The consistency of the defined observability is exemplified using a Burgers' equation.

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