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Partial Observability and its Consistency for PDEs (1401.0235v1)
Published 1 Jan 2014 in math.OC and math.DS
Abstract: In this paper, a quantitative measure of partial observability is defined for PDEs. The quantity is proved to be consistent if the PDE is approximated using well-posed approximation schemes. A first order approximation of an unobservability index using an empirical Gramian is introduced. Several examples are presented to illustrate the concept of partial observability, including Burgers' equation and a one-dimensional nonlinear shallow water equation.