Partial Observability and Its Consistency for Linear PDEs

Kang, Wei; Xu, Liang

doi:10.3182/20130904-3-fr-2041.00011

Cited by 3 publications

(2 citation statements)

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“…Moreover, computational methods of dynamic optimization provide practical tools to numerically approximate the observability of complicated systems that cannot be treated using an analytic approach. This concept is further developed in [9] where partial observability is developed for systems defined by PDEs.…”

Section: Introductionmentioning

confidence: 99%

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Partial Observability for the Shallow Water Equations

King

Kang

2013

2013 Proceedings of the Conference on Control and Its Applications

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In this paper we discuss a quantitative measure of partial observability for the shallow water equations. The quantity is consistent if approximated using well posed approximation schemes. A first order approximation of an unobservability index using empirical gramian is discussed. For linear systems with full state observability, the empirical gramian is equivalent to the observability gramian in control theory. We present algorithms for the computation of partial observability for the shallow water equations. These algorithms approximate the unobservability index using the empirical gramian via the nonlinear system and the linearized system given by the tangent linear model. This work has applications to optimal sensor placement for numerical weather prediction.

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Section: Introductionmentioning

confidence: 99%

“…In §3 we provide the definition for observability for nonlinear PDEs and the unobservability index is defined. In [9] the framework for partial observability is introduced for systems based on PDEs. The empirical gramian is introduced and the relationship between the empirical gramian and the unobservability index is addressed in §4.…”

Section: Introductionmentioning

confidence: 99%