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Symmetry Groups and the Observability of PDEs

Bernd Kolar, Markus Schöberl

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Abstract

Abstract Symmetry groups of PDEs allow to transform solutions continuously into other solutions. In this contribution, we use symmetry groups for studying the observability of systems of nonlinear PDEs with input and output. Based on a differential‐geometric representation of the system, we present conditions for the existence of special symmetry groups that do not change the trajectories of the input and the output. If such a symmetry group exists, the system cannot be observable.

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Abstract Symmetry groups of PDEs allow to transform solutions continuously into other solutions. In this contribution, we use symmetry groups for studying the observability of systems of nonlinear PDEs with input and output. Based on a differential‐geometric representation of the system, we present conditions for the existence of special symmetry groups that do not change the trajectories of the input and the output. If such a symmetry group exists, the system cannot be observable.

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Available abstract

Abstract Symmetry groups of PDEs allow to transform solutions continuously into other solutions. In this contribution, we use symmetry groups for studying the observability of systems of nonlinear PDEs with input and output. Based on a differential‐geometric representation of the system, we present conditions for the existence of special symmetry groups that do not change the trajectories of the input and the output. If such a symmetry group exists, the system cannot be observable.

Key concepts: Observability, Symmetry (geometry), Observable, Symmetry group, Nonlinear system, Mathematics, Rotational symmetry, Group (periodic table)

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