Symbolic computations of non-linear observability

Ezequiel Julian Bianco-Martinez; Murilo Da Silva Baptista; Christophe Letellier

doi:10.1103/PhysRevE.91.062912

Symbolic computations of non-linear observability

Ezequiel Julian Bianco-Martinez, Murilo Da Silva Baptista, Christophe Letellier

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Abstract

Observability is a very useful concept for determining whether the dynamics of complicated systems can be correctly reconstructed from a single (univariate or multivariate) time series. When
the governing equations of dynamical systems are high-dimensional and/or rational, analytical computations
of observability coefficients produce large polynomial functions with a number of terms that become exponentially large with the dimension and the nature of the system. In order to overcome
this difficulty, we introduced here a new symbolic observability coefficient based on a symbolic computation of the determinant of the observability matrix. The computation of such coefficients
is straightforward and can be easily analytically carried out as demonstrated in this paper for a 5D rational system.

Original language	English
Article number	062912
Number of pages	10
Journal	Physical Review. E, Statistical, Nonlinear and Soft Matter Physics
Volume	91
Issue number	6
DOIs	https://doi.org/10.1103/PhysRevE.91.062912
Publication status	Published - 18 Jun 2015

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Bianco-Martinez, E. J., Baptista, M. D. S., & Letellier, C. (2015). Symbolic computations of non-linear observability. Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, 91(6), [062912]. https://doi.org/10.1103/PhysRevE.91.062912

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