Abstract
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 | |
| Publication status | Published - 18 Jun 2015 |
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Symbolic computations of non-linear observability. / Bianco-Martinez, Ezequiel Julian; Baptista, Murilo Da Silva; Letellier, Christophe.
In: Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, Vol. 91, No. 6, 062912, 18.06.2015.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Symbolic computations of non-linear observability
AU - Bianco-Martinez, Ezequiel Julian
AU - Baptista, Murilo Da Silva
AU - Letellier, Christophe
N1 - Date of Acceptance: 22/05/2015 ACKNOWLEDGEMENTS E.B.M. and M.S.B. acknowledge the Engineering and Physical Sciences Research Council (EPSRC), Grant No. EP/I032608/1. This work was done during a stay of E.B.M. at CORIA (Rouen) and a stay of C.L. at ICSMB (Aberdeen).
PY - 2015/6/18
Y1 - 2015/6/18
N2 - 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. Whenthe governing equations of dynamical systems are high-dimensional and/or rational, analytical computationsof 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 overcomethis 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 coefficientsis straightforward and can be easily analytically carried out as demonstrated in this paper for a 5D rational system.
AB - 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. Whenthe governing equations of dynamical systems are high-dimensional and/or rational, analytical computationsof 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 overcomethis 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 coefficientsis straightforward and can be easily analytically carried out as demonstrated in this paper for a 5D rational system.
U2 - 10.1103/PhysRevE.91.062912
DO - 10.1103/PhysRevE.91.062912
M3 - Article
VL - 91
JO - Physical Review. E, Statistical, Nonlinear and Soft Matter Physics
JF - Physical Review. E, Statistical, Nonlinear and Soft Matter Physics
SN - 1539-3755
IS - 6
M1 - 062912
ER -