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. 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.
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. 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.
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 -