3 research outputs found
Observability of dynamical networks from graphic and symbolic approaches
A dynamical network, a graph whose nodes are dynamical systems, is usually
characterized by a large dimensional space which is not always accesible due to
the impossibility of measuring all the variables spanning the state space.
Therefore, it is of the utmost importance to determine a reduced set of
variables providing all the required information for non-ambiguously
distinguish its different states. Inherited from control theory, one possible
approach is based on the use of the observability matrix defined as the
Jacobian matrix of the change of coordinates between the original state space
and the space reconstructed from the measured variables. The observability of a
given system can be accurately assessed by symbolically computing the
complexity of the determinant of the observability matrix and quantified by
symbolic observability coefficients. In this work, we extend the symbolic
observability, previously developed for dynamical systems, to networks made of
coupled -dimensional node dynamics (). From the observability of the
node dynamics, the coupling function between the nodes, and the adjacency
matrix, it is indeed possible to construct the observability of a large network
with an arbitrary topology.Comment: 12 pages, 4 figures made from 12 eps file