paper

A nonlinear graph-based theory for dynamical network observability

arXiv:1803.00851 · doi:10.1103/PhysRevE.98.020303

Abstract

A faithful description of the state of a complex dynamical network would require, in principle, the measurement of all its variables, an infeasible task for systems with practical limited access and composed of many nodes with high dimensional dynamics. However, even if the network dynamics is observable from a reduced set of measured variables, how to reliably identifying such a minimum set of variables providing full observability remains an unsolved problem. From the Jacobian matrix of the governing equations of nonlinear systems, we construct a {\it pruned fluence graph} in which the nodes are the state variables and the links represent {\it only the linear} dynamical interdependences encoded in the Jacobian matrix after ignoring nonlinear relationships. From this graph, we identify the largest connected sub-graphs where there is a path from every node to every other node and there are not outcoming links. In each one of those sub-graphs, at least one node must be measured to correctly monitor the state of the system in a -dimensional reconstructed space. Our procedure is here validated by investigating large-dimensional reaction networks for which the determinant of the observability matrix can be rigorously computed.

5 pages, 2 figures; added references

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