Path-Based Conditions for the Identifiability of Non-additive Nonlinear Networks with Full Measurements

TL;DR

This paper investigates the conditions under which nonlinear networks with full measurements and non-additive dynamics can be uniquely identified, providing new criteria based on graph paths for certain classes of functions.

Contribution

It introduces a path-based sufficient and necessary condition for identifiability in nonlinear networks, extending previous results to non-additive and polynomial cases.

Findings

Vertex-disjoint path condition guarantees identifiability for analytic functions.

For polynomial functions, the path condition is both necessary and sufficient.

The condition is not necessary for additive nonlinear models.

Abstract

We analyze the identifiability of nonlinear networks with node dynamics characterized by functions that are non-additive. We consider the full measurement case (all the nodes are measured) in the path-independent delay scenario where all the excitation signals of a specific node have the same delay in the output of a measured node. Based on the notion of a generic nonlinear matrix associated with the network, we introduce the concept of generic identifiability and characterize the space of functions that satisfies this property. For directed acyclic graphs (DAGs) characterized by analytic functions, we derive a sufficient condition for identifiability based on vertex-disjoint paths from excited nodes to the in-neighbors of each node in the network. Furthermore, when we consider the class of polynomial functions, by using well-known results on algebraic varieties, we prove that the vertex-disjoint path condition is also necessary. Finally, we show that this identifiability condition is not necessary for the additive nonlinear model. Some examples are added to illustrate the results.