Sufficient condition for locally unidentifiable edge weights from any single-state trajectory in networked linear systems

Abstract

In this study, we analyse the local identifiability of parameters in linear systems whose state matrix is given by a graph Laplacian. Graph Laplacian is a matrix given by a graph and the weights of its edges, where the weights represent the parameters in those systems. There are cases in which parameter estimation has to be conducted with a single trajectory data. In this case, detecting whether the parameter is locally unidentifiable (non-locally identifiable (LI)) from a single-state trajectory a priori is important. This is because we need conditions to avoid estimating non-LI parameters. Therefore, we address a problem to find the condition which implies that the parameter is non-LI from any single-state trajectory. Then, we obtain a sufficient condition for the parameter to be non-LI from any single-state trajectory. The condition is given based on the number of vertices and edges of the graph and the number of distinct eigenvalues of the graph Laplacian. This paper also presents an example that satisfies the condition.

Keywords

• parameter estimation
• local identifiability
• linear system
• graph laplacian
• undirected graph