Global Structure Identifiability and Reconstructibility of an NDS with Descriptor Subsystems

TL;DR

This paper establishes matrix rank-based conditions for the global identifiability and reconstructibility of subsystem interactions in a networked dynamic system with descriptor subsystems, aiding in system analysis and experiment design.

Contribution

It derives necessary and sufficient conditions for identifiability and reconstructibility of subsystem interactions in NDS with descriptor form, considering minimal assumptions.

Findings

Identifiability conditions depend on matrix rank criteria.

Reconstructibility can be verified per subsystem, facilitating large-scale analysis.

Output differences are more sensitive near system instability.

Abstract

This paper investigates requirements on a networked dynamic system (NDS) such that its subsystem interactions can be solely determined from experiment data or reconstructed from its overall model. The NDS is constituted from several subsystems whose dynamics are described through a descriptor form. Except regularity on each subsystem and the whole NDS, no other restrictions are put on either subsystem dynamics or subsystem interactions. A matrix rank based necessary and sufficient condition is derived for the global identifiability of subsystem interactions, which leads to several conclusions about NDS structure identifiability when there is some a priori information. This matrix also gives an explicit description for the set of subsystem interactions that can not be distinguished from experiment data only. In addition, under a well-posedness assumption, a necessary and sufficient condition is obtained for the reconstructibility of subsystem interactions from an NDS descriptor form model. This condition can be verified with each subsystem separately and is therefore attractive in the analysis and synthesis of a large-scale NDS. Simulation results show that rather than increases monotonically with the distance of subsystem interactions to the undifferentiable set, the magnitude of the external output differences between two NDSs with distinct subsystem interactions increases much more rapidly when one of them is close to be unstable. In addition, directions of probing signals are also very important in distinguishing external outputs of distinctive NDSs.These findings are expected to be helpful in identification experiment designs, etc.