Alapfogalmak
This work adopts a behavioral perspective to model and analyze linear dynamical networks with only manifest (external or measured) variables, addressing the need to incorporate different experimental settings and providing a unified view of various network models.
Kivonat
This paper presents a behavioral approach to modeling and analyzing linear dynamical networks with only manifest (external or measured) variables. The key contributions are:
Novel graphical representations of behavioral networks are introduced, including signal graphs and system graphs, which provide formal visualizations of the network structure.
An explicit connection between the behavioral network model and the structural vector autoregressive (SVAR) model is established. The regularity of interconnections is shown to be a fundamental assumption underlying SVAR models.
The paper starts by defining the behavioral framework for interconnected linear dynamical systems, where inputs and outputs are not pre-determined. An incidence matrix is used to characterize the sparsity pattern of the interconnection.
Two types of graphical representations are then introduced: the signal graph, which models signals as vertices and systems as edges, and the system graph, which models systems as vertices and signals as edges. These dual representations provide a formal way to visualize the network structure.
The paper then establishes connections between the behavioral network model and the SVAR model, a widely used model in various applications. It is shown that the regularity of interconnections, which requires each component to have distinct and independent outputs, is a fundamental assumption underlying SVAR models. The explicit connections between the graphical representations of the behavioral network and the directed graph of the SVAR model are also discussed.
Finally, the paper discusses situations where the interconnection is not regular, and proposes a way to handle such cases by merging some components into a single component to restore regularity.