Network reconstruction is the process of recovering a unique structured representation of some dynamic system using input-output data and some additional knowledge about the structure of the system. Many network reconstruction algorithms have been proposed in recent years, most dealing with the reconstruction of strictly proper networks (i.e., networks that require delays in all dynamics between measured variables). However, no reconstruction technique presently exists capable of recovering both the structure and dynamics of networks where links are proper (delays in dynamics are not required) and not necessarily strictly proper.The ultimate objective of this dissertation is to develop algorithms capable of reconstructing proper networks, and this objective will be addressed in three parts. The first part lays the foundation for the theory of mathematical representations of proper networks, including an exposition on when such networks are well-posed (i.e., physically realizable). The second part studies the notions of abstractions of a network, which are other networks that preserve certain properties of the original network but contain less structural information. As such, abstractions require less a priori information to reconstruct from data than the original network, which allows previously-unsolvable problems to become solvable. The third part addresses our original objective and presents reconstruction algorithms to recover proper networks in both the time domain and in the frequency domain.
College and Department
Physical and Mathematical Sciences; Computer Science
BYU ScholarsArchive Citation
Woodbury, Nathan Scott, "Representation and Reconstruction of Linear, Time-Invariant Networks" (2019). Theses and Dissertations. 7402.
Dynamic systems, networks, network reconstruction, target specificity, system identification, learning, linear systems, system representations, state space models, generalized state space models, dynamical structure functions, dynamical network functions, DSF, DNF, multi-DSF, feedback, well-posedness, algebraic loops, representability, abstraction, immersion, identifiability, informativity, data, proper systems, strictly proper systems, causality, strict causality, frequency domain, time domain