Network Reconstruction from Intrinsic Noise: Non-Minimum-Phase Systems

Hayden, David; Yuan, Ye; Goncalves, Jorge

Reference : Network Reconstruction from Intrinsic Noise: Non-Minimum-Phase Systems


	Document type :	Scientific congresses, symposiums and conference proceedings : Paper published in a book
	Discipline(s) :	Engineering, computing & technology : Multidisciplinary, general & others
	To cite this reference:	http://hdl.handle.net/10993/20329

Title :	Network Reconstruction from Intrinsic Noise: Non-Minimum-Phase Systems
Language :	English
Author, co-author :	Hayden, David []
	Yuan, Ye []
	Goncalves, Jorge [University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > >]
Publication date :	2014
Main document title :	The proceedings of the The 19th World Congress of The International Federation of Automatic Control
Peer reviewed :	Yes
Event name :	19th World Congress of The International Federation of Automatic Control
Event date :	August 24-29, 2014
Event place (city) :	Cape Town
Event country :	South Africa
Keywords :	[en] Linear networks ; Closed-loop identification ; Identifiability ; Noise power spectrum ; Biological networks
Abstract :	[en] This paper considers the problem of inferring the structure and dynamics of an unknown network driven by unknown noise inputs. Equivalently we seek to identify direct causal dependencies among manifest variables only from observations of these variables. We consider linear, time-invariant systems of minimal order and with one noise source per manifest state. It is known that if the transfer matrix from the inputs to manifest states is minimum phase, then this problem has a unique solution, irrespective of the network topology. Here we consider the general case where the transfer matrix may be non-minimum phase and show that solutions are characterized by an Algebraic Riccati Equation (ARE). Each solution to the ARE corresponds to at most one spectral factor of the output spectral density that satisfies the assumptions made. Hence in general the problem may not have a unique solution, but all solutions can be computed by solving an ARE and their number may be finite.
Permalink :	http://hdl.handle.net/10993/20329

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