Elsevier

Automatica

Volume 47, Issue 6, June 2011, Pages 1230-1235
Automatica

Brief paper
Robust dynamical network structure reconstruction

Abstract

This paper addresses the problem of network reconstruction from data. Previous work identified necessary and sufficient conditions for network reconstruction of LTI systems, assuming perfect measurements (no noise) and perfect system identification. This paper assumes that the conditions for network reconstruction have been met but here we additionally take into account noise and unmodelled dynamics (including nonlinearities). In order to identify the network structure that generated the data, we compute the smallest distances between the measured data and the data that would have been generated by particular network structures. We conclude with biologically inspired network reconstruction examples which include noise and nonlinearities.

Keywords

Robust network reconstruction
Noise and unmodelled dynamics
Systems biology
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References

Ye Yuan was born on October 1986. He received his B.Eng. degree (Valedictorian) from the Department of Automation, Shanghai Jiao Tong University in 2008, M. Phil. from the Department of Engineering, Cambridge University in 2009. He is currently a second-year Ph.D. student in Control Group, Department of Engineering, University of Cambridge. Ye was a visiting student at University of New Mexico, the Hong Kong University of Science and Technology, and Luxembourg Centre for Systems Biomedicine. He is now a visiting student at CDS, Caltech. His research interest lies in the mathematical control theory with applications to network and biology. He is the recipient of Dorothy Hodgkin Postgraduate Awards (Microsoft Research Ph.D. Scholarship), Cambridge Overseas Scholarship and Henry Lester Scholarship.

Guy-Bart Stan was born in Liège, Belgium, in 1977. He received his Ph.D. degree in Applied Sciences (Analysis and Control of Nonlinear Dynamical Systems) from the University of Liège, Belgium in 2005. In 2005, Dr. Stan worked as a Senior Digital Signal Processing Engineer at Philips Applied Technologies, Leuven, Belgium. From 2006 until 2009, he worked as Research Associate in the Control Group of the Department of Engineering at the University of Cambridge, UK, being supported by an EU-FP6 IEF Marie-Curie Fellowship and the UK EPSRC, successively. In 2008, he was a Visiting Scientist at the Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, USA. Since 2009 Dr. Stan is a University Lecturer in Engineering Design for Synthetic Biology Systems in the Department of Bioengineering and the EPSRC-funded Centre for Synthetic Biology and Innovation at Imperial College London. His current research interests include the mathematical modelling, analysis and control of complex biological systems/networks occurring in synthetic biology, systems biology, and technological systems.

Sean Warnick received the B.S.E. degree from Arizona State University in 1993, and the S.M. and Ph.D. degrees in Electrical Engineering and Computer Science from the Massachusetts Institute of Technology in 1995 and 2003, respectively. He attended ASU on scholarship from the Flinn Foundation, graduated summa cum laude, and was named the Outstanding Graduate of the College of Engineering and Applied Sciences. Since 2003 Dr. Warnick has been with the Computer Science Department at Brigham Young University, where he is currently an Associate Professor and Director of the interdisciplinary Information and Decision Algorithms Laboratories. Dr. Warnick has also held visiting appointments at Cambridge University (Summer 2006), the University of Maryland (Summer 2008), and the National Security Agency, where he was named the Distinguished Visiting Professor for three consecutive years (2008–2010). Dr. Warnick’s research interests focus on complex networks of uncertain dynamical systems, where he considers issues of representation, identification and reconstruction, control, security and robustness, and verification and validation.

Jorge Goncalves received his Licenciatura (5-year S.B.) degree from the University of Porto, Portugal, and the M.S. and Ph.D. degrees from the Massachusetts Institute of Technology, Cambridge, MA, all in Electrical Engineering and Computer Science, in 1993, 1995, and 2000, respectively. He then held two postdoctoral positions, first at the Massachusetts Institute of Technology for seven months, and from May 2001 to March 2004 at the California Institute of Technology with the Control and Dynamical Systems division. Since April 2004 he has been a Lecturer in the Information Engineering Division of the Department of Engineering at the University of Cambridge. Since 2005 he has been also a Fellow of Pembroke College, Cambridge. He was a visiting researcher at the University of Luxembourg from June to December 2010. Also he is a visiting researcher at California Institute of Technology (January–September 2011). He was the recipient of the Best Student Paper Award at the Automatic Control Conference, Chicago, IL, June 2000.

His research interests include modelling, analysis and control of complex and hybrid systems. In particular, modelling and analysis in systems and synthetic biology, collaborating with biologists in different areas such as circadian rhythms and gene regulatory networks.

This work was supported in part by EPSRC grant numbers EP/G066477/1 and EP/I029753/1, AFRL FA8750-09-2-0219 and Microsoft Research through the Ph.D. Scholarship Program. The material in this paper was partially presented at the 49th IEEE Conference on Decision and Control, December 15–17, 2010, Atlanta, Georgia, USA. This paper was recommended for publication in revised form by Associate Editor Elling Jacobsen, under the direction of Guest Editor Francis J. Doyle III.