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The consensus problem with positivity constraints: problem statement and state of the art

In this talk we introduce the consensus problem for multi-agent systems, under the assumptions that the agents are homogeneous and described by a single-input positive state-space model, the mutual interactions are cooperative, and the static state-feedback law that each agent adopts to achieve consensus preserves the positivity of the overall system.

First, motivating examples are presented. Necessary conditions for the problem solvability, that allow to address only the special case when the state matrix is irreducible, are then provided. Under this assumption, equivalent sets of sufficient conditions are derived. Special conditions either on the system description or on the Laplacian of the communication graph allow to obtain necessary and sufficient conditions for the problem solvability.

Open problems will be pointed out.

Type of Seminar:
IfA Seminar
Prof. Maria Elena Valcher
University of Padova
Oct 10, 2016   11:15

Contact Person:

Sabrina Baumann
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Biographical Sketch:
Maria Elena Valcher received the Master Degree (cum laude) in Electronic Engineering (1991) and the Ph.D. Degree in Systems Engineering (1995) both from the University of Padova (Italy). Since January 2005 she is Full Professor of Control Theory at the University of Padova.

She is author/co-author of 77 papers appeared on international journals, 97 conference papers and 13 book chapters. Her research interests include multidimensional systems theory, polynomial matrix theory, behavior theory, Boolean control networks, multi-agent systems and consensus problems, switched systems and positive systems.

She was in the Editorial Boards of the IEEE Transactions on Automatic Control (2000-2003), Systems and Control Letters (2004-2010), Automatica (2006-2013), SIAM J. on Control and Optimization (2012-2014), and she is currently in the Editorial Boards of Multidimensional Systems and Signal Processing (2004-today), the European Journal of Control (2013-today) and IEEE Access (2014-now).

She held various positions within the IEEE Control Systems Society: Appointed BoG Member (2003); Elected BoG Member (2004-2006; 2010-2012); Vice President Member Activities (2006-2007); Vice President Conference Activities (2008-2010); President-Elect (2014); President (2015); Junior Past President (2016). She was involved in the organization of several conferences, in particular she was registration Chair of the 2004 IEEE CDC, Publicity Chair of the 2007 MSC, Registration Chair of the 2011 IFAC World Conference and Program Chair of the 2012 IEEE CDC.

She was a member of the 2013, 2014 and 2015 IEEE Control Systems Award committee and a Distinguished Lecturer of the IEEE CSS (2011-2014). She received the 2011 IEEE CSS Distinguished Member Award and she is an IEEE Fellow since 2012. She is currently a member of the 2016 IEEE Fellow Committee, and of the 2016 IEEE TAB Ad Hoc Committee on Women and Under-Represented Groups.