The Role of Network Structure in Controlling Complex Networks

Abstract: Controllability of complex network systems is an active area
of research at the intersection of network science, control theory,
and multi-agent coordination, with multiple applications ranging from
brain dynamics to the smart grid and cyber-physical systems. The basic
question is to understand to what extent the dynamic behavior of the
entire network can be shaped by changing the states of some of its
subsystems, and decipher the role that network structure plays in
achieving this. This talk examines this question in two specific
instances: characterizing network controllability when control nodes
can be scheduled over a time horizon and hierarchical selective
recruitment in brain networks. Regarding controllability, we show how
time-varying control schedules can significantly enhance network
controllability over fixed ones, especially when applied to large
networks. Through the analysis of a novel scale-dependent notion of
nodal centrality, we show that optimal time-varying scheduling
involves the actuation of the most central nodes at appropriate
spatial scales. Regarding hierarchical selective recruitment, we
examine network mechanisms for selective inhibition and top-down
recruitment of subnetworks under linear-threshold dynamics. Motivated
by the study of goal-driven selective attention in neuroscience, we
build on the characterization of key network dynamical properties to
enable, through either feedforward or feedback control, the targeted
inhibition of task-irrelevant subnetworks and the top-down recruitment
of task-relevant ones. Our results allow us to draw interesting
interpretations on the role played by timescale separation, the
structure of intra- and inter-connections among network layers, and
the selective activity of task-irrelevant and task-relevant
subnetworks in the brain.

Jorge Cortes is a Professor with the Department of
Mechanical and Aerospace Engineering at the University of California,
San Diego. He received the Licenciatura degree in mathematics from the
Universidad de Zaragoza, Spain, in 1997, and the Ph.D. degree in
engineering mathematics from the Universidad Carlos III de Madrid,
Spain, in 2001. He held postdoctoral positions at the University of
Twente, The Netherlands, and at the University of Illinois at
Urbana-Champaign, USA. He was an Assistant Professor with the
Department of Applied Mathematics and Statistics at the University of
California, Santa Cruz from 2004 to 2007. He is the author of
"geometric, Control and Numerical Aspects of Nonholonomic Systems"
(New York: Springer-Verlag, 2002) and co-author of "distributed
Control of Robotic Networks" (Princeton: Princeton University Press,
2009). He received a NSF CAREER award in 2006 and was the recipient
of the 2006 Spanish Society of Applied Mathematics Young Researcher
Prize. He has co-authored papers that have won the 2008 IEEE Control
Systems Outstanding Paper Award, the 2009 SIAM Review SIGEST selection
from the SIAM Journal on Control and Optimization, and the 2012
O. Hugo Schuck Best Paper Award in the Theory category. He has been an
IEEE Control Systems Society Distinguished Lecturer (2010-2014) and is
an IEEE Fellow. His current research interests include distributed
control and optimization, network science, opportunistic
state-triggered control, reasoning and decision making under
uncertainty, and distributed coordination in power networks, robotics,
and transportation.