On the controllability and observability of Cartesian product networks

The paper presents an analysis framework for a class of dynamic composite networks. These networks are formed from smaller factor networks via graph Cartesian products. We provide a composition method for extending the controllability and observability of the factor networks to that of the composite network. We then delve into the effectiveness of designing control and estimation algorithms for the composite network via symmetry in the network. Examples and applications are provided throughout the paper to demonstrate the results including a distributed output feedback stabilizer and a social network application.

[1]  H.G. Tanner,et al.  On the controllability of nearest neighbor interconnections , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[2]  Ljupco Kocarev,et al.  Complex Dynamics in Communication Networks , 2005 .

[3]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[4]  Debra L. Boutin.  The determining number of a Cartesian product , 2009 .

[5]  Mehran Mesbahi,et al.  Identification and Infiltration in Consensus-type Networks* *This work has been supported by AFOSR FA9550-09-1-0091. , 2009 .

[6]  Magnus Egerstedt,et al.  Graph Theoretic Methods in Multiagent Networks , 2010, Princeton Series in Applied Mathematics.

[7]  M. Kanat Camlibel,et al.  Controllability of diffusively-coupled multi-agent systems with general and distance regular coupling topologies , 2011, IEEE Conference on Decision and Control and European Control Conference.

[8]  Giuseppe Notarstefano,et al.  Observability and reachability of grid graphs via reduction and symmetries , 2011, IEEE Conference on Decision and Control and European Control Conference.

[9]  Albert-László Barabási,et al.  Controllability of complex networks , 2011, Nature.

[10]  Mehran Mesbahi,et al.  Advection on graphs , 2011, IEEE Conference on Decision and Control and European Control Conference.

[11]  Mehran Mesbahi,et al.  System theory over random consensus networks: Controllability and optimality properties , 2011, IEEE Conference on Decision and Control and European Control Conference.

[12]  Mehran Mesbahi,et al.  Stability analysis of nonlinear networks via M-matrix theory: Beyond linear consensus , 2012, 2012 American Control Conference (ACC).

[13]  Mehran Mesbahi,et al.  On the Controllability Properties of Circulant Networks , 2013, IEEE Transactions on Automatic Control.