Controllability of diffusively-coupled multi-agent systems with general and distance regular coupling topologies

This paper studies the controllability of linearly diffusively coupled multi-agent systems when some agents, called leaders, are under the influence of external control inputs. We bound the system's controllable subspace using combinatorial characteristics of some partitions of the graph describing the neighbor relationships between the agents. In particular, when such graphs are distance regular, we provide a full characterization of the controllable subspace for single leader cases while for multi-leader cases, a necessary condition and a sufficient condition for controllability are given respectively. In the end, we discuss how to choose leaders among the agents to guarantee controllability when the graphs are cycles or complete graphs, which are special subclasses of distance regular graphs.

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

[2]  Brian D. O. Anderson,et al.  Reaching a Consensus in a Dynamically Changing Environment: Convergence Rates, Measurement Delays, and Asynchronous Events , 2008, SIAM J. Control. Optim..

[3]  F. Knorn.  Topics in Cooperative Control , 2011 .

[4]  A. Hora,et al.  Distance-Regular Graphs , 2007 .

[5]  Ming Cao,et al.  Clustering in diffusively coupled networks , 2011, Autom..

[6]  Wei Wu,et al.  Cluster Synchronization of Linearly Coupled Complex Networks Under Pinning Control , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[7]  Mehran Mesbahi,et al.  On state-dependent dynamic graphs and their controllability properties , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[8]  Francesco Bullo,et al.  Distributed Control of Robotic Networks , 2009 .

[9]  Tianping Chen,et al.  Cluster synchronization in networks of coupled nonidentical dynamical systems. , 2009, Chaos.

[10]  M. Egerstedt,et al.  Controllability analysis of multi-agent systems using relaxed equitable partitions , 2010 .

[11]  Charles Delorme,et al.  Laplacian eigenvectors and eigenvalues and almost equitable partitions , 2007, Eur. J. Comb..

[12]  Stanley Burris,et al.  A course in universal algebra , 1981, Graduate texts in mathematics.

[13]  Magnus Egerstedt,et al.  Controllability of Multi-Agent Systems from a Graph-Theoretic Perspective , 2009, SIAM J. Control. Optim..

[14]  Giuseppe Notarstefano,et al.  On the observability of path and cycle graphs , 2010, 49th IEEE Conference on Decision and Control (CDC).

[15]  F. Garofalo,et al.  Controllability of complex networks via pinning. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Gordon F. Royle,et al.  Algebraic Graph Theory , 2001, Graduate texts in mathematics.

[17]  Reza Olfati-Saber,et al.  Consensus and Cooperation in Networked Multi-Agent Systems , 2007, Proceedings of the IEEE.

[18]  Ming Cao,et al.  Cluster synchronization algorithms , 2010, Proceedings of the 2010 American Control Conference.

[19]  Arnold Neumaier,et al.  Theory of Distance-Regular Graphs , 1989 .

[20]  Jie Lin,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2003, IEEE Trans. Autom. Control..

[21]  M. Cao,et al.  Comments on 'Controllability analysis of multi-agent systems using relaxed equitable partitions' , 2012 .