Controllability of heterogeneous multi-agent systems under directed and weighted topology

ABSTRACT This paper considers the controllability problem for both continuous- and discrete-time linear heterogeneous multi-agent systems with directed and weighted communication topology. First, two kinds of neighbour-based control protocols based on the distributed protocol of first-order and second-order multi-agent systems are proposed, under which it is shown that a heterogeneous multi-agent system is controllable if the underlying communication topology is controllable. Then, under special leader selection, the result shows that the controllability of a heterogeneous multi-agent system is solely decided by its communication topology graph. Furthermore, some necessary and/or sufficient conditions are derived for controllability of communication topology from algebraic and graphical perspectives. Finally, simulation examples are presented to demonstrate the effectiveness of the theoretical results.

[1]  Yongqiang Guan,et al.  Decentralized stabilizability of multi-agent systems under fixed and switching topologies , 2013, Syst. Control. Lett..

[2]  Long Wang,et al.  Containment control of heterogeneous multi-agent systems , 2014, Int. J. Control.

[3]  Giuseppe Notarstefano,et al.  Controllability and Observability of Grid Graphs via Reduction and Symmetries , 2012, IEEE Transactions on Automatic Control.

[4]  Guangming Xie,et al.  Controllability of a Leader–Follower Dynamic Network With Switching Topology , 2008, IEEE Transactions on Automatic Control.

[5]  Zhen Wang,et al.  Interconnection topologies for multi-agent coordination under leader-follower framework , 2009, Autom..

[6]  Ye Yuan,et al.  Observability and coarse graining of consensus dynamics through the external equitable partition. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Guangming Xie,et al.  Consensus control for a class of networks of dynamic agents , 2007 .

[8]  Bo Liu,et al.  Controllability of switching networks of multi‐agent systems , 2012 .

[9]  Hai Lin,et al.  Leaders in multi-agent controllability under consensus algorithm and tree topology , 2012, Syst. Control. Lett..

[10]  Mohsen Zamani,et al.  Structural controllability of multi-agent systems , 2009, 2009 American Control Conference.

[11]  Long Wang,et al.  Distributed consensus of heterogeneous multi-agent systems with fixed and switching topologies , 2012, Int. J. Control.

[12]  Long Wang,et al.  A new approach to consensus problems in discrete-time multiagent systems with time-delays , 2006, 2006 American Control Conference.

[13]  Yu-Ping Tian,et al.  Consensus in Heterogeneous Multi-Agent Systems , 2012 .

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

[15]  Zhen Wang,et al.  Controllability of multi-agent systems with time-delay in state and switching topology , 2010, Int. J. Control.

[16]  Christian Commault,et al.  Input addition and leader selection for the controllability of graph-based systems , 2013, Autom..

[17]  Guangming Xie,et al.  Controllability of multi-agent systems based on agreement protocols , 2009, Science in China Series F: Information Sciences.

[18]  M. Kanat Camlibel,et al.  Upper and Lower Bounds for Controllable Subspaces of Networks of Diffusively Coupled Agents , 2014, IEEE Transactions on Automatic Control.

[19]  Hai Lin,et al.  A graph theory based characterization of controllability for multi-agent systems with fixed topology , 2008, 2008 47th IEEE Conference on Decision and Control.

[20]  Long Wang,et al.  Quadratic stabilisability of multi-agent systems under switching topologies , 2014, Int. J. Control.

[21]  Peter Wieland,et al.  From Static to Dynamic Couplings in Consensus and Synchronization among Identical and Non-Identical Systems , 2010 .

[22]  Youcheng Lou,et al.  Controllability analysis of multi-agent systems with directed and weighted interconnection , 2012, Int. J. Control.

[23]  Long Wang,et al.  Finite-Time Consensus Problems for Networks of Dynamic Agents , 2007, IEEE Transactions on Automatic Control.

[24]  Hai Lin,et al.  Protocols Design and Uncontrollable Topologies Construction for Multi-Agent Networks , 2015, IEEE Transactions on Automatic Control.

[25]  Giuseppe Notarstefano,et al.  On the Reachability and Observability of Path and Cycle Graphs , 2011, IEEE Transactions on Automatic Control.

[26]  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).

[27]  Long Wang,et al.  Finite-time consensus of heterogeneous multi-agent systems with and without velocity measurements , 2012, Syst. Control. Lett..

[28]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.

[29]  Hai Lin,et al.  A graph-theoretic characterization of structural controllability for multi-agent system with switching topology , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.