Perfectly Controllable Multi-Agent Networks

This note investigates how to design topology structures to ensure the controllability of multi-agent networks (MASs) under any selection of leaders. We put forward a concept of perfect controllability, which means that a multi-agent system is controllable with no matter how the leaders are chosen. In this situation, both the number and the locations of leader agents are arbitrary. A necessary and sufficient condition is derived for the perfect controllability. Moreover, a step-by-step design procedure is proposed by which topologies are constructed and are proved to be perfectly controllable. The principle of the proposed design method is interpreted by schematic diagrams along with the corresponding topology structures from simple to complex. We show that the results are valid for any number and any location of leaders. Both the construction process and the corresponding topology structures are clearly outlined.

[1]  Zhijian Ji,et al.  Necessary and Sufficient Conditions for Consensus of Second-Order Multiagent Systems Under Directed Topologies Without Global Gain Dependency , 2017, IEEE Trans. Cybern..

[2]  Bahman Gharesifard,et al.  Almost equitable partitions and new necessary conditions for network controllability , 2017, Autom..

[3]  Lin Zhang,et al.  Controllability of multi‐agent systems under directed topology , 2017 .

[4]  Huanshui Zhang,et al.  Output Feedback Control and Stabilization for Networked Control Systems With Packet Losses , 2017, IEEE Transactions on Cybernetics.

[5]  Shun-Pin Hsu.  A necessary and sufficient condition for the controllability of single-leader multi-chain systems , 2017 .

[6]  Ming He,et al.  On Almost Controllability of Dynamical Complex Networks with Noises , 2017, J. Syst. Sci. Complex..

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

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

[9]  Bahman Gharesifard,et al.  Graph Controllability Classes for the Laplacian Leader-Follower Dynamics , 2015, IEEE Transactions on Automatic Control.

[10]  Lei Liu,et al.  Group controllability of continuous-time multi-agent systems , 2018 .

[11]  Wei Ren,et al.  Robustness Analysis of Asynchronous Sampled-Data Multiagent Networks With Time-Varying Delays , 2017, IEEE Transactions on Automatic Control.

[12]  Long Wang,et al.  Nash Equilibrium Topology of Multi-Agent Systems With Competitive Groups , 2017, IEEE Transactions on Industrial Electronics.

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

[14]  Long Wang,et al.  Consensus of Hybrid Multi-Agent Systems , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[15]  Long Wang,et al.  Controllability of multi-agent systems with directed and weighted signed networks , 2018, Syst. Control. Lett..

[16]  Magnus Egerstedt,et al.  Graph Distances and Controllability of Networks , 2016, IEEE Transactions on Automatic Control.

[17]  Mohammad Haeri,et al.  On the Structural and Strong Structural Controllability of Undirected Networks , 2018, IEEE Transactions on Automatic Control.

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

[19]  Shun-Pin Hsu.  Controllability of the multi-agent system modeled by the threshold graph with one repeated degree , 2016, Syst. Control. Lett..

[20]  Zhijian Ji,et al.  Controllability of multiagent systems based on path and cycle graphs , 2018 .

[21]  Xue-Jun Xie,et al.  Stabilization of Positive Switched Linear Systems and Its Application in Consensus of Multiagent Systems , 2017, IEEE Transactions on Automatic Control.

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

[23]  Zhijian Ji,et al.  Bipartite Consensus on Coopetition Networks With Time-Varying Delays , 2018, IEEE Access.

[24]  Haisheng Yu,et al.  A New Perspective to Graphical Characterization of Multiagent Controllability , 2017, IEEE Transactions on Cybernetics.

[25]  Zhong Wang,et al.  Dynamic Output Feedback Guaranteed-Cost Synchronization for Multiagent Networks With Given Cost Budgets , 2018, IEEE Access.

[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.  Non-fragility of multi-agent controllability , 2017, Science China Information Sciences.

[28]  Fengzhong Li,et al.  Consensus via Time-Varying Feedback for Uncertain Stochastic Nonlinear Multiagent Systems , 2019, IEEE Transactions on Cybernetics.

[29]  Ning Cai,et al.  A Novel Clustering Method Based on Quasi-Consensus Motions of Dynamical Multiagent Systems , 2017, Complex..

[30]  Long Wang,et al.  Controllability of discrete‐time multiagent systems with switching topology , 2018 .

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