University of Groningen On second-order consensus in multi-agent dynamical systems with directed topologies and time delays

This paper establishes some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems with directed topologies and time delays. First, theoretical analysis is carried out for the basic, but fundamentally important case where agents’ second-order dynamics are governed by the position and velocity terms. A necessary and sufficient condition is derived to ensure second-order consensus and it is found that both the real and imaginary parts of the eigenvalues of the Laplacian matrix of the corresponding network topology play key roles in reaching consensus. Based on this result, a second-order consensus algorithm is constructed for the multi-agent system with communication delays. A necessary and sufficient condition is then proposed, which shows that consensus can be achieved in a multi-agent system whose topology contains a directed spanning tree if and only if the time delay is less than a critical value. Finally, simulation examples are given to verify the theoretical analysis.

[1]  Craig W. Reynolds Flocks, herds, and schools: a distributed behavioral model , 1987, SIGGRAPH.

[2]  Yu-Ping Tian,et al.  Consensus of Multi-Agent Systems With Diverse Input and Communication Delays , 2008, IEEE Transactions on Automatic Control.

[3]  Jinde Cao,et al.  Global Synchronization of Linearly Hybrid Coupled Networks with Time-Varying Delay , 2008, SIAM J. Appl. Dyn. Syst..

[4]  Pierre-Alexandre Bliman,et al.  Average consensus problems in networks of agents with delayed communications , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[5]  M. Fiedler Algebraic connectivity of graphs , 1973 .

[6]  L. Chua,et al.  Synchronization in an array of linearly coupled dynamical systems , 1995 .

[7]  Wenwu Yu,et al.  On pinning synchronization of complex dynamical networks , 2009, Autom..

[8]  Yiguang Hong,et al.  Distributed Observers Design for Leader-Following Control of Multi-Agent Networks (Extended Version) , 2017, 1801.00258.

[9]  Jinde Cao,et al.  Local Synchronization of a Complex Network Model , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[10]  Guanrong Chen,et al.  A time-varying complex dynamical network model and its controlled synchronization criteria , 2005, IEEE Transactions on Automatic Control.

[11]  Ella M. Atkins,et al.  Second-order Consensus Protocols in Multiple Vehicle Systems with Local Interactions , 2005 .

[12]  Charles R. Johnson,et al.  Topics in Matrix Analysis , 1991 .

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

[14]  Jinde Cao,et al.  Stability and Hopf Bifurcation of a General Delayed Recurrent Neural Network , 2008, IEEE Transactions on Neural Networks.

[15]  Vicsek,et al.  Novel type of phase transition in a system of self-driven particles. , 1995, Physical review letters.

[16]  Wei Ren,et al.  On Consensus Algorithms for Double-Integrator Dynamics , 2007, IEEE Transactions on Automatic Control.

[17]  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..

[18]  Jinde Cao,et al.  Stability and Hopf bifurcation analysis on a four-neuron BAM neural network with time delays , 2006 .

[19]  Reza Olfati-Saber,et al.  Flocking for multi-agent dynamic systems: algorithms and theory , 2006, IEEE Transactions on Automatic Control.

[20]  Junan Lu,et al.  Adaptive synchronization of an uncertain complex dynamical network , 2006, IEEE Transactions on Automatic Control.

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

[22]  Randal W. Beard,et al.  Consensus seeking in multiagent systems under dynamically changing interaction topologies , 2005, IEEE Transactions on Automatic Control.