The consensus protocol for multi-agent systems based on the algebraic connectivity

The paper studies the consensus protocol of the time invariant multi-agent continuous systems. Based on the direct graph Laplacian matrix theory and it's the second smallest eigenvalue of communication topology, we study the continuous-time integrator agents dynamics system. The issue of stability of the systems is analyzed and the convergence problem of the information states is also discussed. Two examples are presented to show the effectiveness of the results of this paper.

[1]  M. Degroot.  Reaching a Consensus , 1974 .

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

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

[4]  Mehran Mesbahi,et al.  On maximizing the second smallest eigenvalue of a state-dependent graph Laplacian , 2006, IEEE Transactions on Automatic Control.

[5]  Timothy W. McLain,et al.  Coordination Variables and Consensus Building in Multiple Vehicle Systems , 2004 .

[6]  Jon Atli Benediktsson,et al.  Consensus theoretic classification methods , 1992, IEEE Trans. Syst. Man Cybern..

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

[8]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

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

[10]  Manfredi Maggiore,et al.  State Agreement for Continuous-Time Coupled Nonlinear Systems , 2007, SIAM J. Control. Optim..

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