Agreement problems in networks with directed graphs and switching topology

In this paper, we provide tools for convergence and performance analysis of an agreement protocol for a network of integrator agents with directed information flow. We also analyze algorithmic robustness of this consensus protocol for networks with mobile nodes and switching topology. A connection is established between the Fiedler eigenvalue of the graph Laplacian and the performance of this agreement protocol. We demonstrate that a class of directed graphs, called balanced graphs, have a crucial role in solving average-consensus problems. Based on the properties of balanced graphs, a group disagreement function (i.e. Lyapunov function) is proposed for convergence analysis of this agreement protocol for networks with directed graphs and switching topology.

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

[2]  M. Fiedler.  A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory , 1975 .

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

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

[5]  Nancy A. Lynch,et al.  Distributed Algorithms , 1992, Lecture Notes in Computer Science.

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

[7]  J. Toner,et al.  Flocks, herds, and schools: A quantitative theory of flocking , 1998, cond-mat/9804180.

[8]  Vijay Kumar,et al.  Modeling and control of formations of nonholonomic mobile robots , 2001, IEEE Trans. Robotics Autom..

[9]  Mehran Mesbahi,et al.  Formation flying control of multiple spacecraft via graphs , 2001 .

[10]  Fernando Paganini,et al.  Scalable laws for stable network congestion control , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

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

[12]  Tamio Arai,et al.  A distributed control scheme for multiple robotic vehicles to make group formations , 2001, Robotics Auton. Syst..

[13]  Richard M. Murray,et al.  INFORMATION FLOW AND COOPERATIVE CONTROL OF VEHICLE FORMATIONS , 2002 .

[14]  J. A. Fax,et al.  Graph Laplacians and Stabilization of Vehicle Formations , 2002 .

[15]  Randal W. Beard,et al.  A decentralized approach to formation maneuvers , 2003, IEEE Trans. Robotics Autom..

[16]  R. Murray,et al.  Consensus protocols for networks of dynamic agents , 2003, Proceedings of the 2003 American Control Conference, 2003..

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