Second-order consensus for multiagent systems with directed topologies and nonlinear dynamics

  • Authors:

  • Wenwu Yu;Guanrong Chen;Ming Cao;Jürgen Kurths

  • Affiliations:

  • Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong;Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong;Faculty of Mathematics and Natural Sciences, Industrial Technology and Management, University of Groningen, Groningen, The Netherlands;Humboldt University of Berlin, Berlin, Germany and Research Domain IV-Transdisciplinary Concepts and Methods, Potsdam Institute for Climate Impact Research, Potsdam, Germany

  • Venue:
  • IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics - Special issue on game theory
  • Year:
  • 2010

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Abstract

This paper considers a second-order consensus problem for multiagent systems with nonlinear dynamics and directed topologies where each agent is governed by both position and velocity consensus terms with a time-varying asymptotic velocity. To describe the system's ability for reaching consensus, a new concept about the generalized algebraic connectivity is defined for strongly connected networks and then extended to the strongly connected components of the directed network containing a spanning tree. Some sufficient conditions are derived for reaching second-order consensus in multiagent systems with nonlinear dynamics based on algebraic graph theory, matrix theory, and Lyapunov control approach. Finally, simulation examples are given to verify the theoretical analysis.