4.7 Article

Second-Order Consensus Seeking in Multi-Agent Systems With Nonlinear Dynamics Over Random Switching Directed Networks

Journal

Publisher

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCSI.2012.2226507

Keywords

Directed spanning tree; local consensus; multi-agent systems; nonlinear dynamics; random switching; second-order consensus; time-delay(-free) coupling

Funding

  1. Fundamental Research Funds for the Central Universities
  2. Scholarship Award for Excellent Doctoral Student
  3. Ministry of Education [0903005109081-011]
  4. National Natural Science Foundation of China [60973114, 61170249]
  5. Research Fund of Preferential Development Domain for the Doctoral Program of Ministry of Education of China [201101911130005]
  6. State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University [2007DA10512711206]
  7. Program for Changjiang Scholars
  8. National Priority Research Project [NPRP 4-1162-1-181]
  9. Qatar National Research Fund
  10. [CDJXS12180002]

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This paper discusses the second-order local consensus problem for multi-agent systems with nonlinear dynamics over dynamically switching random directed networks. By applying the orthogonal decomposition method, the state vector of resulted error dynamical system can be decomposed as two transversal components, one of which evolves along the consensus manifold and the other evolves transversally with the consensus manifold. Several sufficient conditions for reaching almost surely second-order local consensus are derived for the cases of time-delay-free coupling and time-delay coupling, respectively. For the case of time-delay-free coupling, we find that if there exists one directed spanning tree in the network which corresponds to the fixed time-averaged topology and the switching rate of the dynamic network is not more than a critical value which is also estimated analytically, then second-order dynamical consensus can be guaranteed for the choice of suitable parameters. For the case of time-delay coupling, we not only prove that under some assumptions, the second-order consensus can be reached exponentially, but also give an analytical estimation of the upper bounds of convergence rate and the switching rate. Finally, numerical simulations are provided to illustrate the feasibility and effectiveness of the obtained theoretical results.

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