1. Consensus in Multi-agent Systems with Second-order Dynamics Wenwu Yu Department of Mathematics Southeast University, Nanjing, China Supervisor: Guanrong Chen Department of Electronic Engineering City University of Hong Kong CCCN 2010, Suzhou

2. Outline Background Consensus with Linear and Nonlinear Dynamics Other Related Topics Conclusions

3. Background Swarm Flocking Unmanned Air Vehicles (UAVS) formation control distributed sensor networks robotic teams …

4. Fish Swarm

5. Bird Flocking

6. Unmanned Air Vehicles (UAVS)

7. formation control

8. distributed sensor networks

9. Robotic teams

10. First-order Consensus

11. Results: First-order Consensus Fixed Topologies: A directed spanning tree or connected (Olfati-Saber and Murray TAC 2004, Ren and Beard TAC 2005, Lin, et al. TAC 2005) Time-varying Topologies: Graph is jointly connected (union of graphs) (Jadbabaie et al. TAC 2003, Moreau TAC 2005, Ren and Beard TAC 2005, Tanner et al. TAC 2007) Stochastic Switching (Hatano and Mesbahi TAC 2005) Stochastic Matrix and Convexity

12. Second-order consensus (linear) W. Ren IJRNC 2007 1.Different from First-order 2. Wide applications for modeling

13. Results: Second-order Consensus

14. Yu, Chen, and Cao Automatica 2010

15. Second-order consensus (nonlinear) Yu, Chen, Cao, and Kurths TSMC-B 2010

16. Results: nonlinear dynamics

17. Related Topics Time delays: single delay (Yu, Chen, Cao Automatica 2010), multiple delays (Yang, Zhu, Zhang EJC 2010, Meng, Yu, Ren EJC 2010) Pinning control: Song, Cao, Yu, SCL 2010 Communication constrains with intermittent control: Wen, Duan, Yu, Chen 2010 Stochastic switching: Markovian (Zhang, Tian Automatica 2009) Time-varying switching: Hong et al. Automatica 2008

18. Existence of Quadratic Lyapunov Functions? Olshevsky and Tsitsiklis TAC 2010

19. Conclusions Switching Topologies Pinning Control Filtering Nonlinear Dynamics

20. Q & A Thank you ! http://www.ee.cityu.edu.hk/~wwyu wenwuyu@gmail.com