1. Synchronization via Pinning Control on General Networks
Wenwu Yu
Department of Mathematics
Southeast University, Nanjing, China
CCCN 2011, Chengdu

2. Outline Background Synchronization via pinning control: brief review
New works
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. distributed sensor networks

8. Pinning Control? Traditional Control (All nodes)
Pinning Control (A fraction of nodes)

9. formation control
Controller

10. Robotic teams
Controllers

11. Achilles' Heel

12. Problem Formulation

13. Recent Results
Random and high-degree pinning schemes: (Wang and Chen Physica A 2002, Li, Wang, and Chen TCAS-I 2005)
Distributed leader-following control (Hong et al. Automatica 2008, Yu et al. SCL 2009, Su et al. TAC 2009, Chen et al. Automatica 2009)
Pinning Controllability (Sorrentino PRE 2007, Porfiri and Bernardo Automatica 2008)
Controlling only one node (Chen et al. TCAS-I 2007)
Adaptive Pinning Control (Zhou et al. TAC 2006, Yu et al. Automatica 2009, Lu Chaos 2007)
Time delay (Xiang et al. CMA 2007, Liu et al. Physica A 2007)

14. (2) Challenging problem: minimum number of nodes?
(1) Directed Networks?
Matrix Analysis (Song and Cao TCAS-I 2010, Zhou Automatica 2008)
Algebraic Graph Theory (Wu Chaos 2008, Lu et al. 2010)
(2) Challenging problem: minimum number of nodes?

15. Xiang and Chen Automatica 2007

16. Criterion A strongly connected network:
vertices with very small in-degrees should be pinned first
the vertices with very large out-degrees may be pinned
A directed spanning tree:
strongly connected components with very few connections from other components should be controlled
the components with many connections from other components can achieve synchronization even without controls

17. Example

19. Conclusions
Algebraic Graph Theory
Matrix Analysis
Laplacian Matrix

20. Q & A
Thank you !