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

Outline Background Synchronization via pinning control: brief review New works Conclusions

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

Fish Swarm

Bird Flocking

Unmanned Air Vehicles (UAVS)

distributed sensor networks

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

formation control Controller

Robotic teams Controllers

Achilles' Heel

Problem Formulation

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)

(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?

Xiang and Chen Automatica 2007

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

Example

Conclusions Algebraic Graph Theory Matrix Analysis Laplacian Matrix

Q & A Thank you ! wenwuyu@gmail.com