复杂网络控制中的若干问题 汪小帆 上海交通大学 xfwang@sjtu

1. 复杂网络控制中的若干问题 汪小帆 上海交通大学 xfwang@sjtu.edu.cn 2010. 8. 9 zhiyuan.sjtu.edu.cn

2. Network Science Focus on structural • Discovery: What do real networks look like even if we can’t actually look at them? • Modeling:How to model them? • Impact:How does the topology of a network affect its function? • Control:How can the topological characteristics be used to improve the function of a network? zhiyuan.sjtu.edu.cn

3. 社会网络控制 • 如何控制疾病、流言、时尚、舆情等的传播？ • 如何引导与控制社会集群行为？（973） • 如何形成（最佳）共识？（Consensus） zhiyuan.sjtu.edu.cn

4. 交通网络控制 • 如何基于对网络结构的认识改善网络性能？ • 如何避免经常发生的人为设计缺陷导致的瓶颈？ 上海沪闵高架今开通 严重拥堵造成多起事故 新民晚报 2003-12-29 zhiyuan.sjtu.edu.cn

5. 通信网络控制 • 如何控制网络拥塞？ • 如何控制病毒传播？ zhiyuan.sjtu.edu.cn

6. 电力网络控制 • 如何控制相继故障？ zhiyuan.sjtu.edu.cn

7. 金融网络控制 • 如何控制金融危机的产生与扩散？ zhiyuan.sjtu.edu.cn

8. 多自主体网络控制 • 机器人网络协调控制 • 分布式传感器网络控制（感知中国） zhiyuan.sjtu.edu.cn

9. Exploring Links Links? Network Science Control Science Networked System Control Theory? zhiyuan.sjtu.edu.cn

10. Network Science(NetSci) VS. Control Science(ConSci) Same Problems, Different Methods Control Design Model Complex Network Model Objective Objective Links? Physical Network Close-loop Network Network properties (connectivity, efficiency, robustness) are critical zhiyuan.sjtu.edu.cn

11. Pinning Control: Marries ConSci & NetSci • Feasibility：Can the goal of control be achieved by only directly control a fraction of nodes? --- Control Science • Efficiency: How to select the nodes to be controlled so that the goal can be achieved with a low cost? --- Network Science Focus: complexity of the network structure zhiyuan.sjtu.edu.cn

12. Pinning Control of Complex Networks • Fixed topology case: • Feasibility: Only if the network is connected • Efficiency: Depends on structure (and nodes) • An example: How to utilize the community structure of a complex network? • Should focus more on structure! zhiyuan.sjtu.edu.cn

13. Detecting Community Structure: Challenges • Hierarchical • Overlapping zhiyuan.sjtu.edu.cn

14. Detecting Community Structure: Challenges • Evolution, Emergence zhiyuan.sjtu.edu.cn

15. Network Science Control Science Evolving Networks with Time-Varying Topologies zhiyuan.sjtu.edu.cn

16. Coordination in Networks with Time-Varying Topologies Swarming Flocking • A large number of agents (network) • limited information (local rules) • organize into a coordinated motion (emergence) Consensus Rendezvous zhiyuan.sjtu.edu.cn

17. A Complex Network View • Each agent has limited communication capability. • Node  Agent • At any time t, there is an edge between two agents if ||qi(t)-qj(t)||<r A spatial complex dynamical network with time-varying (switching) topology zhiyuan.sjtu.edu.cn

18. Insight from Computer Graphics Classical Boids Model, 1987 Create an easy way to create realistic-looking animations of flocking • Velocity Matching (Alignment) attempt to match velocity with nearby flockmates • Flock Centering (Cohesion) stay close to nearby flockmates • Collision Avoidance (Separation) avoid collisions with nearby agents Reynolds , “Flocks, Herd, and Schools: A Distributed Behavioral Model”, Computer Graphics, 21(4),1987. zhiyuan.sjtu.edu.cn

19. Goals of Control: Control Perspective: Algorithm Challenge • How to design distributed control algorithm for each agent so that flocking can be achieved? Position Velocity Velocity Alignment Cohesion Separation Quasi-lattice zhiyuan.sjtu.edu.cn

20. Basic Flocking Algorithm Separation & Cohesion Alignment Stability  Connectivity! • In Theory: G(t) connected for all t Flocking • In Practice: G(0) connected Fragmentation Olfati-Saber, IEEE T-AC，2006; Tanner er al., IEEE T-AC, 2007 zhiyuan.sjtu.edu.cn

21. Flocking with a Virtual Leader Separation & Cohesion Alignment Tracking • In Theory & In Practice: Always lead to flocking! Olfati-Saber, Flocking for Multi-Agent Dynamic Systems: Algorithms and Theory, IEEE Trans AC，2006 zhiyuan.sjtu.edu.cn

22. A View from Complex Network Theory • Without leader: Initial connected Fragmentation • With leader: Initial disconnected Flocking zhiyuan.sjtu.edu.cn

23. Simulations Initial positions are chosen randomly so that the initial net is highly disconnected. No. of edges increases and has a tendency to render the net connected. zhiyuan.sjtu.edu.cn

24. Flocking algorithm with minority of informed agents Uninformed agent Separation & Cohesion Alignment Informed agent Tracking zhiyuan.sjtu.edu.cn

25. Flocking with minority of informed agents Our interests: behavior of the group when only a small fraction of agents are informed agents. Our contributions: Theory:Not only all informed agents but also some uninformed agents will DO track the virtual leader. Simulation:Majority of uninformed agents will INDEED track the virtual leader. ---Emergence of giant component! zhiyuan.sjtu.edu.cn

26. Simulation Results: N=100, M0=10 zhiyuan.sjtu.edu.cn

27. Network Science Focus on structural • Discovery: What do real networks look like even if we can’t actually look at them? • Modeling:How to model them? • Impact:How does the topology of a network affect its function? • Control:How can the topological characteristics be used to improve the function of a network? zhiyuan.sjtu.edu.cn

28. 谢谢！ xfwang@sjtu.edu.cn zhiyuan.sjtu.edu.cn