1. Observability-Based Approach to Optimal Design of Networks Atiye Alaeddini Spring 2016

2. Observability-Based Design Blind cavefish generate a flow field as they swim through the water; the flow field is distorted by various environmental features (e.g. obstacles) when fish swim near them. Informative Path Planning During exploration, rats make rhythmic back- and-forth sweeps of their long facial whiskers. Sending a robot to an unstructured world 2

3. Preliminaries Observability Definition Observability Metric Problem Setup Epidemic Detection in A Network Privacy in A Network Conclusion & Future Work Presentation Outline 3

4. Observability Definition & Observability Metrics 4

5. Observability Intuition for observability: From observing the sensor(s) for a finite period of time, can I find the state at previous times? Question: Can observability help us to design a network? 5

6. How to Measure Observability? a linear system 6

7. Epidemic Detection in a Network 7

8. Motivation What do we know? a network of connected agents, with limited sensing facilities Epidemic Processes: Viruses, diseases Online viruses, worms Fashion Adoption of technologies Behavior Ideas If I have a few number of sensors, where do I place them? SS city water distribution network, and data on how contaminants spread Inferring networks of diffusion from 1 million news sources real network of 105 students And many more examples …. 8

9. Problem Definition 9

10. Optimization Problem 10

11. Optimization Algorithm Outer Approximation (Duran and Grossmann, 1986)  Motivation: avoid solving huge number of NLPs  Exploit MILP/NLP solvers: decompose integer and nonlinear part.  This algorithm gives a lower bound of the optimal value. MILP Optimization Problem MILP NLP linearization Update Points 11

12. Virus Spreading Model (SIS) 12

13. Markov Process 13

14. Sparse or Dense Network & minimum number of observing nodes Sparse Structure Dense Structure Ordinary Node Observing Node 14

15. Privacy in Networked Systems 15

16. Motivation When agents exchange sensitive data, our concern is ensuring that privacy is kept. A minimum observable topology of interaction will be proposed, which translates to minimization of the data being exposed to a foreign agent. 16

17. Online Learning Setup A convex set You Adversary 17

18. Regret 18

19. Keep The Network Safe! A hacker attacks the network by connecting to a node in network. We need to do something! 19

20. Mathematical Modeling Dynamics of the network Loss function (trace of the empirical observability Gramian) Optimization Problem: 20

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22. Dynamic foreign agents connecting to multiple nodes 22

23. Regret 23

24. Future Work  Considering uncertainties in interaction parameters in the network in the problem of epidemic detection  Finding an efficient method to approximate the observability Gramian for nonlinear systems 24

25. Thanks! Atiye Alaeddini 25

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27. Observability Index 27

28. Distributed Online Learning Centralized Computation [1] A. Chapman, E. Schoof, and M. Mesbahi, “Distributed online topology design for network level disturbance rejection,” IEEE CDC, pp. 817–822, 2013. Distributed Network 28