1 / 41

Big Data and Control Theory

Big Data and Control Theory. Anil Aswani, Pat Bouffard, Young-Hwan Chang, Jeremy Gillula, Haomiao Huang, Soulaiman Itani, Mike Vitus, and Claire Tomlin February 23 2012. Control Theory. Control Theory. Control Theory. Control Theory. Control Theory. Control Theory. Control Theory.

curta
Download Presentation

Big Data and Control Theory

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Big Data and Control Theory Anil Aswani, Pat Bouffard, Young-Hwan Chang, Jeremy Gillula, Haomiao Huang, Soulaiman Itani, Mike Vitus, and Claire Tomlin February 23 2012

  2. Control Theory

  3. Control Theory

  4. Control Theory

  5. Control Theory

  6. Control Theory

  7. Control Theory

  8. Control Theory Control inputs are based on the mathematical model

  9. Hybrid Control Theory

  10. Examples Air traffic control HER2 inhibition in breast cancer High performance flight Grouping and conflict classification Maneuvering through modes Multiple equilibria 3 1 2 [Shaw] [Seamster] [Kahah] [Itani, Gray, Moasser]

  11. 1. High Performance Flight

  12. Reachable Sets Backwards Reachable Set unsafe In blue, system will stay safe In red, system may become unsafe On boundary, apply control to stay out of red

  13. Example: Collision Avoidance Pilots instructed to attempt to collide vehicles

  14. Impulse Example: Back-Flip Recovery Drift

  15. Back-flip Recovery Drift Impulse

  16. Back-Flip: Results

  17. These methods assume a model…. • What if the model is not well known? • Dynamics not well characterized • Human input • Can the model be learned from data?

  18. Learn models from data… • … but stay safe while learning • Safety: • A nominal model with error bounds • Reachable sets computed to ensure safety in worst case • Reachable sets computed using Model Predictive Control (MPC) • Performance: • Use online learning to update nominal model • Cost function used to generate control action within the safe set • Learning-basedModel Predictive Control

  19. Learning-based Model Predictive Control • Unknown system dynamics represented using an oracle • At each time step • Optimization solved, Oracle updated

  20. Learning-based Model Predictive Control • Unknown system dynamics represented using an oracle • At each time step • Optimization solved, Oracle updated Performance LBMPC Safety

  21. Example: Learning to fly • Physics improve statistics • Fewer parameters • Less noise • Linear model • Physics for structure • Experimental coefficients

  22. Example: Learning to fly video

  23. 2. Air Traffic Control 3 1 2

  24. Closely Spaced Parallels San Francisco Airport 750 ft separation

  25. Keeping the humans in the loop NASA Ames The FAA predicts commercial operations to increase 2.1% annually1 “The FAA is trying to take controllers so far out-of-the-loop… that they can't get back into the loop when the computer quits.” Don Brown, former air traffic controller, Safety Rep for National Air Traffic Controllers Assoc.2 Improving automation requires maintaining controller awareness, which requires models of controller cognition 1FAA Forecast Fact Sheet – Fiscal Years 2011-2031 2Don Brown, “Can the FAA Get Rid of Air Traffic Controllers?” The Atlantic Online, March 6, 2011

  26. deviated aircraft intruder Initial Studies [Alex Bayen]

  27. Qualitative Models Quantitative Models Monitor for conflicts Decide/schedule resolution Cognitive Analysis Grouping, conflict classification, and maneuvers ?? 3 Generate conflict resolution plan Plan checking 1 2 Command resolution actions Air traffic controller cognitive strategies are known, but it’s very difficult to get parameters for quantitative models. Seamster, T., Redding, R., Cannon, J., Ryder, J., and Purcell, J., “Cognitive Task Analysis of Expertise in Air Traffic Control.” The International Journal of Aviation Psychology, No. 3, 1993.

  28. Infeasible to get data from real controllers • Most experiments use retired controllers or student volunteers • Retired controllers are rare, students get bored, where to get more data? Trajectories, aircraft states, player inputs Contrails: Air traffic control game for Android Replay Engine on Server

  29. The advantages of Big Data: Contrails to date A Typical ATC experiment1 1391 installs 10,391 games played 28 participants 168 trials (6 each) Local US college students Max individual sample (est): 100 planes 10+ countries Most active user: 9489 planes Contrails install base as of 2/14/2012 Android Market Statistics Users by country, as of 2/14/2012 1M. Stone et al., “Prospective memory in dynamic environments: Effects of load, delay, and phonological rehearsal.” Memory, 2001.

  30. 3. Treating breast cancer

  31. Western Blots Tens of data points

  32. Reverse Phase Protein Arrays (RPPA) Tens of Thousands of data points [Gordon Mills, MD Anderson Cancer Center]

  33. Mass Cytometry – Time of Flight (CyTOF) Inductively Coupled Plasma (ICP) (Time Of Flight) mass spectrometer

  34. CyTOF data Tens to hundreds of millions of data points [Brend, Eli]

  35. (a) HER2 inhibition is persistent, but its effects on HER3 and AKT inhibition are transient (b) After 48 hours of applying Gefitinib, HER3 is transferred from the cytoplasm to the cell membrane (c) pHER3 does not survive the application of Gefitinib when AKT is activated [Sergina et al, 2007]

  36. Model identification • Identifying network structure • Reactions modeled as simple mass action or catalytic equations • Abstract variables modeling the transport mechanism

  37. Model implications Control engineering point of view: • steer the state of the cells to a new equilibrium • low AKT correlated with cell death, seek equilibrium with low AKT • low membrane HER3 may prevent recovery of AKT • different drugs could be applied at different times: • reduce membrane HER3 AKT

  38. Model implications Control engineering point of view: • steer the state of the cells to a new equilibrium • low AKT correlated with cell death, seek equilibrium with low AKT • low membrane HER3 may prevent recovery of AKT • different drugs could be applied at different times: • reduce membrane HER3 AKT

  39. Model implications Control engineering point of view: • steer the state of the cells to a new equilibrium • low AKT correlated with cell death, seek equilibrium with low AKT • low membrane HER3 may prevent recovery of AKT • different drugs could be applied at different times: • reduce membrane HER3 • inhibit HER2 first drug is used to get the cells to a state more vulnerable to second AKT lapatinib

  40. Experimental Results 0.1ng/ml HRG (to model the HRG in the body) 10ng/ml HRG (over activation) Preliminary test on SKBR3, 250nM Lap was applied after treatment with HRG. Apoptosis rates shown:

  41. Conclusions • “Physics-based” models not always available: • Systems that involve human action • Systems with thousands of variables • Big Data has and will augment our abilities to identify, interact with, and control these systems • Current projects: • ActionWebs: • Energy-efficient HVAC control • Energy-efficient Air Traffic Control • Learning human action from data • Biology: • Cancer • Development • Metabolic networks

More Related