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
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Control Theory
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Control Theory
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Control Theory
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Control Theory
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Control Theory
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Control Theory
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Control Theory
Control inputs are based on the mathematical model
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Hybrid Control Theory
Examples
HER2 inhibition in breast cancer
High performance flight
Air traffic control
Maneuvering through modes
Grouping and conflict
classification
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[Shaw] [Seamster] [Kahah] [Itani, Gray, Moasser]
2
Multiple equilibria
3
1. High Performance Flight
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Reachable Sets
Backwards
Reachable Set
unsafe
In red, system
may become
unsafe
In blue,
system will
stay safe
On boundary, apply control to stay out of red
Example: Collision Avoidance
Pilots instructed to attempt to collide vehicles
Example: Back-Flip
Recovery
Drift
Impulse
Back-flip
Recovery
Drift
Impulse
Back-Flip: Results
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?
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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-based Model Predictive Control
Learning-based Model Predictive Control
• Unknown system dynamics represented using an
oracle
• At each time step
– Optimization solved, Oracle updated
Learning-based Model Predictive Control
• Unknown system dynamics represented using an
oracle
• At each time step
– Optimization solved, Oracle updated
Performance
LBMPC
Safety
Example: Learning to fly
• Linear model
– Physics for structure
– Experimental
coefficients
• Physics improve
statistics
– Fewer parameters
– Less noise
Example: Learning to fly
video
2. Air Traffic Control
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1
2
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Closely Spaced Parallels
750 ft separation
San Francisco Airport
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-theloop… 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
Initial Studies
deviated aircraft
intruder
[Alex Bayen]
Cognitive Analysis
Grouping, conflict
classification, and
maneuvers
1
2
Qualitative Models
Monitor for
conflicts
Quantitative Models
Decide/schedule
resolution
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Generate
conflict
resolution plan
?
?
Plan checking
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.
• 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
The advantages of Big Data:
A Typical ATC experiment1
Contrails to date
28 participants
168 trials (6 each)
1391 installs
10,391 games played
Local US college students
10+ countries
Max individual sample (est): 100
planes
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.
3. Treating breast cancer
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Western Blots
Tens of
data
points
Reverse Phase Protein
Arrays (RPPA)
Tens of
Thousands
of data
points
[Gordon Mills, MD Anderson Cancer Center]
Mass Cytometry – Time of Flight
(CyTOF)
Inductively Coupled Plasma (ICP)
(Time Of Flight) mass spectrometer
CyTOF data
Tens to
hundreds
of millions
of data
points
[Brend, Eli]
tinib. SKBR3 cells were treated for the times indicated and cell lysates were
plenished with new media and fresh drug every 24 hours. These data show that
patinib but 5 mM drug is required to durably inhibit HER2/3 signaling.
(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]
Model identification
• Identifying network
structure
• Reactions modeled
as simple mass
action or catalytic
equations
• Abstract variables
modeling the
transport mechanism
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:
1. reduce membrane
HER3
AKT
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:
1. reduce membrane
HER3
AKT
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:
1. reduce membrane
HER3
2. inhibit HER2
first drug is used to get the
cells to a state more
vulnerable to second
AKT
lapatinib
Experimental Results
Preliminary test on SKBR3, 250nM Lap was applied after
treatment with HRG. Apoptosis rates shown:
Treatment
Lap
Lap
Lap
Lap
Ave.
Scheme
Scheme Scheme Scheme
Ave
%
apoptosis
13.5
13.56 6.89
11.3
41.9
51.85
59.35
0.1ng/ml HRG (to
10ng/ml HRG (over
model the HRG in the activation)
body)
51.0
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
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