Universal Laws and Architecturesngns/docs/Review_2010/Doyle... · 2011-01-13 · Universal Laws and...
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Universal Laws and Architectures
John DoyleJohn G Braun Professor
Control and Dynamical Systems, BioEng, ElecEngCaltech
Third Year Review: October27, 2010
Plus a cast of thousands
Theory DataAnalysis
Numerical Experiments
LabExperiments
FieldExercises
Real-WorldOperations
• First principles• Rigorous math• Algorithms• Proofs
• Correct statistics
• Only as good as underlying data
• Simulation• Synthetic,
clean data
• Stylized• Controlled• Clean,
realworld data
• SemiControlled
• Messy, realworld data
• Unpredictable• After action
reports in lieu of data
Doyle
Universal Laws and Architectures
layeredmultiscale
Laws, laws, and architecture
• Conservation laws, constraints, hard limits– Important tradeoffs are between – Control, computation, communication, energy,
materials, measurement– Existing theory is fragmented and incompatible– Continuing progress on unifications
• Power laws, data, models, high variability
• Architecture= “constraints that deconstrain”– Expand “layering as optimization”– Include human in loop and physical action/control– Achieving hard limits
Triaged today
• Power laws, data, models, high variability
– Estimating tails, MLE and WLS
– High variability in markets
• Architecture
– Dynamics in layered architectures
– Case studies: TCP/IP, cell, brain, wildfire ecology, …
– Naming and addressing details
– Beam forming details
IEEE TRANS ON SYSTEMS, MAN, AND CYBERNETICS, JULY 2010Alderson and Doyle
• Each focuses on one dimension• Important tradeoffs are across these dimensions• Need “clean slate” theories• Progress is encouraging• (Old mysteries are also being resolved)
was
tefu
l
fragile?
slow
?• Thermodynamics (Carnot) • Communications (Shannon)• Control (Bode)• Computation (Turing)
Standard system theories are severely limited
Robust• Secure• Scalable• Evolvable• Verifiable• Maintainable• Designable• …
Fragile• Not …• Unverifiable• Frozen•…
Most dimensions are robustness
Collapse for visualization
fragile
fragile
wasteful
fragile
Conservation laws
waste time
waste resources
• Important tradeoffs are across these dimensions
• Speed vs efficiency vs robustness vs …• Robustness is most important for
complexity• Collapse efficiency dimensions
Conservation laws
wasteful
fragile
?
?
?
?
Bad theory?
�???�
?
?
Bad architectures?
wasteful
fragile
gap?
Sharpen hard bounds
Case studies
wasteful
fragile
Conservation laws
Architecture Good architectures allow for effective
tradeoffs
wasteful
fragile
Sharpen hard bounds
�bad �
Find and fix bugs
Complementary approaches
wasteful
fragile
Case studies
�bad �
Find and fix bugs
wasteful
fragile
TCPIP
Physical
MACSwitch
MAC MACPt to Pt Pt to Pt
Diverse applications
Layered architectures
App AppApplications
Router
App AppApplications
Router
3.5 viewpoints on layered architecture:• Operating systems• Programming languages• Control and dynamical systems
• Operations research, optimization• Information theory
Naming and addressing
• Names to locate objects• 2.5 ways to resolve a name
1. Exhaustive search, table lookup2. Name gives hints
• Extra ½ is for indirection• Address = name that involves locations
Operating systems
• OS allocates and shares diverse resources among diverse applications
• “Strict layering” is crucial• e.g. clearly separate
– Application name space– Logical (virtual) name/address space– Physical (name/) address space
• Name resolution within applications• Name/address translation across layers
Benefits of stricter layering
“Black box” effects of stricter layering• Portability of applications• Security of physical address space• Robustness to application crashes• Scalability of virtual/real addressing• Local variables and addresses
• Optimization/control by duality?
Problems with incomplete layering
“Black box” benefits are lost• Global variables? @$%*&!^%@& • Poor portability of applications• Insecurity of physical address space• Fragile to application crashes• No scalability of virtual/real addressing
• Limits optimization/control by duality?
App
kernel
user
In operating systems:Don’t cross layers
Direct access to
physical memory?
In programming:No global variables
App AppApplications
Router
App AppIPC
Global and direct access to
physical address!
Robust?• Secure• Scalable• Verifiable• Evolvable• Maintainable• Designable• …
DNS
IP addresses interfaces not
nodes
Physical
IP
TCP
Application
Naming and addressing need to be • resolved within layer• translated between layers• not exposed outside of layer
Related issues• DNS• NATS• Firewalls• Multihoming• Mobility• Routing table size• Overlays• …
Embeddedvirtual
actuator/ sensor
Network cable
Controller
Lib
App
DIF
Networked/embedded/layered
Lib
Physical plant
Embeddedvirtual
actuator/ sensor
Network cable
Controller
DIF
Physical plant
Meta-layering of cyber-phys control
Architecture Good architectures allow for effective
tradeoffs
wasteful
fragile
Embeddedvirtual
actuator/ sensor
DIF
Collapsing the stack at the edges
Lib
Physical plant
Exploiting the physical
Collapsing the stack at the edges
Architecture Good architectures allow for effective
tradeoffs
wasteful
fragile
Exploiting the physical
Collapsing the stack at the edges
Programmable Antenna Design UsingProgrammable Antenna Design UsingConvex OptimizationConvex Optimization
Lavaei, Babakhani, Hajimiri, and Doyle
Caltech
Theory: Lavaei, Doyle Experiment: Babakhani, Ali Hajimiri
I
Q
Papers by Lavaei, Babakhani, Hajimiri, and Doyle,
"Design of Passively Controllable Smart Antennas for Wireless Sensor Networks," Submitted to IEEE Transactions on Automatic Control.
"Solving Large-Scale Hybrid Circuit-Antenna Problems," To appear in IEEE Transactions on Circuits and Systems I, 2010.
"'Passively Controllable Smart Antennas," to appear in IEEE Global Communications Conference (GLOBECOM), Miami, Florida, 2010.
"Finding Globally Optimum Solutions in Antenna Optimization Problems," in IEEE International Symposium on Antennas and Propagation, Toronto, Canada, 2010.
"Programmable Antenna Design Using Convex Optimization," in Math. Theory of Networks and Systems, Budapest,2010 (invited paper).
"A Study of Near-Field Direct Antenna Modulation Systems Using Convex Optimization," in American Control Conference, Baltimore, 2010.
"Solving Large-Scale Linear Circuit Problems via Convex Optimization," in Proc. 48th IEEE Conf on Dec. and Control, Shanghai, China, 2009.
33
Summary of resultsSummary of results
34
� A passively controllable smart (PCS) antenna that can be implemented as an integrated circuit and be programmed in real time.
� Can be used for smart data transmission.� For the first time, excellent beam-forming
patterns obtained with a small-sized antenna.� The programming of the PCS antenna
overcomes apparent intractability.� Potentially completely changes what is possible
at wireless physical layer
Sharpen hard bounds
�bad �
Find and fix bugs
Complementary approaches
wasteful
fragile
Case studies
Sharpen hard bounds
wasteful
fragile
Case studies that achieve bounds
Theory plus biology case study
Hard tradeoffs between• Fragility (disturbance rejection)• Metabolic overhead
– Amount (of enzymes)– Complexity (of enzymes)
• Glycolytic oscillations • Most ubiquitous and studied “circuit” in science or
engineering • New insights and experiments• Resolves longstanding mysteries• Biology component funded by NIH and Army ICB
• Fragility (disturbance rejection)
• Metabolic overhead
– Amount (of enzymes)
– Complexity (of enzymes)
Fragility
hard limitsimple enzyme
Enzyme amount
complex enzyme
simple enzyme
Fragility
Enzyme amount
complex enzyme
lnz p
z p
��
� � 2 20
1ln ln
z z pS j d
z z p� �
� �
� �� � �� �� �� ��Theorem
� � 2 20
1ln ln
z z pS j d
z z p� �
� �
� �� � �� �� �� ��Theorem
0 5 10
-1
-0.8
-0.6
-0.4
-0.2
0
0.2Time Simulation
0 5 10-1
-0.5
0
0.5
1
1.5
2
Log|
S|
Sensitivity Function
h=2h=3h=4
g=0, k=3
TimeFrequency
� �ln S j�
Fragility (standard control theory) rigorous, firstprinciples.
simple enzyme
Enzyme amount
complex enzyme
� � 2 20
1ln ln
z z pS j d
z z p� �
� �
� �� � �� �� �� ��Theorem
• z and p are functions of enzyme complexity and amount• standard biochemistry models• phenomenological• first principles?
k
z p
z p
��
10-1
100
10110
0
101
Fragility Biological architectures achieve hard limits and use complex enzymes
and networks
� � 2 20
1ln ln
z z pS j d
z z p� �
� �
� �� � �� �� �� ��
complex enzyme
Enzyme amount
Fragility
Metabolic overhead
Architecture
“Conservation laws”
Good architectures allow for effective
tradeoffs
Alternative biocircuitswith shared architecture
Architecture Good architectures allow for effective
tradeoffs
wasteful
fragile
Phenomenology1. Incorporate domain specifics2. First principles models
Fragilityhard limits
simple
Overhead, waste
complex
• General• Rigorous• First principle
• Domain specific• Ad hoc• Phenomenological
Plugging in domain details
?
Fragility
Overhead, waste
• General• Rigorous• First principle
• Domain specific• Ad hoc• Phenomenological
Plugging in domain details
?
• Fundamental multiscale physics
• Start classically
• Foundations, origins of
– noise
– dissipation
– amplification
IEEE TRANS ON AUTOMATIC CONTROL, to appear, FEBRUARY, 2011Sandberg, Delvenne, and Doyle
Layers in hardware
So well-known as to be taken for granted• Digital abstraction and modularity• Analog substrate is active and lossy• Microscopic world is lossless
• Reconcile these in a clear and coherent way• Exploit designable physical layer more
s
�
1�
+step response
s
���
step response
V(t)
s
�
1�
+step response
0 0.5 1 1.5 2 2.50
0.5
1
1.5
Time (sec)
Am
plitu
de
1 te ���
10� �dissipative,
lossy
But the microscope world is lossless (energy is conserved). Where does dissipation come from?
s
�+
step response
V(t)
2 2k
s
s ��� LosslessApproximate
s
�
1�
+step response
dissipative,lossy
s
�+
step response
V(t)
step response
2 2k
s
s ���
LosslessApproximate
2 2k
s
s ��� LosslessApproximate
step response
2 2k
s
s ���
LosslessApproximate
T=1
0 0.5 1 1.5 2 2.5-1.5
-1
-0.5
0
0.5
1
1.5
Time (sec)
Am
plitu
de
n=10
T=1
n=10
0 0.2 0.4 0.6 0.8 1-1.5
-1
-0.5
0
0.5
1
1.5
0 0.2 0.4 0.6 0.8 1-1.5
-1
-0.5
0
0.5
1
1.5
n=100
0 0.2 0.4 0.6 0.8 10
0.5
1
1.5
Time (sec)
s
�+
step response
V(t)
2 2k
s
s ��� LosslessApproximate
T=1n=10
n=4
0 0.5 1 1.5 2 2.5-1.5
-1
-0.5
0
0.5
1
1.5
Time (sec)
Am
plitu
de
n=10
step response
2 2k
s
s ���
LosslessApproximate
2 2k
s
s ���
random initial
conditions
n=100 0.2 0.4 0.6 0.8 1
-2
-1.5
-1
-0.5
0
0.5
1
1.5Response to Initial Conditions
Time (sec)
Am
plitu
de
T=1
0 0.2 0.4 0.6 0.8 1-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8Response to Initial Conditions
Time (sec)
Am
plitu
de
n=100
n=100 0.2 0.4 0.6 0.8 1
-2
-1.5
-1
-0.5
0
0.5
1
1.5Response to Initial Conditions
Time (sec)
Am
plitu
de
T=10 0.2 0.4 0.6 0.8 1
-1.5
-1
-0.5
0
0.5
1
1.5
0 0.2 0.4 0.6 0.8 1-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8Response to Initial Conditions
Time (sec)
Am
plitu
deDissipation
Fluctuation
Theorem: Fluctuation � Dissipation
Theorem: Fluctuation Dissipation
Theorem: Linear passive ifflinear lossless approximation
Theorem: Linear active needs nonlinear lossless approximation
System
Sense Est.
+ ( )e t-ˆ( )y t
( )y t
( )y t�
“Physical” implementation
Back action
Sensor “noise”
Consequences
Back action
System
Sense Est.
+ ( )e t-ˆ( )y t
( )y t
� � � �2 2( )E y t kTt O t� � �
• Sensor at temp T• Short interval (0,t)
( )y t�
Sensor “noise”
� � � �2 ( ) 1kT
E e t Ot
� �
Theorem
� � � �2 ( ) 1kT
E e t Ot
� �
System
Sense Est.
+ ( )e t-ˆ( )y t
( )y t
( )y t�
back-action
error
� �2 ( )E y t kT� �( )y t�
( )e t
Sensor “noise”
� � � �2 ( ) 1kT
E e t Ot
� �
System
Sense Est.
+ ( )e t-ˆ( )y t
( )y t
( )y t�
error� �2 ( )
kTE e t
t�
( )e t
Back action
System
Sense Est.
+ ( )e t-ˆ( )y t
( )y t
( )y t�
back-action
� �2 ( )E y t
kTt
�
�
� �2 ( )E y t kT� �
( )y t�
� � � �2 ( ) 1kT
E e t Ot
� �
System
Sense Est.
+ ( )e t-ˆ( )y t
( )y t
( )y t�
back-action
error
� �2 ( )E y t
kTt
�
�
� �2 ( )kT
E e tt
�
� �2 ( )E y t kT� �
� �( ) ( )y t e t kT O t� � �
( )y t�
( )e t
Theorem:
System
Sense Est.
+ ( )e t-ˆ( )y t
( )y t
( )y t�
error
Cold sensors are better
and faster (but not cheaper)
� �( ) ( )y t e t O tkT� � �
( )y t�back-action
( )e t
System
Sense Est.
+ ( )e t-ˆ( )y t
( )y t
( )y t�
back-action
error
( ) ( )y t e t kT� �
larger tmore data
smaller tless data
� �2 ( )E y t
kTt
�
�
� �2 ( )kT
E e tt
�
System
Sense Est.
+ ( )e t-ˆ( )y t
( )y t
( )y t�
back-action
error
� �2 ( )E y t
kTt
�
�
� �2 ( )kT
E e tt
�
� �( ) ( )y t e t kT O t� � �
A transient and far-from-equilibriumupgrade of statistical mechanics
back-action
error
A transient and far-from-equilibriumupgrade of statistical mechanics
• Estimation to control• Efficiency of devices, enzymes• Classical to quantum
10-3
10-2
10-1
10010
0
101
102
103
mix
unmix
rank k 1
kk x��
Power laws
10-2
10-1
100
10-3
10-2
10-1
10010
0
101
102
103
mix
unmix
rank k1
kk x��
SoCalFaults.pdf
4 2lpnf-w
2 bigsur
12 3lpnf-nw
• Mix and unmixed fits well with a=-.5 in body,• Mix tail is deviating as expected
These are the closest to our assumptions:• Coastal• Chaparral • large watersheds• limited urban boundary
102
103
104
10510
0
101
102 mechanistic
model
4 2lpnf-w
2 bigsur
12 3lpnf-nw
mix
• Mix and unmixed fits well with a=-.5 in body,• Mix tail is deviating as expected
These are the closest to our assumptions:• Coastal• Chaparral • large watersheds• limited urban boundary
102
103
104
10510
0
101
102
4 2lpnf-w
2 bigsur
12 3lpnf-nw
mix
• Mix and unmixed fits well with a=-.5 in body,• Mix tail is deviating as expected
These are the closest to our assumptions:• Coastal• Chaparral • large watersheds• limited urban boundary
102
103
104
10510
0
101
102
model
102
103
104
105
106
107
100
101
102
4 2lpnf-w
2 bigsur
12 3lpnf-nw
Cutoffs are crucial
Size of all of CAhectares
Pareto distribution with finite-scale effect
100
101
102
100
101
102
103
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MLE � WLS� WLS with cutoff
Triaged today
• Power laws, data, models, high variability– Estimating tails, MLE and WLS– High variability in markets
• Architecture– Dynamics in layered architectures– Case studies: TCP/IP, cell, brain, wildfire
ecology, …– Naming and addressing details– Beam forming details
Laws, laws, and architecture
• Conservation laws, constraints, hard limits– Important tradeoffs are between – Computation, control, communication, energy,
materials, measurement– Existing theory is fragmented and incompatible– Continuing progress on unifications
• Power laws, data, models, high variability
• Architecture= “constraints that deconstrain”– Expand “layering as optimization”– Include human in loop and physical action/control– Achieving hard limits
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