Universal laws and architecture:Challenges for Sustainable Infrastructure
John DoyleJohn G Braun Professor
Control and Dynamical Systems, EE, BioECaltech
“Universal laws and architectures?”
• Universal “conservation laws” (constraints)• Universal architectures (constraints that deconstrain)• Mention recent papers*• Focus on broader context not in papers• Lots of theorems• Case studies: evolution, physiology, bacterial biosphere, ,
glycolytic oscillations, Internet/IT, neuroscience, smartgrid, aerospace, wildfire ecology, turbulence, stat mech, earthquakes, heart rate variability
*try to get you to read them?
Collaborators and contributors(partial list, out of date,…)
Theory: Parrilo, Carlson, Murray, Vinnicombe, Paganini, Papachristodoulou, Prajna, Goncalves, Fazel, Liu, Lall, D’Andrea, Jadbabaie, Dahleh, Martins, Recht, many more current and former students, …
Biology: Chandra, Buzi, Csete,Yi, El-Samad, Khammash, Tanaka, Arkin, Savageau, Simon, Gross, Kitano, Hucka, Gillespie, Petzold, F Doyle, Stelling, Caporale,…
Web/Internet: Chen, Low, Lavaei, Sojoudi, Li, Alderson, Willinger, Kelly, Zhu,Yu, Wang, Chandy, Trossen, Griffin,…
Turbulence: Gayme, McKeon, Bamieh, Bobba, Gharib, Marsden, …Physics: Sandberg, Delvenne, Barahona, Carlson, Asimakopoulos,
Matni,…Disturbance ecology: Moritz, Carlson,…Neuroscience: Lamperski, Grafton, Gazzaniga, Mitra,…
Current Caltech Former Caltech OtherLongterm Visitor
Thanks to
• NSF• ARO• ONR • Braun family• Lee Center for Advanced Networking (Caltech)• Philips
• NIH/NIGMS? AFOSR? DARPA?
• Special thanks to Hiroaki Kitano (ERATO)
Happy families are all alike; every unhappy family is unhappy in its own way.
Leo Tolstoy, Anna Karenina,
Chapter 1, first line
• What does this even mean? • Given incredible diversity of people and environments?• It has to be a statement about organization.
• Happy family = empathy + cooperation + simple rules?• Constraints on components and architecture
wasteful
fragile
efficient
robust
Happy families are all alike; every unhappy family is unhappy in its own way.
Want robust and efficient systems and architectures
Are robust, efficient systems/architectures
“all alike”?
accessibleaccountableaccurateadaptableadministrableaffordableauditableautonomyavailablecredibleprocess
capablecompatiblecomposable configurablecorrectnesscustomizabledebugabledegradabledeterminabledemonstrable
dependabledeployablediscoverable distributabledurableeffectiveefficientevolvableextensiblefailure transparentfault-tolerantfidelityflexibleinspectableinstallableIntegrityinterchangeableinteroperable learnablemaintainable
manageablemobilemodifiablemodularnomadicoperableorthogonalityportableprecisionpredictableproducibleprovablerecoverablerelevantreliablerepeatablereproducibleresilientresponsivereusable robust
safety scalableseamlessself-sustainableserviceablesupportablesecurablesimplicitystablestandards
compliantsurvivablesustainabletailorabletestabletimelytraceableubiquitousunderstandableupgradableusable
Requirements on systems and architectures
happy?
accessibleaccountableaccurateadaptableadministrableaffordableauditableautonomyavailablecredibleprocess
capablecompatiblecomposable configurablecorrectnesscustomizabledebugabledegradabledeterminabledemonstrable
dependabledeployablediscoverable distributabledurableeffectiveefficientevolvableextensiblefailure transparentfault-tolerantfidelityflexibleinspectableinstallableIntegrityinterchangeableinteroperable learnablemaintainable
manageablemobilemodifiablemodularnomadicoperableorthogonalityportableprecisionpredictableproducibleprovablerecoverablerelevantreliablerepeatablereproducibleresilientresponsivereusable robust
safety scalableseamlessself-sustainableserviceablesupportablesecurablesimplicitystablestandards
compliantsurvivablesustainabletailorabletestabletimelytraceableubiquitousunderstandableupgradableusable
Requirements on systems and architectures
happy?
accessibleaccountableaccurateadaptableadministrableaffordableauditableautonomyavailablecredibleprocess
capablecompatiblecomposable configurablecorrectnesscustomizabledebugabledegradabledeterminabledemonstrable
dependabledeployablediscoverable distributabledurableeffectiveefficientevolvableextensiblefailure transparentfault-tolerantfidelityflexibleinspectableinstallableIntegrityinterchangeableinteroperable learnablemaintainable
manageablemobilemodifiablemodularnomadicoperableorthogonalityportableprecisionpredictableproducibleprovablerecoverablerelevantreliablerepeatablereproducibleresilientresponsivereusable robust
safety scalableseamlessself-sustainableserviceablesupportablesecurablesimplicitystablestandards
compliantsurvivablesustainabletailorabletestabletimelytraceableubiquitousunderstandableupgradableusable
Requirements on systems and architectures
wasteful
fragile
efficient
robust
wasteful
fragile
efficient
robust
Happy families are all alike; every unhappy family is unhappy in its own way.
Want robust and efficient systems and architectures
In what sense are robust, efficient systems/architectures
all alike?
inefficientwasteful
weak fragile
efficient(slow)
strongrobust
Biology
Human evolution Apes
feetskeletonmuscleskinguthands
inefficientwasteful
weak fragile
efficient(slow)
strongrobust
Biology
Hard tradeoffs?
Apes
Architecture?
inefficientwasteful
weak fragile
efficient(slow)
strongrobust
Biology
sticksstonesfire
+Technology
inefficientwasteful
weak fragile
efficient(slow)
strongrobust
Biology+Technology
++Technology
wasteful
fragile
efficient
robust Hard tradeoffs?
Architecture?
Constraints(that deconstrain)
wasteful
fragile
efficient
robust
Next 3 speakers
Biology
sticksstonesfire
+Technology
feetskeletonmuscleskinguthands
Human complexity?
wasteful
fragile
efficient
robust
Robust Fragile
Human complexity
Metabolism Regeneration & repair Healing wound /infect
Obesity, diabetes Cancer AutoImmune/Inflame
Start with physiology
Lots of triage
Robust Fragile
Mechanism?
Metabolism Regeneration & repair Healing wound /infect
Fat accumulation Insulin resistance Proliferation Inflammation
Obesity, diabetes Cancer AutoImmune/Inflame
Fat accumulation Insulin resistance Proliferation Inflammation
Robust Fragile
What’s the difference?
Metabolism Regeneration & repair Healing wound /infect
Obesity, diabetes Cancer AutoImmune/Inflame
Fat accumulation Insulin resistance Proliferation Inflammation
ControlledDynamic
UncontrolledChronic
ControlledDynamic
UncontrolledChronic
Low meanHigh variability
High meanLow variability
Fat accumulation Insulin resistance Proliferation Inflammation
Death
Robust Fragile
Restoring robustness?
Metabolism Regeneration & repair Healing wound /infect
Obesity, diabetes Cancer AutoImmune/Inflame
Fat accumulation Insulin resistance Proliferation Inflammation
ControlledDynamic
UncontrolledChronic
Low meanHigh variability
High meanLow variability
Fat accumulation Insulin resistance Proliferation Inflammation
Robust Fragile Metabolism Regeneration & repair Healing wound /infect
Obesity, diabetes Cancer AutoImmune/Inflame
Fat accumulation Insulin resistance Proliferation Inflammation
• Fragility Hijacking, side effects, unintended… • Of mechanisms evolved for robustness • Complexity control, robust/fragile tradeoffs• Math: robust/fragile constraints (“conservation laws”)
Accident or necessity?
Both
Human complexity?
wasteful
fragile
efficient
robust
Robust Yet Fragile
Human complexity
Metabolism Regeneration & repair Immune/inflammation Microbe symbionts Neuro-endocrine Complex societies Advanced technologies Risk “management”
Obesity, diabetes Cancer AutoImmune/Inflame Parasites, infection Addiction, psychosis,… Epidemics, war,… Disasters, global &!%$# Obfuscate, amplify,…
Accident or necessity?
In the real (vs virtual) world
What matters:
• Action
What doesn’t:
• Data
• Information
• Computation
• Learning
• Decision
• …
Don’t worry ...• “Like, dude, like, chill…” • “There’s an app for that.”• “The ‘new sciences’ of …”• “There’s a gene…• “The market will...”• “Order for free…”• “The rapture is near.”
Don’t worry ...• “Like, dude, like, chill…” • “There’s an app for that.”• “The ‘new sciences’ of …”• “There’s a gene…• “The market will...”• “Order for free…”• “The rapture is near.”
Come back to this later
IEEE TRANS ON SYSTEMS, MAN, AND CYBERNETICS, JULY 2010, Alderson and Doyle
Csete and Doyle
Feathers and
flapping? Or lift, drag, propulsion, and control?
The dangers of naïve biomemetics
Getting it (W)rightGetting it (W)right,, 1901 1901• “We know how to construct airplanes...” (lift and drag)• “… also know how to build engines.” (propulsion)• “Inability to balance and steer still confronts students of the flying problem.” (control)• “When this one feature has been worked out, the age of flying will have arrived, for all other difficulties are of minor importance.”
Wilbur Wright on CWilbur Wright on Control,ontrol, 1901 1901
Getting it rightGetting it right,, 2011 2011• “...know how to construct sustainable infrastructures...”• “… also know how to build their components.”• “Inability to control and manage fragilities ....” • “When this one feature has been worked out, the age of sustainability will have arrived, for all other difficulties are of minor importance.”
Fragilities? • Unintended crashes, hijacking, parasitism, evolution• Need robust, efficient, evolvable architectures• Policy trumps technology (next talks)• Aligning incentives (next talks)
wasteful
fragile
efficient
robust
Hard tradeoffs?
Chandra, Buzi, and Doyle
simple enzyme
Fragility
Metabolic Overhead
complex enzyme
lnz p
z p
2 20
1ln ln
z z pS j d
z z p
Theorem!
Glycolytic “circuit” and oscillations
• Perfect circuit case study – Every cell (1030), heavily studied– Experiments, models, simulation, …, all “well-known”
• Oscillations?– Remain persistent mystery (decades,…?)– Frozen accident? Edge of chaos? Emergulence?
• New insight: constraints and tradeoffs– “Universal” robustness/efficiency tradeoff – Evolution + physiology + “CDS” theory– Issues & theory: broadly relevant and “universal”
• Extreme responses typical
ubiquitous
Glycolytic “circuit” and oscillations
• End of an old story (why oscillations)– no purpose per se– side effect of hard robustness/efficiency tradeoffs– just needed a theorem
• Beginning of a new one – robustness/efficiency tradeoffs– complexity and architecture– need more theorems and applications
robust
efficient wasteful
fragile
Tradeoffs?
Hard limit
Robust=maintain energy level w/fluctuating demand
Efficient=minimize metabolic overhead
Want robust and efficient
Control, OR Comms
Compute Physics
ShannonBode
TuringGodel
EinsteinHeisenberg
Carnot
Boltzmann
Theory?Deep, but fragmented, incoherent, incomplete
Nash
Von Neumann
KalmanPontryagin
Control Comms
Compute Physics
ShannonBode
TuringGodel
Einstein
Heisenberg
Carnot
Boltzmann
wasteful?
fragile?
slow?
?
• Each theory one dimension• Tradeoffs across dimensions• Assume architectures a priori• Progress is encouraging, but…
.1%
1%
10%
100%
http://phe.rockefeller.edu/Daedalus/Elektron/
F Efficiency
When will steam engines be 200% efficient?
Exponential improvement
Note: this is real data!
.1%
1%
10%
50%
http://phe.rockefeller.edu/Daedalus/Elektron/
When will steam engines be 200% efficient?
1
F
F
F Efficiency
Oops… never.
wasteful
fragile
robust
efficient
At best we get one
Technology?
wasteful
fragile
robust
efficient
Often neither
???
Bad theory?
???
?
?
Bad architectures?
wasteful
fragile
gap?
robust
efficient
Case studies
wasteful
fragile
Sharpen hard bounds
Hard limit
Conservation “laws”?
simple enzyme
Fragility
Overhead
complex enzyme
lnz p
z p
2 20
1ln ln
z z pS j d
z z p
Theorem!
z and p functions of enzyme complexity and
amount
What reviewers say• “The approach to establish universality for all biological and
physiological systems is simply wrong. It cannot be done…” • “…does not seem to have an understanding or appreciation of
the vast diversity of biological and physiological systems…” • “… a mathematical scheme without any real connections to
biological or medical problems…” • “…desire to develop rigorous framework is understandable, but
usually this can be done only by imposing a high degree of abstraction, which would then make the model useless …”
• “While the notion of universality is well justified in physics, it is perhaps not so useful in biological sciences and medicine. To develop a set of universal principles for biological and physiological systems is mostly likely a dream that will never be realized, due to the vast diversity in such systems.”
Glycolytic “circuit” and oscillations
• End of an old story (why oscillations)– no purpose per se– side effect of hard robustness/efficiency tradeoffs– just needed a theorem
• Beginning of a new one – robustness/efficiency tradeoffs– complexity and architecture– need more theorems and applications
wasteful
fragile
efficient
robust
Hard tradeoffs?
Architecture?
TCPIP
Physical
MACSwitch
MAC MACPt to Pt Pt to Pt
Diverse applications
Layered architectures
Proceedings of the IEEE, Jan 2007
Chang, Low, Calderbank, and Doyle
TCPIP
Physical
Diverse applications
Too good?
Diverse
TCPIP
Deconstrained(Hardware)
Deconstrained(Applications)
Layered architectures
ConstrainedNetworks
“constraints that deconstrain” (Gerhart and Kirschner)
OS
Deconstrained(Hardware)
Deconstrained(Applications)
Layered architectures
ConstrainedPCs
“constraints that deconstrain” (Gerhart and Kirschner)
OS
Deconstrained(Hardware)
Deconstrained(Applications)
Layered architectures
Constrained Control, share, virtualize, and manage resources
ProcessingMemoryI/O
Few global variablesFew global variables
Don’t cross layersDon’t cross layers
TCP/IP
Deconstrained(Hardware)
Deconstrained(Applications)
Layered architectures
Constrained Control, share, virtualize, and manage resources
Processing?Memory?I/OCommsLatency?
Few global variables?Few global variables?
Don’t cross layers?Don’t cross layers?
Cata
bolis
m
AA
Ribosome
RNA
RNAp
transl.Proteins
xRNA transc.
Prec
urso
rs
Nucl.
AA
DNA
DNAp
Repl. Gene
ATP
ATP
Enzymes
Building Blocks
Shared protocols
Deconstrained (diverse)
Environments
Deconstrained (diverse) Genomes
Bacterial biosphere
Architecture =
Constraints that
Deconstrain
Layered architectures
Cat
abol
ism
AA
Ribosome
RNARNAp
transl.Proteins
xRNAtransc.
Pre
curs
ors
Nucl.
AA
DNADNAp
Repl. Gene
ATP
ATP
Enzymes
Building Blocks
Crosslayer autocatalysis
Macro-layers
Inside every cellalmost
Cata
bolis
m
AA
Ribosome
RNA
RNAp
transl.Proteins
xRNA transc.
Prec
urso
rs
Nucl.
AA
DNA
DNAp
Repl. Gene
ATP
ATP
Enzymes
Building Blocks
Core conserved constraints facilitate
tradeoffs
Deconstrained phenotype
Deconstrained genome
What makes the bacterial biosphere so adaptable?
Active control of the genome (facilitated variation)
Environment
Action
Layered architecture
This paper aims to bridge progress in neuroscience involving sophisticated quantitative analysis of behavior, including the use of robust control, with other relevant conceptual and theoretical frameworks from systems engineering, systems biology, and mathematics.
Doyle and Csete, Proc Nat Acad Sci USA, online JULY 25 2011
Meta-layers
Physiology
Organs
Prediction GoalsActions
errorsActions
Cor
tex
Fast,Limited scope
Slow,Broad scope
Which blue line is longer?
“Seeing is dreaming?”
“Seeing is believing?”
sense
move Spine
delay=death
sense
move Spine
Reflex
Reflect
sense
move Spine
Reflex
Reflect
sense
move Spine
Reflect
Reflex
Layered
sense
move Spine
Reflect
Reflex
Layered
Physiology
Organs
Neu
rons
Neu
rons
Neu
rons
Cor
tex
Cel
ls
Cor
tex
Cor
tex
Layered architectures
Cells
Physiology
Organs
Meta-layers
Prediction
GoalsActions
errors
ActionsCo
rtex
Simulation
Seeing is dreaming
Consciousperception
Consciousperception
Which blue line is longer?
Which blue line is longer?
Which blue line is longer?
Which blue line is longer?
Which blue line is longer?
Which blue line is longer?
Simulation
Seeing is dreaming
Consciousperception
Consciousperception
Physiology
Organs
Prediction
GoalsActions
errors
Actions
Seeing is believing
Consciousperception
Prediction
Goals
Consciousperception
Seeing is dreaming
sourcereceiver
signalinggene expression
metabolismlineage
Biological pathways
sourcereceiver
control
energy
materials
signalinggene expression
metabolismlineage
More complex
feedback
sourcereceiver
control
energymaterials
Physiology
Organs
Prediction
GoalsActions
errors
Actions
Prediction
Goals
Consciousperception
fast
fast
Meta-layers
Physiology
Organs
Prediction GoalsActions
errorsActions
Cor
tex
Fast,Limited scope
Slow,Broad scope
Unfortunately, we’re not sure how this all works.
Meta-layers
Physiology
Organs
Prediction GoalsActions
errorsActions
Cor
tex
Fast,Limited scope
Slow,Broad scope
Which blue line is longer?
“Seeing is dreaming?”
“Seeing is believing?”
Meta-layers
Physiology
Organs
Prediction GoalsActions
errorsActions
Cor
tex
Fast,Limited scope
Slow,Broad scope
Meta-layers
Physiolog y
Organs
Pre
dic t io
n
Goal s
Actio
ns
er rors
Actio
ns
Cortex
Fast,Limited scope
Slow,Broad scope
UAV
Com
ms
Meta-layers
Physiolog y
Organs
Pre
dic t io
n
Goal s
Actio
ns
er rors
Actio
ns
Cortex
Fast,Limited scope
Slow,Broad scope
Dis
turb
ance
Plant
RemoteSensor
Sensor
Actuator
Interface
Control
Layered architectures
Com
ms D
istu
rban
ce
Plant
RemoteSensor
Sensor
Actuator
Interface
Control
Layered architectures
Com
ms D
istu
rban
ce
Plant
RemoteSensor
Sensor
Actuator
Interface
Control
?
Deconstrained(Hardware)
Deconstrained(Applications)
Next layered architectures
Constrained
Control, share, virtualize, and manage resources
Other examples
Clothing
Lego
Money
Cell biology
OutfitBody Environment
Shirt
Slacks
JacketTie T-Shirt
Socks
Shoes CoatShorts
OutfitBody Environment
OutfitBody Environment
• Complexity Robustness • Layers must be hidden to be robust• Choice (management and control) is more complex than assembly
Mgmt/ctrl
Assembly
OutfitBody Environment
Outfit
Outfit
Cloth
Thread
Fiber
Garment
Cloth
Thread
Fiber
Garment
Cloth
Thread
Fiber
Garment
Layering within garments (textiles)
Cloth
Thread
Fiber
Garments
Cloth
Thread
Fiber
Garments
Weave
Sew
Spin
Universal strategies?
Prevents unraveling of lower layers
Cloth
Thread
Fiber
Garments
Xform
Xform
Xform
Universal strategies?
Garments have limited access to
threads and fibers
constraints on cross-layer interactions
quantization for robustness
Even though garments seem analog/continuous
Prevents unraveling of lower layers
Cloth
Thread
Fiber
Garments
Xform Ctrl Mgmt
Networked, universal,
layeredXform Ctrl Mgmt
Xform Ctrl Mgmt
Xform Ctrl Mgmt
Co
ntro
l
Su
pp
lyComplexity?
Fiber
Geographically diverse sources
Diverse fabric
Functionally diverse garments
General purpose machines Diverse Thread
sew
knit, weave
spin
OS
Deconstrained(Hardware)
Deconstrained(Applications)
Layered architectures
Constrained Control, share, virtualize, and manage resources
ProcessingMemoryI/O
Few global variablesFew global variables
Don’t cross layersDon’t cross layersDirect
access to physical
memory?
Cat
abol
ism
AA
Ribosome
RNA
RNAp
transl.Proteins
xRNA transc.
Pre
curs
ors
Nucl.
AA
DNA
DNAp
Repl.Gene
ATP
ATP
Enzymes
Building Blocks
Shared protocols
Deconstrained (diverse)
Environments
Deconstrained (diverse) Genomes
Bacterial biosphere
Architecture =
Constraints that
Deconstrain
Few global variablesFew global variables
Don’t cross layersDon’t cross layers
Meta-layers
Physiology
Organs
Prediction
Goals
Actions
errors
Actions
Cortex
Fast,Limited scope
Slow,Broad scope
Which blue line is longer?
“Seeing is dreaming?”
“Seeing is believing?”
Few global variablesFew global variables
Don’t cross layersDon’t cross layers
Com
ms
Meta-layers
Physiolog y
Organs
Pre
dic t io
n
Goal s
Actio
ns
er rors
Actio
ns
Cortex
Fast,Limited scope
Slow,Broad scope
Dis
turb
ance
Plant
RemoteSensor
Sensor
Actuator
Interface
Control
Layered architectures
Few global variablesFew global variables
Don’t cross layersDon’t cross layers
Problems with leaky layering
Modularity 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?
Fragilities of layering/virtualization
• Hijacking, parasitism, predation– Universals are vulnerable– Universals are valuable
• Breakdowns/failures/unintended/… not transparent
• Hyper-evolvable but with frozen core
TCP/IP
Deconstrained(Hardware)
Deconstrained(Applications)Original design challenge?
Constrained
• Trusted end systems• Unreliable hardware
Facilitated wild evolutionCreated
• whole new ecosystem• complete opposite
TCP/IP
Deconstrained(Hardware)
Deconstrained(Applications)
Layered architectures
Constrained Control, share, virtualize, and manage resources
Processing?Memory?I/OCommsLatency?
Few global variables?Few global variables?
Don’t cross layers?Don’t cross layers?
App AppIPC
Global and direct access to
physical address!
Robust?• Secure• Scalable• Verifiable• Evolvable• Maintainable• Designable• …
DNS
IP addresses interfaces
(not nodes)
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”• VPNs• NATS• Firewalls• Multihoming• Mobility• Routing table size• Overlays• …
?
Deconstrained(Hardware)
Deconstrained(Applications)
Next layered architectures
Constrained Control, share, virtualize, and manage resources
CommsMemory, storageLatencyProcessingCyber-physical
Few global variablesFew global variables
Don’t cross layersDon’t cross layers
Every layer has
different diverse graphs.
Architecture is least graph topology.
Architecture facilitates arbitrary graphs.
Persistent errors and confusion (“network science”)
Physical
IP
TCP
Application
Notices of the AMS, 2009
wasteful
fragile
slowGood case studies
Hard limit
bad
worse
Fix bugs
“New sciences” of “complexity” and “networks”?
D. Alderson, NPS 122
“New sciences” of “complexity” and “networks”? worse
• Edge of chaos• Self-organized criticality• Scale-free “networks”• Creation “science”• Intelligent design• Financial engineering• Risk management• “Merchants of doubt”• …
Not today
Science as • Pure fashion• Ideology• Political• Evangelical• Nontech trumps tech
IEEE TRANS ON SYSTEMS, MAN, AND CYBERNETICS, JULY 2010, Alderson and Doyle
Statistical physics
Complex networks
edge of chaos, self-organized criticality, scale-free,…
Complex systems?
Fragile
• Scale• Dynamics• Nonlinearity• Nonequlibrium• Open• Feedback• Adaptation• Intractability• Emergence• …
Even small amounts can create bewildering complexity
Complex systems?
Fragile
• Scale• Dynamics• Nonlinearity• Nonequlibrium• Open• Feedback• Adaptation• Intractability• Emergence• …
• Scale• Dynamics• Nonlinearity• Nonequlibrium• Open• Feedback• Adaptation• Intractability• Emergence• …
Robust
Complex systems?
• Resources• Controlled• Organized• Structured• Extreme• Architected• …
Robust complexity
• Scale• Dynamics• Nonlinearity• Nonequlibrium• Open• Feedback• Adaptation• Intractability• Emergence• …
New words
Fragile complexity
Emergulent
Emergulence at the edge of
chaocritiplexity
• Scale• Dynamics• Nonlinearity• Nonequlibrium• Open• Feedback• Adaptation• Intractability• Emergence• …
“New sciences” of complexity and networks
Statistical physics
Complex networks
edge of chaos, self-organized criticality, scale-free,…
IEEE TRANS ON AUTOMATIC CONTROL, FEBRUARY, 2011Sandberg, Delvenne, and Doyle
http://arxiv.org/abs/1009.2830
Stat physics, fluids, QM
Complex networks
“orthophysics”
J. Fluid Mech (2010)
Transition to Turbulence
FlowStreamlinedLaminar Flow
Turbulent Flow
Increasing Drag,
Fuel/Energy Use and
Cost
Turbulence and drag?
Physics of Fluids (2011)
wU
z x
y
uzx
yFlow
upflowhigh-speed
region
downflowlow speed
streak
Blunted turbulent velocity profile
Laminar
Turbulent
wU3D coupling
Coherent structures and turbulent drag
wasteful
fragile Laminar
Turbulent
efficient
robust
Blunted turbulent velocity profile
Laminar
Turbulent
wU
?
Transition to Turbulence
FlowStreamlinedLaminar Flow
Turbulent Flow
Increasing Drag,
Fuel/Energy Use and
Cost
Turbulence and drag?
uzx
yFlow
Coherent structures
wU
z x
y
wU
z x
y
Blunted turbulent velocity profile
Laminar
Turbulent
wU
0u
1uu u p u
t R
“turbulence is a highly nonlinear
phenomena”
0u
1uu u p u
t R
Small Large
RobustSimple
2d, linearOrganizedComputer
Fragilechaocritical3d, nonlinear
Irreducibile?
Complexity?
mildly nonlinear
highly nonlinear
Model
wasteful
fragile Laminar
Turbulent
efficient
robust
Laminar
Turbulent
wU
?Control?
Supplementary materials has a demo.
Doyle and Csete, Proc Nat Acad Sci USA, online JULY 25 2011
m
M
L
Fragility
up + eyes
lnz p
z p
2 20
1ln ln
z z pS j d
z z p
Theorem
up, no eyes
This is a cartoon, but can be made
precise.
L
hopeless
down
lower focus
L
u
x
m
M
m
M
Linearized pendulum on a cart
0
1ln 0S j d
Easy, even with eyes closedNo matter what the length
0
ln 0
Gratuitous fragility
Fragile robustness
S j d
Gratuitous fragility versus
fragile robustness
0
1ln S j d p
1 1g
p z r rL
small largep L
Up is hard for shorter lengths
Down easy, even with • eyes closed• all lengths
Fragility
complex
This is a cartoon, but can be made
precise.
L
0
1ln S j d p
1p
L
L
Too fragile Why oscillations?
Side effects of hard tradeoffs
L
1
1 1
1 1
g mz p z r r
L M
p z r
p z r
m
M
Eyes closed
2 20
1ln ln
z z pS j d
z z p
Want r and z large (but p small).
Fragility
up + eyes
lnz p
z p
2 20
1ln ln
z z pS j d
z z p
Theorem
up, no eyes
This is a cartoon, but can be made
precise.
L
hopeless
down
lower focus