john doyle caltech - control and dynamical systems
TRANSCRIPT
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Co-factors
Fatty acids
Sugars
Nucleotides
Amino Acids
Catabolism
Polymerization and complex
assembly
Proteins
Pre
curs
ors
Autocatalytic feedback Taxis and
transportN
utr
ients
Carriers
Core metabolism
Genes
DNA
replication
Trans*
John DoyleJohn G Braun Professor
Control and Dynamical Systems,
BioEng, and ElecEng
Caltech
G!G!
GDP GTP
GDPGTP
In
In
Out
P
Ligand
Receptor
"#
"#
RGS
www.cds.caltech.edu/~doyle
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Multiscale
Physics
Systems
Biology
Network
Centric,
Pervasive,
Embedded,
Ubiquitous
Core
theory
challenges
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Core theory challenges
• Hard limits
• Short proofs
• Small models
• Architecture
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Architecture?
• “The bacterial cell and the Internet have
– architectures
– that are robust and evolvable”
• What does “architecture” mean?
• What does it mean for an “architecture” to
be robust and evolvable?
• Robust yet fragile?
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Robust
1. Efficient, flexible
metabolism
2. Complex development
and
3. Immune systems
4. Regeneration & renewal
5. Complex societies
1. Obesity and diabetes
and
2. Rich parasite
ecosystem
3. Auto-immune disease
4. Cancer
5. Epidemics, war,
genocide, …
Yet Fragile
Human robustness and fragility
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Hard limits and tradeoffs
On systems and their components
• Thermodynamics (Carnot)
• Communications (Shannon)
• Control (Bode)
• Computation (Turing/Gödel)
• Fragmented and incompatible
• We need a more integrated view
and have the beginnings
Assume
different
architectures
a priori.
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The nature of simplicity
Simple questions:
• Simple models
• Elegant theorems
• Elegant experiments
Simple answers:
• Predictable results
• Short proofs
• Simple outcomes
Reductionist science: Reduce the apparent
complexity of the world to an underlying simplicity.
Physics has for centuries epitomized the success of
this approach.
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1930s: The end of certainty
Simple questions:
• Simple models
• Elegant theorems
• Elegant experiments
Simple answers:
• Predictable results
• Short proofs
• Simple outcomes
• Godel: Incompleteness
• Turing: Undecidability
• Profoundly effected mathematics and computation.
• Little impact on science.
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1960s-Present: “Emergent complexity”
Simple questions:
• Simple models
• Elegant theorems
• Elegant experiments
Complexity:
• Unpredictabity
• Chaos, fractals
• Critical phase transitions
• Self-similarity
• Universality
• Pattern formation
• Edge-of-chaos
• Order for free
• Self-organized criticality
• Scale-free networks
Dominates scientific
thinking today
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“Emergent” complexity
• Simple question
• Undecidable
• No short proof
• Chaos
• Fractals
Mandelbrot
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The “New Science of Complexity”
“Emergence”Unpredictable
SimplicityPredictable
Simple
question
Even simple systems with little uncertainty
can yield completely unpredictable behavior.
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1900s: The triumph (and horror)
of organization
Simple questions:
• Simple models
• Elegant theorems
• Elegant experiments
Simple answers:
• Predictable results
• Short proofs
• Simple outcomes
• Complex, uncertain, hostile environments
• Unreliable, uncertain, changing components
• Limited testing and experimentation
• Yet predictable, robust, reliable, adaptable,
evolvable systems
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Cruise control
Electronic ignition
Temperature control
Electronic fuel injection
Anti-lock brakes
Electronic
transmission
Electric power steering (PAS)
Air bags
Active suspension
EGR control
Organized
complexity
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Organized complexity
• Requires highly organized
interactions, by design or
evolution
• Completely different theory and
technology from emergence
Simple answers:
• Predictable results
• Short proofs
• Simple outcomes
• Complex, uncertain, hostile environments
• Unreliable, uncertain, changing components
• Limited testing and experimentation
• Yet predictable, robust, reliable, adaptable,
evolvable systems
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Mathematics and technology
Emergence and organization are opposites,
but can be viewed in a unified framework.
Emergenc
eUnpredictable
OrganizationSimplicityPredictable
ComplexSimple Question
Answer
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Irreducible complexity?
?EmergenceUnpredictable
OrganizationSimplicityPredictable
ComplexSimple Question
Answer
Complexity and unpredictability are
the key to successful cryptography
and other security technologies.
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The
complete
picture
Irreducibi
lityEmergenc
eComplex
OrganizationSimplicitySimple
ComplexSimple Question
Answer
Simple, predictable, reliable, robust
versus
Complex, unpredictable, fragile
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The
complete
picture
Irreducibi
lityEmergenc
eComplex
OrganizationSimplicitySimple
ComplexSimple Question
Answer
Simple, predictable, reliable, robust
versus
Complex, unpredictable, fragile
! Nightmare "
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The complete picture
Irreduci
bilityEmergenc
eComplex
OrganizationSimplicitySimple
ComplexSimple Question
Answer
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The challenge
Long
Short
LargeSmall Models
Proofs
How can we treat complex networks and systems
with small models and short proofs?
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The complete picture
Irreduci
bilityEmergenc
eLong
OrganizationSimplicityShort
LargeSmall Models
Proofs
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Breaking hard problems
• SOSTOOLS proof theory and software (Parrilo,
Prajna, Papachristodoulou, …)
• Nested family of (dual) proof algorithms
• Each family is polynomial time
• Recovers many “gold standard” algorithms as
special cases, and immediately improves
• Nonlinear, hybrid, stochastic, …
• No a priori polynomial bound on depth (otherwise
P=NP=coNP)
• Conjecture: Complexity implies fragility
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Architecture?
• “The bacterial cell and the Internet have
– architectures
– that are robust and evolvable (yet fragile) ”
• What does “architecture” mean?
• What does it mean for an “architecture” to
be robust and evolvable?
• Robust yet fragile?
• Rigorous and coherent theory?
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A look back and forward• The Internet architecture was designed without a
“theory.”
• Many academic theorists told the engineers itwould never work.
• We now have a nascent theory that confirms thatthe engineers were right (Kelly, Low,Vinnicombe, Paganini, Papachristodoulou, …)
• Parallel stories exist in “theoretical biology.”
• For future networks, “systems of systems,” andother new technologies, as well as systems biologyof the cell, organism and brain, …
• …let’s hope we can avoid a repeat of this history.(Looks like we have a good start…)
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Architecture?
• “The bacterial cell and the Internet have
– architectures
– that are robust and evolvable”
• For the Internet, we know how all the parts
work, and we can ask the architects
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The Internet hourglass
Web FTP Mail News Video Audio ping napster
Applications
Ethernet 802.11 SatelliteOpticalPower lines BluetoothATM
Link technologies
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The Internet hourglass
IP
Web FTP Mail News Video Audio ping napster
Applications
TCP
Ethernet 802.11 SatelliteOpticalPower lines BluetoothATM
Link technologies
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The Internet hourglass
IP
Web FTP Mail News Video Audio ping napster
Applications
TCP
Ethernet 802.11 SatelliteOpticalPower lines BluetoothATM
Link technologies
IP under
everything
IP on
everything
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IP
TCP/
AQM
Applications
Link
Top of “waist” provides
robustness to variety and
uncertainty above
Bottom of “waist” provides
robustness to variety
and uncertainty below
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IP IPIP IP IP
TCP
Application
TCP
Application
TCP
Application
Routing
Provisioning
Ver
tica
l d
eco
mp
osi
tio
n
Pro
toco
l S
tack
Each layer can evolve
independently provided:
1. Follow the rules
2. Everyone else does
“good enough” with
their layer
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IP IPIP IP IP
TCP
Application
TCP
Application
TCP
Application
Routing
Provisioning
Horizontal decomposition
Each level is decentralized and asynchronous
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• Each layer is abstracted as an optimizationproblem
• Operation of a layer is a distributed solution
• Results of one problem (layer) are parameters ofothers
• Operate at different timescales
Xx
pcRx
xUi
iix
!
"
#$
)( tosubj
)( max0
Layering as optimization decomposition
application
transport
network
link
physical
Application: utility
IP: routing Link: scheduling
Phy: power
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Examples
application
transport
network
link
physical
Optimal web layer: Zhu, Yu, Doyle ’01
HTTP/TCP: Chang, Liu ’04
TCP: Kelly, Maulloo, Tan ’98, ……
TCP/IP: Wang et al ’05, ……
TCP/power control: Xiao et al ’01,
Chiang ’04, ……
TCP/MAC: Chen et al ’05, ……
Rate control/routing/scheduling: Eryilmax et al ’05, Lin etal ’05, Neely, et al ’05, Stolyar ’05, this paper
detailed survey in Proc. of IEEE, 2006
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!"#$#
%"&$'(#
packets
TCP/AQM
analysis
Arbitrarily complex network
• Topology
• Number of routers and hosts
• Nonlinear
• Delays
Kelly, etc
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!"#$#
%"&$'(#
packets
TCP/AQM
analysis
Arbitrarily complex network
• Topology
• Number of routers and hosts
• Nonlinear
• Delays
Vinnicombe, etc
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!"#$#
%"&$'(#
packets
“FAST”
TCP/AQM
theoryArbitrarily complex network
• Topology
• Number of routers and hosts
• Nonlinear
• DelaysShort proof
• Global stability
• Equilibrium optimizes
aggregate user utility
Papachristodoulou, Li
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Architecture?
• “The bacterial cell and the Internet have
– architectures
– that are robust and evolvable”
• For the Internet, we know how all the parts
work, and we can ask the architects
• For biology, we know how some parts
work, and evolution is the “architect”
(another source of confusion)
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Bio: Huge variety of environments, metabolisms
Internet: Huge variety of applications
Huge variety of components
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Bio: Huge variety of environments, metabolisms
Internet: Huge variety of applications
Huge variety of components
Both components
and applications are
highly uncertain.
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Bio: Huge variety of environments, metabolisms
Internet: Huge variety of applications
Huge variety of components
Huge variety of genomes
Huge variety of physical networks
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Bio: Huge variety of environments, metabolisms
Internet: Huge variety of applications
Huge variety of components
Huge variety of genomes
Huge variety of physical networks
Feedback
control
Identical
control
architecture
Hourglass architectures
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5:Application/function: variable supply/demand
4:TCP
3:IP
2:Potential physical network
1:Hardware components
4:Allosteric
3:Transcriptional
TCP/IP Metabolism/biochem
Feedback
Control
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Networked dynamical systems
Complexity
of
dynamics
Complexity
of interconnection
Single
Agent
Nonlinear/uncertain
hybrid/stochastic etc.
Multi-agent
systems
Flocking/synchronization
consensus
Complex
networked
systems
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Complexity
of
dynamics
Complexity
of interconnection
Single
Agent
Nonlinear/uncertain
hybrid/stochastic etc.
Multi-agent
systems
Flocking/synchronization
consensus
Complex
networked
systems
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“Emergent” complexity
• Simple question
• Undecidable
• Chaos
• Fractals
Mandelbrot
Simulations and conjectures but no “proofs’
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Networked dynamical systems
Complexity
of
dynamics
Complexity
of interconnection
Single
Agent
Nonlinear/uncertain
hybrid/stochastic etc.
Multi-agent
systems
Flocking/synchronization
consensus
Complex
networked
systems
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Complexity
of
dynamics
Complexity
of interconnection
Single
Agent
Nonlinear/uncertain
hybrid/stochastic etc.
Multi-agent
systems
Flocking/synchronization
consensus
Complex
networked
systems
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Statistical Physics andStatistical Physics and
emergence of collective behavioremergence of collective behavior
Simulations and conjectures but no “proofs’
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Working systems but no “proofs’
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Spectacular progress
Complexity
of
dynamics
Complexity
of interconnection
Single
Agent
Nonlinear/uncertain
hybrid/stochastic etc.
Multi-agent
systems
Flocking/synchronization
consensus
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Open questions
Complexity
of
dynamics
Complexity
of interconnection
Single
Agent
Nonlinear/uncertain
hybrid/stochastic etc.
Multi-agent
systems
Flocking/synchronization
consensus
Complex
networked
systems?
?
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Core theory challenges
• Hard limits
• Short proofs
• Small models
• Architecture
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Today’s tutorial
• Hard limits (morning)
• Short proofs (afternoon)
• Small models
• Architecture
• Common background, standard results