Transcript 1. Intro - Science of Security

Theoretical foundations:
Architecture, control, networks,
robustness, and complexity
John Doyle
John G Braun Professor
Control and Dynamical Systems
BioEngineering, Electrical Engineering
Caltech
math
NetSE: Network Science and Engineering
Good news and bad news:
Spectacular recent progress in (more integrated)
• foundations for a mathematical theory of
• network robustness, control, and architecture
Spectacular continued confusion and errors in
• various “new sciences” of
• “networks”
• “complexity”
• Etc, etc,..
math
NetSE: Network Science and Engineering
Good news and bad news:
Spectacular recent progress in (more integrated)
• foundations for a mathematical theory of
• network robustness, control, and architecture
Are there lessons to be learned in trying to create a
theory of impossible things (e.g. security)?
NetME: Progress and promise
• Internet theory: layering, control, traffic, topology,
architecture (?)
• Unifying theories of hard limits and optimal
synthesis (Shannon, Bode, Carnot, Turing/Godel)
• Comparative physiology of successful network
architectures
• Universal architectural features (layering, hourglass,
bowtie) in technology and biology
• Duality and optimization as unifying framework
(algorithms, distributed, dynamic, layered, nested
relaxations, etc…)
Diverse case studies
•
•
•
•
•
Internet and extensions
Cell/systems biology
Ecosystems (e.g. CA coastal wildfire)
Biomedical and physiology
Toy example: Lego
• Earthquake dynamics and statistics
• Disasters statistics
• Infrastructure: Electric power, Transportation,
Manufacturing
• Multiscale physics (Turbulence, Foundations of
Statistical mechanics, Friction, Fracture, Granular
Flows)
Early Internet
“pre-theory”
• Principles
• …but no math
“theory” per se
• Good engineers
always lead theory
(and science)
• Theory adds depth,
rigor, scalability, etc
Early theory
(post deployment)
• Measurement
• Statistics
• Packet-level
dynamic
simulation
Theory and the Internet
Levels of
understanding
Topics
Verbal/cartoon
Traffic
Data and
statistics
Modeling and
simulation
Topology
Control and
dynamics
Analysis
Layering
Synthesis
Architectures
“The Matrix”
- subfields of networking, and progress therein..
ARCHITECTURE
Traffic Topology
Verbal
Data/stat
Mod/sim
Analysis
Synthesis
C&D
Layering
???
Traffic (1993-2000)
Traffic
Verbal
Data/stat
Mod/sim
Analysis
Synthesis
• Heavy tails (HT) in net
traffic???
• Careful measurements
• Appropriate statistics
• Connecting traffic to
application behavior
• “optimal” web layout
 HT files
 HT traffic
Unnecessary confusion
(and its resolution)
Traffic Topology
Verbal
Data/stat
Mod/sim
Analysis
Synthesis
2
10
High degree hublike core
Low degree
mesh-like core
1
identical
power-law
degrees
10
Completely different
networks can have the
same node degrees.
0
10
0
10
1
10
2
10
3
10
• Low degree core
• High performance
and robustness
• Efficient, economic
• High degree “hubs”
• Poor performance
and robustness
• Wasteful, expensive
Nothing like the
real Internet.
See PNAS, Sigcomm, TransNet papers for details.
Network
technology
Yet
One of the
most-read
papers ever
on the
Internet!
Network
science?
Why is this “science” not?
Much “network science” and
“complex systems” literature
is equally specious
Huge and recent progress
Traffic
Verbal
Data/stat
Mod/sim
Analysis
Synthesis
Topology
C&D
Layering Architect.
The Internet hourglass
my
computer
router
router
HTTP
TCP
IP
LINK
web
server
my
computer
Diverse
router
router
web
server
HTTP
TCP
IP
LINK
Diverse
Diverse
Application
Highly
conserved
core
control
processes
TCP/AQM
IP
Layered
MAC
Physical
Diverse
Diverse
Application
TCP/AQM
Highly
conservedHidden to most
core
usersIPand
control technologies
processes
Layered
MAC
Physical
Diverse
Application
Highly
conserved
core
control
processes
Hardware
Diverse
Operating
system
Layered
Diverse
Operating
system
Diverse
Hardware
Layered
Layered
Application Diverse
Conserved
core control
TCP
IP
Diverse
function
Physical
Universal
Control
Diverse Hourglass
components
Diverse
Layering as optimization decomposition
• Each layer is abstracted as an optimization
problem
• Operation of a layer is a distributed solution
• Results of one problem (layer) are parameters of
others
• Operate at different timescales
Application: utility
application
transport
network
link
physical
max
x0
U ( x )
i
i
i
Phy: power
subj to Rx  c( p )
x X
IP: routing
Link: scheduling
Architecture as optimization decomposition
System constraints: utility
• reflect real human behavior
• real-time control of physical systems
U ( x )  U
i
i
0
i
subj to x  X
Component constraints
• heterogeneous, physical infrastructure
• realistic dynamics
• robustness to uncertainties
Architecture as optimization decomposition
Emergent
constraints:
• Integrated
• Control
• Energy
• Materials
• Computation
U ( x )  U
i
i
0
i
subj to x  X
Protocol
constraints:
• distributed
• layered?
• real-time
control
rate
form/activity
level
rate
form/activity
level
rate
Reaction rate
Enzyme form/activity
Proteins
Enzyme level/
Translation rate
form/activity
RNAs
RNA level/
Transcription rate
DNAs
Academic stovepipes
EE, CS, ME, MS, APh, ChE, Bio, Geo, Eco, …
Apps
Tools/
tech
Apps
Apps
Apps
Tools/
tech
Tools/
tech
Apps
Tools/
tech
Tools/
tech
New applications
Funding
twine
Apps
Apps Apps
AppsApps
Tools/
Tools/Tools/
tech Tools/
Tools/
tech tech
tech tech
“Multidisciplinary cross-sterilization”
New applications
Layering
academia?
?????
Apps Apps Apps
Apps
Tools/ Tools/ Tools/ Apps
Tools/
tech tech tech
tech
Tools/
tech
fan-in
of diverse
inputs
universal
carriers
Bowties: flows
within layers
fan-out
of diverse
outputs
Diverse
function
Universal
Control
Diverse
components
Hourglass:
layering of
control and
interfaces
Constraints
that
deconstrain
Variety
of
files
•
•
•
packets
Variety
of
files
Main bowtie
in Internet S
All advanced technologies have protocols
specifying “knot” of carriers, building blocks,
interfaces, etc
Facilitates control, enabling robustness and
evolvability
Creates fragilities to hijacking and cascading
failure
Variety
of
files
packets
Applications
TCP
IP
Link
Variety
of
files
Many bowties
in Internet
fan-in
of diverse
inputs
universal
carriers
Internet is
very special
Diverse
function
Universal
Control
Diverse
components
fan-out
of diverse
outputs
•
•
•
•
•
Pure communication
Simple dynamics
No “metabolism”
No assembly
No autocatalysis
Electric
power
network
Variety of
producers
Variety of
consumers
• Good designs transform/manipulate
energy
• Subject (and close) to hard limits
Standard
interface
Energy
carriers
Variety of
producers
•
•
•
•
•
110 V, 60 Hz AC
(230V, 50 Hz AC)
Gasoline
ATP, glucose, etc
Proton motive force
Variety of
consumers
Architecture
Biology
Evolution of the Internet
Circuits, Pathways, Molecules,
Two foci:
• Components (VLSI, optics, web apps …)
– Rapid change, diversity, and rearrangement
• Architecture (TCP/IP)
– Largely fixed and universal
Architecture of the cell
Network elements
Components
Architecture
• Well understood
• Changes rapidly
• Takes architecture for
granted
• Focus of most research
and innovation in both
science and engineering
• Widely viewed as most
important
• Poorly understood
• Changes rarely
• If well-designed is
largely invisible
• Source of most confusion
• Most essential?
• Growing importance?
The dangers of
naïve biomemetics
Feathers
and
flapping?
Or lift, drag, propulsion,
and control?
Getting it (W)right, 1901
• “We know how to construct airplanes.” (lift and drag)
• “..and to build engines.” (propulsion)
• “Inability to balance/steer [is the] 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 Control, 1901
Getting it right, 2010, Control++
Architecture, networks,
robustness, and complexity
•
•
•
•
Words we use all the time
Often as their own antonym
Thus potential sources of confusion
Today: discuss a few basic ideas that seem
necessary
• Illustrate with familiar examples
• Should be at the heart of NetSE
Essential ideas
Robust
yet
fragile
Constraints
that
deconstrain
local  global
Human complexity
Robust
Yet Fragile
 Efficient, flexible metabolism  Obesity and diabetes
 Rich microbial symbionts and  Parasites, infection
 Immune systems
 Inflammation, Auto-Im.
 Regeneration & renewal
 Cancer
 Complex societies
 Epidemics, war, …
 Advanced technologies
 Catastrophic failures
Robust






Implications/
Generalizations
Efficient, flexible metabolism
Rich microbial symbionts and
Immune systems
Regeneration & renewal
Complex societies
Advanced technologies






Yet Fragile
Obesity and diabetes
Parasites, infection
Inflammation, Auto-Im.
Cancer
Epidemics, war, …
Catastrophic failures
• Complexity driven by control and robust/fragile
• More than minimal functionality
• Easy to create robustness, harder to avoid fragility
• Hijacking and side effects of mechanisms evolved
for robustness
• New robust/fragile conservation laws
Robust yet fragile
Biology (and advanced tech) show extremes
• Robust Yet Fragile
• Simplicity and complexity
• Unity and diversity
• Evolvable and frozen
What makes this possible and/ or inevitable?
Architecture (= constraints)
Let’s dig deeper.
Hard limits and tradeoffs
On systems and their components
• Thermodynamics (Carnot)
• Communications (Shannon)
• Control (Bode)
• Computation (Turing/Gödel)
No networks
Assume
different
architectures
a priori.
Hard limits and tradeoffs
On systems and their components
• Thermodynamics (Carnot)
• Communications (Shannon)
• Control (Bode)
• Computation (Turing/Gödel)
• Fragmented and incompatible
• Cannot be used as a basis for
comparing architectures
• New unifications are encouraging
No dynamics
or feedback
Hard limits and tradeoffs
On systems and their components
• Thermodynamics (Carnot)
• Communications (Shannon)
• Control (Bode)
• Computation (Turing/Gödel)
• Include dynamics and feedback
• Extend to networks
• New unifications are encouraging
Robust/
fragile
is unifying
concept
[a system] can have
[a property] robust for
[a set of perturbations]
Fragile
Yet be fragile for
Robust
[a different property]
Or [a different perturbation]
[a system] can have
[a property] robust for
[a set of perturbations]
• Some fragilities are inevitable
in robust complex systems.
Fragile
Robust
• But if robustness/fragility are conserved, what does it
mean for a system to be robust or fragile?
Emergent
Fragile
• Some fragilities are inevitable
in robust complex systems.
Robust
• But if robustness/fragility are conserved, what does it
mean for a system to be robust or fragile?
• Robust systems systematically manage this tradeoff.
• Fragile systems waste robustness.
Hard limits
RHP z and p

z
z p
ln S  j  2
d   ln
2

0
z 
z p
1
Variable
Process
Nominal
Value?
q
autocatalysis
1

k
inhibition
1
2nd enzyme
1
z p
1 2 1

z  p hk 0q 1 1  2  1

2
2 2
 2.41
rate
form/activity
level
rate
form/activity
level
rate
Reaction rate
Enzyme form/activity
Proteins
Enzyme level/
Translation rate
form/activity
RNAs
RNA level/
Transcription rate
DNAs
Catabolism
Precursors
Inside every cell
Carriers
Nucleotides
Catabolism
Precursors
Core metabolism
Carriers
Nucleotides
Precursors
Catabolism
Carriers
Gly
G1P
G6P
Catabolism
F6P
F1-6BP
Gly3p
ATP
13BPG
3PG
2PG
NADH
Oxa
PEP
Pyr
ACA
TCA
Cit
Gly
Precursors
G1P
G6P
F6P
metabolites
F1-6BP
Gly3p
13BPG
3PG
2PG
Oxa
PEP
Pyr
ACA
TCA
Cit
Gly
G1P
G6P
Enzymatically
catalyzed reactions
F6P
F1-6BP
Gly3p
13BPG
3PG
2PG
Oxa
PEP
Pyr
ACA
TCA
Cit
Gly
Precursors
G1P
G6P
F6P
Autocatalytic
F1-6BP
Gly3p
Carriers
ATP
13BPG
3PG
2PG
Oxa
PEP
Pyr
ACA
TCA
NADH
Cit
Gly
G1P
G6P
Regulatory
F6P
F1-6BP
Gly3p
ATP
13BPG
3PG
2PG
Oxa
PEP
Pyr
ACA
TCA
NADH
Cit
Gly
G1P
G6P
F6P
F1-6BP
Gly3p
13BPG
3PG
2PG
Oxa
PEP
Pyr
ACA
TCA
Cit
If we drew the feedback loops the
diagram would be unreadable.
Gly
G1P
G6P
F6P
F1-6BP
Gly3p
ATP
13BPG
3PG
2PG
Oxa
PEP
Pyr
ACA
TCA
NADH
Cit
Stoichiometry or mass
and energy balance
Biology is not a graph.
dx
 Sv( x)
dt
 Mass & 
 Reaction 


  Energy  

flux

 Balance  
Interna
l
Nutrients
Products
dx
 Sv( x)
dt
Stoichiometry plus
regulation
 Mass & 
 Reaction 
d


 Mass&Energy    Energy  

flux
dt

 Balance  
 Matrix of integers
 “Simple,” can be
known exactly
 Amenable to high
throughput assays
and manipulation
 Bowtie architecture
 Vector of (complex?) functions
 Difficult to determine and
manipulate
 Effected by stochastics and
spatial/mechanical structure
 Hourglass architecture
 Can be modeled by optimal
controller (?!?)
dx
 S
Sv( x)
dt
 Mass & 
 Reaction 


  Energy  

flux

 Balance  
Gly
G1P
G6P
F6P
F1-6BP
Gly3p
ATP
Stoichiometry
matrix
13BPG
3PG
2PG
Oxa
PEP
Pyr
ACA
TCA
NADH
Cit
dx
 Sv( x)
dt
 Mass & 
 Reaction 


  Energy  

flux

 Balance  
Gly
G1P
G6P
F6P
F1-6BP
Gly3p
Regulation of enzyme levels by
transcription/translation/degradation
13BPG
3PG
2PG
Oxa
PEP
level
Pyr
ACA
TCA
Cit
dx
 Sv( x)
dt
 Mass & 
 Reaction 


  Energy  

flux

 Balance  
Gly
G1P
G6P
F6P
F1-6BP
form/activity
Gly3p
ATP
13BPG
Allosteric regulation
of enzymes
3PG
2PG
Oxa
PEP
Pyr
ACA
TCA
NADH
Cit
 Mass & 
 Reaction 
dx


 Sv( x)   Energy  

flux
dt

 Balance  
Gly
G1P
G6P
rate
F6P
form/activity
F1-6BP
Gly3p
level
ATP
13BPG
3PG
2PG
Oxa
PEP
Pyr
ACA
TCA
NADH
Cit
 Mass & 
 Reaction 
dx


 Sv( x)   Energy  

rate
dt

 Balance  
Gly
G1P
G6P
rate
F6P
Layered
F1-6BP
architecture
Gly3p
form/activity
level
ATP
13BPG
3PG
2PG
Oxa
PEP
Pyr
ACA
TCA
NADH
Cit
rate
form/activity
level
Control
of
protein
levels
Reaction rate
Enzyme form/activity
Proteins
Enzyme level/
Translation rate
RNAs
DNAs
rate
form/activity
level
rate
form/activity
level
rate
Reaction rate
Enzyme form/activity
Proteins
Enzyme level/
Translation rate
form/activity
RNAs
RNA level/
Transcription rate
DNAs
Transcription
RNA Transc.
RNAp
Gene
xRNA
RNA level/
Transcription rate
DNA level
RNA level
product
Enz
Controlled,
dynamic
RNA Transc.
RNAp
Gene
xRNA
RNA level/
Transcription rate
DNA level
Precursors
AA
tRNA
trans.
mRNA
RNA Transc.
RNAp
Enzyme level/
Enzymes
Translation rate
Gene
xRNA
ncRNA
RNA level/
Transcription rate
DNA level
reactions
S
Enz1 reaction3
AA
trans.
products Reaction
P
rate
Enzyme
form/activity
Enz2
Enzyme level/
Enzymes Translation rate
mRNA
Ribosome
tRNA
RNA Transc.
RNAp
ncRNA
xRNA
Gene
RNA
form/activity
RNA level/
Transcription rate
What to call
the
sublayers?
Reaction rate
Enzyme form/activity
rate
form/activity
level
What is where
Enzyme level/
Translation rate
RNA form/activity
RNA level/
Transcription rate
Catabolism
Precursors
Nutrients
Taxis and
transport
Same
12
in all
Core metabolism
cells
Nucleotides
Carriers
Same
8
in all
cells
Taxis and
transport
Autocatalytic feedback
12
Polymerization
and complex
assembly
Precursors
Catabolism
Co-factors
Genes
Carriers
DNA
replication
Huge
Variety
8
100
Trans*
Proteins
Nutrients
Core metabolism
104 to  ∞
in one
organisms
Autocatalytic feedback
Polymerization
and complex
assembly
Huge
Variety
Proteins
Genes
DNA
replication
Trans*
104 to  ∞
in one
organisms
Precursors
Biosynthesis
Massively
autocatalytic
Co-factors
RNA Transc.
xRNA RNA level/
Transcription rate
RNAp
Gene
DNA level
Precursors
Catabolism
AA
RNA Transc.
Gene
xRNA
RNAp
Precursors
Catabolism
AA
transl.
tRNA
Enzymes
Ribosome
ncRNA
mRNA
RNA Transc.
Gene
xRNA
RNAp
Precursors
Catabolism
AA
transl.
Enzymes
tRNA
Autocatalysis
everywhere
Ribosome
RNA transc. xRNA
RNAp
S
reactions
P
Enz1 reaction3
tRNA
ncRNA
AA
trans.
products
Reaction rate
Enzyme form/activity
Enz2
Enzyme level/
Translation rate
Enzymes
Enz2
RNA form/activity
mRNA
RNA Transc.
Gene
RNAp
xRNA
RNA level/
Transcription rate
Ribosome
reactions
All
products
feedback
everywhere
products
reaction3
Proteins
trans.
These
won’t be
drawn in
detail
Transc.
ncRNA
S
reactions
P
Enz1 reaction3
tRNA
ncRNA
AA
trans.
products
Reaction rate
Enzyme form/activity
Enz2
Enzyme level/
Translation rate
Enzymes
Enz2
RNA form/activity
mRNA
RNA Transc.
Gene
RNAp
xRNA
RNA level/
Transcription rate
Ribosome
S
reactions
P
Enz1 reaction3
tRNA
ncRNA
AA
trans.
Reaction rate
Enz2
Enzymes
Enzyme form/activity
Enzyme level/
Translation rate
RNA form/activity
mRNA
RNA Transc.
Gene
RNAp
xRNA
RNA level/
Transcription rate
Ribosome
S
reactions
Enz1 reaction3
P
products
Reaction rate
Enz2
Enzyme form/activity
Running only the top layers
Mature red
blood cells
live 120 days
Diverse
Application
Diverse
application
s and
genomes
Genome
Diverse
Horizontal gene transfer
HGT and
Shared
Protocols
Bacteria
Eukaryotes
Animals
Archaea
Fungi
Plants
Algae
What is locus
of early
evolution?
Horizontal gene transfer
HGT and
Shared
Protocols
Bacteria
Eukaryotes
Animals
Archaea
Gene
Fungi
Plants
Algae
DNA level
Controlled,
dynamic
reactions
S
HGT and
Shared
Protocols
Bacteria
products Reaction
P
rate
Eukaryotes
Enz1 reaction3
Enz2
Animals
Fungi
Plants
Archaea
AA
trans.
Enzyme
form/activity
Enzyme level/
Enzymes Translation rate
Algae
mRNA
Ribosome
tRNA
RNA Transc.
RNAp
ncRNA
xRNA
Gene
RNA
form/activity
RNA level/
Transcription rate
Gly
G1P
G6P
F6P
F1-6BP
Gly3p
ATP
13BPG
3PG
2PG
Oxa
PEP
Pyr
ACA
TCA
NADH
Cit
Gly
G1P
G6P
F6P
F1-6BP
Gly3p
ATP
ATP
13BPG
3PG
2PG
Oxa
PEP
Pyr
ACA
TCA
NADH
Cit
Autocatalytic
x
 1
 0  kx x
 
Control
 q  Vx q
 1  1   xh
 
F6P
F1-6BP
Gly3p
ATP
13BPG
3PG
y
1  q 
 1  k y y


Autocatalytic
x
 1
 0  kx x
 
Control
 q  Vx q
 1  1   xh
 
F6P
F1-6BP
Gly3p
13BPG
3PG
ATP
y
1  q 
 1  k y y


Autocatalytic
x
 1
 0  kx x
 
Control
 q  Vx q
 1  1   xh
 
Minimal metabolism model
• x = ultimate product (ATP)
• y = intermediate metabolite
• Two feedbacks of x:
– Autocatalytic
– Control
y
1  q 
 1  k y y


Hard limits
RHP z and p

z
z p
ln S  j  2
d   ln
2

0
z 
z p
1
Variable
Process
Nominal
Value?
q
autocatalysis
1

k
inhibition
1
2nd enzyme
1
z p
1 2 1

z  p hk 0q 1 1  2  1

2
2 2
 2.41
Autocatalytic
 q  Vx q
 1  1   xh
 
x
Control
y
 1
 0  (1   )
 
1  q 
 1  k y y


x
produced
ky y
y
consumed
k y ( y)
y
Autocatalytic
x
Control
k1 ( x)
y
consumed
produced
k1 ( x)
x
x
 1
 0  (1   )
 
consumed
 x   q 
1  q 
 1
 y    1  k x  x    1  ky   0  (1   )
   


 
Autocatalytic
 q  Vx q
 1  1   xh
 
 1
 0  (1   )
 
x
y
k y ( y)
y
1  q 
 1  k y y


Autocatalytic
 q  Vx q
 1  1   xh
 
x
Control
y
 1
 0  (1   )
 
1  q 
 1  k y y


k y ( y)
k1 ( x)
Autocatalytic
 q  Vx q
 1  1   xh
 
 1
 0  (1   )
 
x
Control
y
Robust
Strong inhibition
1  q 
 1  k y y


Yet Fragile
Enzyme complexity,
Oscillations
Low autocatalysis
Inefficiency,
High reaction rates
metabolic load
[ATP]
1.05
Ideal
1
h >>1
0.95
Time response
0.9
Sh = F( x) h
0.85
h=1
Fourier
Transform
0
5
10
15
20
Time (minutes)
0.8
h >>1
0.6
Log(|Sn/S0|)
of error
0.8
0.4
0.2
Spectrum
h=1
0
log  S h   log  S1 
-0.2
-0.4
-0.6
-0.8
0
2
4
Frequency
6
8
10
[ATP]
1.05
1
h >> 1
0.95
Time response
0.9
0.85
Yet
fragile
h=1
0.8
0
5
10
15
20
Time (minutes)
0.8
h >>1
Robust
Log(Sn/S0)
0.6
0.4
0.2
Spectrum
h=1
0
-0.2
ln Sh  j   ln S0  j 
-0.4
-0.6
-0.8
0
2
4
Frequency
6
8
10

  ln S  j  d  0
0
Yet
fragile
0.8
h=3
Robust
Log(Sn/S0)
0.6
0.4
0.2
h=0
0
-0.2
-0.4
-0.6
-0.8
0
2
4
Frequency
6
8
10


0  ln S  j  d    0 ln S  j  d   0

Yet
fragile
0.8
Robust
Log(Sn/S0)
0.6
0.4
0.2
h=0
0
-0.2
-0.4
-0.6
-0.8
0
2
4
Frequency
6
8
10
This tradeoff is a law.
log|S |
Transients,
Oscillations

x ) d  constant
 log F(Biological
complexity is
n
Tighter
regulation
dominated by the evolution of
mechanisms to more finely tune
this robustness/fragility tradeoff.
Hard limits
RHP p
1

ln S  j  d 


0
 Re p
0
z p
 ln
z p
0
RHP z
1

z
ln S  j  2
d
2

 0
z 
1

z
d  1
2
2

 0 z 
Benefits must be “paid for”
within bandwidth z
Necessity, not accident

z
z p
ln S  j  2
d   ln
2

0
z 
z p
1
“Optimal”
controller
 1
 0  1   
 
x
“Optimal”
enzyme
y
1  q 
 1  ky


q=α=0
q=α=1
Necessity,
not
accident
hˆ  2
hˆ  10
hˆ  1.5
hˆ  .5
hˆ  1.5
hˆ  1.25
0
10
0
10
• Necessity or accident?
• Alternative designs
Synthesis
challenges
Robust
Yet Fragile
large hˆ
Enzyme complexity,
small 
Oscillations
large k
Inefficiency,
small q
metabolic load
• Other rates and
uncertainty
• Computational
complexity
– Higher order
dynamics
– Global, nonlinear
– Comparisons with
data
• Robustness is key
Hard limits and tradeoffs
On systems and their components
• Thermodynamics (Carnot)
• Communications (Shannon)
• Control (Bode)
• Computation (Turing/Gödel)
• Include dynamics and feedback
• Extend to networks
• New unifications are encouraging
Robust/
fragile
is unifying
concept
cost = amplification
goal: make this small
 log S  d

 log S  d


• benefits = attenuation of disturbance
• goal: make this as negative as possible
Constraint:
 log S  d   log S  d

benefits

costs
Bode
e=d-u
Plant
-u
d
S   
E  
D  
a
u
delay

Control
 log S d   log S  d
benefits
costs
 a
stabilize
Bode
e=d-u
Plant
-u
d
S   
E  
D  
a
u
delay

Control
 log S d   log S  d
benefits
costs
 a
stabilize
-
e=d-u
Plant
u
CC
Control
Channel
Control
 log S  d

 log(a ) 
d
Disturbance
d
Remote
Sensor
CS
Sensor
Channel
r
Encode
CC
 log S  d CS

Nuno C Martins and Munther A Dahleh, Feedback Control in the Presence of Noisy
Channels: “Bode-Like” Fundamental Limitations of Performance.
Nuno C. Martins, Munther A. Dahleh and John C. Doyle Fundamental Limitations
of Disturbance Attenuation in the Presence of Side Information
(Both in IEEE Transactions on Automatic Control)
http://www.glue.umd.edu/~nmartins/
Electric
power
network
Variety of
producers
Variety of
consumers
• Good designs transform/manipulate energy
• Subject (and close) to hard limits
Standard
interface
Energy
carriers
Variety of
producers
•
•
•
•
•
110 V, 60 Hz AC
(230V, 50 Hz AC)
Gasoline
ATP, glucose, etc
Proton motive force
Variety of
consumers
d
e=d-u
Plant
Disturbance
Fragile
d
Remote
Sensor
Control
Channel
Control
log(a )
Sensor
Channel
benefits
r
Robust
Encode
stabilize
 log S d  log(a) 
costs
CC
remote control
feedback
 log S  d CS

remote
sensing
• Robust designs transform/manipulate robustness
• Subject (and close) to hard limits
• Fragile designs are far away from hard limits and
waste robustness.
Hard limits and tradeoffs
On systems and their components
• Thermodynamics (Carnot)
• Communications (Shannon)
• Control (Bode)
• Computation (Turing/Gödel)
• Include dynamics and feedback
• Extend to networks
• New unifications are encouraging
Robust/
fragile
is unifying
concept
[a system] can have
[a property] robust for
[a set of perturbations]
Fragile
Yet be fragile for
Robust
[a different property]
Or [a different perturbation]
[a system] can have
[a property] robust for
[a set of perturbations]
• Some fragilities are inevitable
in robust complex systems.
Fragile
Robust
• But if robustness/fragility are conserved, what does it
mean for a system to be robust or fragile?
Emergent
Fragile
• Some fragilities are inevitable
in robust complex systems.
Robust
• But if robustness/fragility are conserved, what does it
mean for a system to be robust or fragile?
• Robust systems systematically manage this tradeoff.
• Fragile systems waste robustness.