Architecture, networks, and complexity John Doyle John G Braun Professor Control and dynamical...

Architecture, networks, and complexity

John Doyle

John G Braun Professor

Control and dynamical systemsBioEngineering, Electrical Engineering

Caltech

NRC theory report: Bad news and good news

Bad: Attempts to connect with theory• Topology, modularity, information,…Good: Biology motivation• Diversity• Metabolism• Cell interior• Architecture (is not topology)• Robustness• Decision• Behavior

Alternative: Essential ideas• Listening to physicians, biologists, and

engineers

• Robust yet fragile (RYF)• “Constraints that deconstrain” (G&K)• Unity creating diversity

• Network architecture • Layering• Control and dynamics (C&D)• Hourglasses and Bowties

Collaborators and contributors(partial list)

Biology: Csete,Yi, El-Samad, Khammash, Tanaka, Arkin, Savageau, Simon, AfCS, Kurata, Smolke, Gross, Kitano, Hucka, Sauro, Finney, Bolouri, Gillespie, Petzold, F Doyle, Stelling, Caporale,…

Theory: Parrilo, Carlson, Murray, Vinnicombe, Paganini, Mitra Papachristodoulou, Prajna, Goncalves, Fazel, Liu, Lall, D’Andrea, Jadbabaie, Dahleh, Martins, Recht, many more current and former students, …

Web/Internet: Li, Alderson, Chen, Low, Willinger, Kelly, Zhu,Yu, Wang, Chandy, …

Turbulence: Bamieh, Bobba, McKeown, Gharib, Marsden, …Physics: Sandberg, Mabuchi, Doherty, Barahona, Reynolds,Disturbance ecology: Moritz, Carlson,…Finance: Martinez, Primbs, Yamada, Giannelli,…

Current Caltech Former Caltech OtherLongterm Visitor

Thanks to you for inviting me, and

• NSF ITR• AFOSR • NIH/NIGMS • ARO/ICB• DARPA• Lee Center for Advanced Networking (Caltech)• Boeing • Pfizer• Hiroaki Kitano (ERATO)• Braun family

MultiscalePhysics

SystemsBiology & Medicine

Network Centric,Pervasive,Embedded,Ubiquitous

Core theory

challenges

My interests

Sustainability?

SystemsBiology & Medicine

Bacterial networks• Necessity in chemotaxis• Design principles in heat shock response• Architecture of metabolism• Origin of high variability and power laws• Architecture of the cell• Control of core metabolism and glycolytic oscillations

SBML/SBWSOSTOOLSWildfire ecologyPhysiology and medicine (new)

Publications: Science, Nature, Cell, PNAS, PLOS, Bioinfo., Trends, IEEE Proc., IET SysBio, FEBS, PRL,…

Wilbur Wright on CWilbur Wright on Control,ontrol, 1901 1901• “We know how to construct airplanes.” (lift and drag)• “Men 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.”

Feathers and

flapping? Or lift, drag, propulsion, and control?

Recommendations

• (Obviously…) More and better theory

• Need an “architecture” for research that is as networked as biology and our best technologies

• Create the right “waist” of the research hourglass

• E.g. find the constraints that deconstrain

Robust Yet Fragile

Human complexity

Efficient, flexible metabolism Complex development and Immune systems Regeneration & renewal Complex societies Advanced technologies

Obesity and diabetes Rich microbe ecosystem Inflammation, Auto-Im. Cancer Epidemics, war, … Catastrophic failures

• Evolved mechanisms for robustness allow for, even facilitate, novel, severe fragilities elsewhere

• often involving hijacking/exploiting the same mechanism• There are hard constraints (i.e. theorems with proofs)

food intake

Glucose

Oxygen

Amino acids

Fatty acids

Organs

Tissues

Cells

Molecules

Universal metabolic system

Blood

Peter Sterling and Allostasis

VTA

Prefrontalcortex

Accumbensdopamine

Universal reward systemssportsmusicdancecrafts arttoolmaking sexfood

Dopamine,

Ghrelin,

Leptin,…

VTA

Prefrontalcortex

Accumbensdopamine

Universal reward systemssportsmusicdancecrafts arttoolmaking sexfood

Glucose

Oxygen

Organs

Tissues

Cells

Molecules

Universal metabolic system

Bloodfood

VTA

Prefrontalcortex

Accumbensdopamine

workfamily communitynature

Universal reward systems

Robust and adaptive, yet …

food sextoolmakingsportsmusicdancecrafts art

sexfoodtoolmakingsportsmusicdancecrafts art

VTA

Prefrontalcortex

Accumbensdopamine



sexfoodtoolmakingsportsmusicdancecrafts art

VTA

Prefrontalcortex

Accumbensdopamine

Vicarious

money

saltsugar/fatnicotinealcohol

industrialagriculture

market/consumerculture


sextoolmakingsportsmusicdancecrafts art

VTA

Prefrontalcortex

Accumbensdopamine

Vicarious

money


cocaineamphetamine

Vicarious

money


high sodium

obesity

overwork

smoking

alcoholism

drug abuse

hyper-tension

athero-sclerosis

diabetes

inflammation

immunesuppression

coronary,cerebro-vascular,reno-vascular

cancer

cirrhosis

accidents/homicide/suicide

Vicarious

money


high sodium

obesity

overwork

smoking

alcoholism

drug abuse

hyper-tension

athero-sclerosis

diabetes

inflammation

immunesuppression

coronary,cerebro-vascular,reno-vascular

cancer

cirrhosis

accidents/homicide/suicide

VTA dopamine

Glucose

Oxygen

Robust Yet Fragile

Human complexity



• Evolved mechanisms for robustness allow for, even facilitate, novel, severe fragilities elsewhere

• often involving hijacking/exploiting the same mechanism• There are hard constraints (i.e. theorems with proofs)

Robust yet fragileSystems can have robustness of

– Some properties to– Some perturbations in – Some components and/or environment

Yet fragile to other properties or perturbations.

Many issues are special cases, e.g.:• Efficiency: robustness to resource scarcity• Scalability: robustness to changes in scale• Evolvability: robustness of lineages on long times

to possibly large perturbations

Case studies

Today (primary):• Cell biology

Today (secondary):• Internet• Toy example: Lego• Wildfire ecology• Physiology• Power grid• Manufacturing• Transportation

Other possibilities:• Turbulence• Statistical mechanics• Physiology (e.g. HR

variability, exercise and fatigue, trauma and intensive care)

• RYF physio (e.g. diabetes, obesity, addiction, …)

• Disasters statistics (earthquakes)

Bio and hi-tech nets

Exhibit extremes of

• Robust Yet Fragile

• Simplicity and complexity

• Unity and diversity

• Evolvable and frozen

• Constrained and deconstrained

What makes this possible and/ or inevitable?

Architecture

• We use this word all the time.• What do we really mean by it?• What would a theory look like?

Architecture

Robust Yet Fragile

Human complexity



• It is much easier to create the robust features than to prevent the fragilities.

• There are poorly understood “conservation laws” at work

Robust yet fragile

Most essential challenge in technology, society, politics, ecosystems, medicine, etc:

• Managing spiraling complexity/fragility

• Not predicting what is likely or typical

• But understanding what is catastrophic (though perhaps rare)

What community will step up and be central in this challenge?

Components and materials

Systems requirements: functional, efficient,robust, evolvable,

scalable

Robust yet fragile

System and architecture

Perturbations

Perturbations

Component

System-level

Emergent Protocols

Architecture= Constraints

Aim: a universal taxonomy of complex systems and theories

• Describe systems/components in terms of constraints on what is possible

• Decompose constraints into component, system-level, protocols, and emergent

• Not necessarily unique, but hopefully illuminating nonetheless

Contraints that deconstrain

fan-in of diverse

inputs

fan-out of diverse

outputs

universal carriers

Diversefunction

Diversecomponents

UniversalControl

Universal architectures

• Hourglasses for layering of control

• Bowties for flows within layers

Evolution of theory

• Verbal arguments (stories, cartoons, diagrams)• Data and statistics (plots, tables)• Modeling and simulation (dynamics, numerics)• Analysis (theorems, proofs)• Synthesis (hard limits on the achievable, reverse

engineering good designs, forward engineering new designs)

All levels interact and iterate

Example: Theory of planetary motion

• Verbal (Ptolemy, Copernicus)• Data & stats (Brahe, Galileo, Kepler)• Model & sim (Newton, Einstein)• Analysis (Lagrange, Hamilton,

Poincare)• Synthesis (NASA/JPL)

All levels interact and iterate

Drill down

• Describe theory• Show some math• Just to give a flavor• You can ignore details• Always return to verbal

descriptions and hand-waving summaries

Verbal

Data/stat

Mod/sim

Analysis

Synthesis

Synthesis theories: Limits and tradeoffs

On systems and their components

• Thermodynamics (Carnot)

• Communications (Shannon)

• Control (Bode)

• Computation (Turing/Gödel)

Assume different architectures a priori.

No networks

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 unifyingconcept

Why glycolytic oscillations?

• Various answers depend on meaning of “why”• Will go deeper into “why” using stages…• Start with simplest possible models• Motivate generalizable and scalable methods• Extremely familiar and “done” problem in biology

and dynamics at the small circuit level• Convenient to introduce new theory and thinking

using the most familiar possible examples

Basics of glyc-oscillations

• Verbal arguments (stories, cartoons, diagrams)• Data and statistics (plots, tables)

Result: Cells and extracts show oscillatory behavior.

Why?

Why? Modeling and simulation

• Verbal arguments (stories, cartoons, diagrams)• Data and statistics (plots, tables)• Modeling and simulation (dynamics, numerics)

• Why = propose mechanism, model, simulate, compare with data

• Has been done extensively for this problem• What’s new? Simplicity and robustness

1 1

q

h

q Vx

x

1

1 y

qk y

y

x

Control

1

0 xk x Autocatalytic

reaction reactionmetabolite

consumption

1 1

1 1 01

q

y xh

x q qVxk y k x

y x

Catabolism

Pre

curs

ors

Carriers

Co-factors

Fatty acids

Sugars

NucleotidesAmino Acids

Core metabolism

Catabolism

Pre

curs

ors

Carriers

Catabolism

TCAPyr

Oxa

Cit

ACA

Gly

G1P

G6P

F6P

F1-6BP

PEP

Gly3p

13BPG

3PG

2PG

ATP

NADH

TCAPyr

Oxa

Cit

ACA

Gly

G1P

G6P

F6P

F1-6BP

PEP

Gly3p

13BPG

3PG

2PG

Pre

curs

ors

TCAPyr

Oxa

Cit

ACA

Gly

G1P

G6P

F6P

F1-6BP

PEP

Gly3p

13BPG

3PG

2PG

ATP

Autocatalytic

NADH

Pre

curs

ors

Carriers

TCA

Gly

G1P

G6P

F6P

F1-6BP

PEP Pyr

Gly3p

13BPG

3PG

2PG

ATP

NADH

Oxa

Cit

ACA

Regulatory

TCAPyr

Oxa

Cit

ACA

Gly

G1P

G6P

F6P

F1-6BP

PEP

Gly3p

13BPG

3PG

2PG

TCA

Gly

G1P

G6P

F6P

F1-6BP

PEP Pyr

Gly3p

13BPG

3PG

2PG

ATP

NADH

Oxa

Cit

ACA

If we drew the feedback loops the diagram would be unreadable.

( )

Mass &Reaction

Energyflux

Balance

dxSv x

dt

Stoichiometry or mass and energy balance

Nutrients Products

Internal

Biology is not a graph.

( )

Mass &Reaction

Mass&Energy Energyflux

Balance

dxSv x

dt

d

dt

Stoichiometry plus regulation

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 (?!?)

TCA

Gly

G1P

G6P

F6P

F1-6BP

PEP Pyr

Gly3p

13BPG

3PG

2PG

ATP

NADH

Oxa

Cit

ACA

( )

Mass &Reaction

Energyflux

Balance

dxSv x

dt

Stoichiometry matrix

S

Regulation of enzyme levels by transcription/translation/degradation

TCA

Gly

G1P

G6P

F6P

F1-6BP

PEP Pyr

Gly3p

13BPG

3PG

2PG

Oxa

Cit

ACA

( )

Mass &Reaction

Energyflux

Balance

dxSv x

dt

TCA

Gly

G1P

G6P

F6P

F1-6BP

PEP Pyr

Gly3p

13BPG

3PG

2PG

ATP

NADH

Oxa

Cit

ACA

( )

Mass &Reaction

Energyflux

Balance

dxSv x

dt

Allosteric regulation of enzymes

TCA

Gly

G1P

G6P

F6P

F1-6BP

PEP Pyr

Gly3p

13BPG

3PG

2PG

ATP

NADH

Oxa

Cit

ACA

Mass &Reaction

( ) Energyflux

Balance

dxSv x

dt


Regulation of enzyme levels

TCA

Gly

G1P

G6P

F6P

F1-6BP

PEP Pyr

Gly3p

13BPG

3PG

2PG

ATP

NADH

Oxa

Cit

ACA


Regulation of enzyme levels

Fast response

Slow

TCA

Gly

G1P

G6P

F6P

F1-6BP

PEP Pyr

Gly3p

13BPG

3PG

2PG

ATP

NADH

Oxa

Cit

ACA

F6P

F1-6BP

Gly3p

13BPG

3PG

ATP

1 1

q

h

q Vx

x

1

1 y

qk y

1

0 xk x

y

x

Control

Autocatalytic

F6P

F1-6BPGly3p

13BPG

3PG

ATP

1 1

q

h

q Vx

x

1

1 y

qk y

1

0 xk x

y

x

Control

Autocatalytic

1

0 xk x

1 1

q

h

q Vx

x

1

1 y

qk y

y

x

Control

Autocatalytic

1 1

1 1 01 y x

q

h

x q qVxk y k x

y x

Autocatalytic

1

0 xk x

1 1

q

h

q Vx

x

1

1 y

qk y

y

x

Control

11 1

1 1 0

q

h

y

x

Vx

xx q q

k yy

k x

Autocatalytic

( )

Mass &Reaction

Energyflux

Balance

dxSv x

dt

1 1

1 1 01

q

y xh

x q qVxk y k x

y x

1

0 xk x

1 1

q

h

q Vx

x

1

1 y

qk y

y

x

1 1

1 1 01 1

q

h

x q qVxky x

y V x

WOLOG normalize concentration and time

1 1

1 1 01 y x

q

h

x q qVxk y k x

y x

1

0 xk x

1 1

q

h

q Vx

x

1

1 y

qk y

y

x

1 1

1 1 01 1

q

h

x q qVxky x

y V x

Linearization:

1 1

1 1 0

11

x q qx ky x

y

q hV

st

nd

NominalVariable Process

Value?

autocatalysis 1

inhibition 2.5

1 enzyme 3

2 enzyme .3

q

h

V

k

0 1

0 1

x

y

Steady state: 1x

time10 15 20

-1

-0.5

0

0.5

1x error

Linearization:

1 1

1 1 0

11

x q qx ky x

y

q hV

st

nd


Value?

autocatalysis 1

inhibition 2.5

1 enzyme 3

2 enzyme .3

q

h

V

k

x error

time0 5 10 15 20

-1

-0.5

0

0.5

1

V=3

V=10

V=1.1

Linearization:

1 1

1 1 0

11

x q qx ky x

y

q hV

st

nd


Value?

autocatalysis 1

inhibition 2.5

1 enzyme 3

2 enzyme .3

q

h

V

k

Why? Modeling and simulation

• Why = propose mechanism, model, simulate, compare with data

• Scalable to larger systems? Yes• Nonlinear? Yes• Explore parameter space? Awkward• Explore sets of uncertain models? Awkward

Why: Analysis

• Verbal arguments (stories, cartoons, diagrams)• Data and statistics (plots, tables)• Modeling and simulation (dynamics, numerics)• Analysis (theorems, proofs)

• Why = parameter regimes of instability, global results with nonlinearities

Linearization:

1 1

1 1 0

11

x q qx ky x

y

q hV

st

nd


Value?

autocatalysis 1

inhibition 2.5

1 enzyme 3

2 enzyme .3

q

h

V

k

Stable iff

11

1 11 1

k

q

kq h q

V q

• Explicit regions of (in)stability• Easy to compare with experiments• Oscillations caused by

• nonzero q (autocatalytic)• small k (low enzyme)• large V (high flux)• large h (strong inhibition)

• Slow response caused by• large q (autocatalytic)• small V (low flux)• small h (weak inhibition)

oscillationsslow

Linearization:

1 1

1 1 0

11

x q qx ky x

y

q hV

st

nd


Value?

autocatalysis 1

inhibition 2.5

1 enzyme 3

2 enzyme .3

q

h

V

k

Stable iff

11

1 11 1

k

q

kq h q

V q

.1 6k V 1 1

1k

h qV q

0 5 10 15 20-1

-0.5

0

0.5

1

oscillations

Stable iff

11

1 11 1

k

q

kq h q

V q

.1 6k V 1 1

1k

h qV q

0 5 10 15 20-1

-0.5

0

0.5

1

0 10 20 30 40 50 600

0.5

1

1.5Nonlinear

Linearization:

1 1

1 1 0

11

x q qx ky x

y

q hV

st

nd


Value?

autocatalysis 1

inhibition 2.5

1 enzyme 3

2 enzyme .3

q

h

V

k

Stable iff

11

1 11 1

k

q

kq h q

V q

11 1q h

V 0 5 10 15 20

-1

-0.5

0

0.5

1

1.1V

.1h

Linearization:

1 1

1 1 0

11

x q qx ky x

y

q hV

st

nd


Value?

autocatalysis 1

inhibition 2.5

1 enzyme 3

2 enzyme .3

q

h

V

k

0 5 10 15 20-1

-0.5

0

0.5

1

1h

3.3h

Conservation law?

Analysis issues

• Why = parameter regimes of instability, global results with nonlinearities

• Scalable to larger systems? Less than sim• Nonlinear? Yes• Explore parameter space? Better than sim• Explore sets of uncertain models? Better than sim• Prove what models can’t do? Yes

• Major research frontier

Why: Synthesis

• Are there intrinsic tradeoffs or is this a “frozen accident”? (The former.)

• What are the relevant engineering principles? • How to separate necessity from accident? • Are there hard limits or conservation laws that

apply? (Yes)• Is biology near these limits? (Apparently)• Why does autocatalysis and other efficiency issues

aggravate regulation? (Stay tuned)

0 5 10 15 20-1

-0.5

0

0.5

1

1h

3.3h

x

time

)

Fourier

Transform

of error

h hS x = F(

ln lnh nomS S

Spectrum

freq

3.3h

1h 0 1 2 3 4 5

-2

-1

0

1

2

3

0 5 10 15 20-1

-0.5

0

0.5

1

1h

3.3h

x

time

ln

ln

h

nom

S

S

freq

3.3h

1h 0 1 2 3 4 5

-2

-1

0

1

2

3

0

1ln

10

S j d

Vh

V

Theorem:

x

time

ln

ln

h

nom

S

S

freq

0

1ln

10

S j d

Vh

V

Theorem:

5V 1k

0 5 10 15 20-1

-0.5

0

0.5

1

0 1 2 3 4 5-2

-1

0

1

2

3

.3k .1k

Why: Synthesis

• There are too many hard limits on achievable performance to show in one hour…

• Most are aggravated by – large q (more autocatalysis)

– small V and k (less enzyme)

• Thus tradeoffs between control response and efficiency

• Can summarize with hand-waving argument.• Why = it’s an inevitable consequence of

engineering tradoffs.

1

0 xk x

1 1

q

h

q Vx

x

1

1 y

qk y

y

x

1 1

1 1 01 1

q

h

x q qVxky x

y V x

Why: Synthesis (to do)

• There are hard contraints and tradeoffs• Biology is hard up against these limits• Yet there remains “design freedom”• Why these particular “choices”?

• What has evolution optimized?

• Robustness (and evolvability)?

0 5 10 15 200.8

0.85

0.9

0.95

1

1.05

Time (minutes)

[AT

P]

h = 3

h = 0

0 2 4 6 8 10-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Frequency

Lo

g(S

n/S

0)

h = 3

h = 0

Spectrum

Time response

Robust

Yet fragile

0 2 4 6 8 10-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Frequency

Lo

g(S

n/S

0)

h = 3

h = 0 Robust

Yet fragile

0 2 4 6 8 10-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Frequency

Lo

g(S

n/S

0)

h = 0 Robust

Yet fragile

log ) ?nx d constant F(

0 2 4 6 8 10-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Frequency

Lo

g(S

n/S

0)

h = 3

h = 2

h = 1

h = 0

log )nxF(

Tighter steady-stateregulation

Transients, Oscillations

log )nx d constant F(

Theorem

log )nx d constant F(

log|S |

Tighter regulation

Transients, Oscillations

Biological complexity is dominated by the evolution of

mechanisms to more finely tune this robustness/fragility tradeoff.

This tradeoff is a law.

log S d

log S d

benefits costs

log S d

log S d

• benefits = attenuation of disturbance• goal: make this as negative as possible

cost = amplificationgoal: make this small

Constraint:

-e=d-u

Control

uPlant

d

delay

u

log 0S d

Bode

ES

D

• What helps or hurts this tradeoff?• Helps: advanced warning, remote sensing• Hurts: instability, remote control

-e=d-u

Control

uPlant

d

delay

u

log S dL

/ L

ES

D

L

Freudenberg and Looze, 1984

a

-e=d-u

Control

uPlant

d

delay

u

log S d

Bode

a

ES

D

log S d

benefits costs stabilize

a

-e=d-u

Control

uPlant

d

delay

u

log S d

Bode

a

ES

D

log S d


Negative is good

Disturbance-e=d-u

ControlSensor

ChannelEncode

PlantRemoteSensor

dd

r

ControlChannel SC

u

CC

log S d

log S d

SC

CClog( )a

http://www.glue.umd.edu/~nmartins/

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/bode1.pdf

http://www.glue.umd.edu/~nmartins/bode1.pdf

http://www.glue.umd.edu/~nmartins/earlywarning.pdf

http://www.glue.umd.edu/~nmartins/earlywarning.pdf

Variety of producers

Electric powernetwork

Variety ofconsumers

• Good designs transform/manipulate energy• Subject to hard limits

Variety ofconsumers


Energy carriers

• 110 V, 60 Hz AC• (230V, 50 Hz AC)• Gasoline• ATP, glucose, etc• Proton motive force

Standard interface

Constraint that deconstrains

• Good designs transform/manipulate robustness• Subject to hard limits• Unifies theorems of Shannon and Bode (1940s)• Claim: This is the most crucial (known) limit

against which network complexity must cope

Disturbance-e=d-u

ControlSensor

ChannelEncode

PlantRemoteSensor

dd

r

ControlChannel

log S d

log S d

benefits

feedback

SC

CCstabilizeremotesensing

remote control

log( )a

costs

Robust

log( )a

Fragile

a

-e=d-u

Control

uPlant

d

delay

u

log S d

Bode

a

ES

D

log S d


log S d a

a

-e=d-u

Control

uPlant

d

delay

u

log S d

Bode

log S d


Negative is good

a

ES

D

log S d a

log( )alog S d

log S d

benefits costs

Robust

log( )a Yet fragile

Bode’s integral formula

log( )alog S d

log( )a

log S d

benefits costs

Disturbance-e=d-u

Control

u

Plant

d delayd

delay

u

Cost of control

Cost of stabilization

-e=d-u

Control

Plant ControlChannel

u

CC Cost of remote control

log( )alog S d

log S d

benefits costs

log( )alog S d

CC

Disturbance-e=d-u

Control

Plant

dd

ControlChannel

u

CC

log S d

log S d

benefits

feedback

CCstabilize remote control

log( )a

costs

Disturbance-e=d-u

ControlSensor

ChannelEncode

PlantRemoteSensor

dd

r

ControlChannel

SC

u

CC

log S d

log S d

benefits

feedback

SC

CCstabilize

remotesensing

remote control

log( )a

costs

Benefit of remote sensing

log( )alog S d

log S d

benefits costs

C

log( )alog S d

CC

Disturbance-e=d-u

ControlSensor

ChannelEncode

PlantRemoteSensor

dd

r

ControlChannel

SC

u

CC

Disturbance-e=d-u

ControlSensor

ChannelEncode

PlantRemoteSensor

dd

r

ControlChannel

SC

u

CC

log S d

log S d

benefits

feedback

SC

CCstabilize

remotesensing

remote control

log( )a

costs

Disturbance-e=d-u

ControlSensor

ChannelEncode

PlantRemoteSensor

dd

r

ControlChannel SC

u

CC

Bode/Shannon is likely a better p-to-p comms theory to serve as a foundation for networks than either Bode or Shannon alone.

log S d

log S d

SC

CClog( )a



Variety ofconsumers

• Good designs transform/manipulate energy• Subject to hard limits

• Good designs transform/manipulate robustness• Subject to hard limits• Unifies theorems of Shannon and Bode (1940s)• Claim: This is the most crucial (known) limit

against which network complexity must cope

Disturbance-e=d-u

ControlSensor

ChannelEncode

PlantRemoteSensor

dd

r

ControlChannel

log S d

log S d

benefits

feedback

SC

CCstabilizeremotesensing

remote control

log( )a

costs

Robust

log( )a

Fragile

[a system] can have[a property] robust for [a set of perturbations]

Yet be fragile for

Or [a different perturbation]

[a different property]Robust

Fragile

[a system] can have[a property] robust for [a set of perturbations]

Robust

Fragile

• But if robustness/fragility are conserved, what does it mean for a system to be robust or fragile?

• Some fragilities are inevitable in robust complex systems.

• But if robustness/fragility are conserved, what does it mean for a system to be robust or fragile?

Robust

Fragile

• Robust systems systematically manage this tradeoff.• Fragile systems waste robustness.

• Some fragilities are inevitable in robust complex systems.

Emergent



Variety ofconsumers

• Good designs transform/manipulate energy• Subject (and close) to hard limits

• Robust designs transform/manipulate robustness• Subject (and close) to hard limits• Fragile designs are far away from hard limits and

waste robustness.

Disturbance-e=d-u

ControlSensor

ChannelEncode

PlantRemoteSensor

dControlChannel

log S d

log S d

SC

CClog( )a

Robust

log( )a

FragileControl

ControlChannel

Cat

abol

ism

Genes

Co-factorsFatty acidsSugars

Nucleotides

Amino Acids Proteins

Pre

curs

ors

DNA replication

Trans*

Carriers

Components and materials:Energy, moieties

Systems requirements: functional, efficient,

robust, evolvable

Hard constraints:Thermo (Carnot)Info (Shannon)Control (Bode)Compute (Turing)

Protocols

Constraints

Diverse

Diverse

UniversalControl

Questions?

End of part 1

Architecture, networks, and complexity John Doyle John G Braun Professor Control and dynamical...

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Transcript of Architecture, networks, and complexity John Doyle John G Braun Professor Control and dynamical...