ONR MURI: NexGeNetSci

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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