John Doyle

1
A new physics?

• John Doyle
• Control and Dynamical Systems, Electrical
  Engineering, Bioengineering
• Caltech

2
Collaboratorsand contributors(partial list)

• Turbulence Bamieh, Dahleh, Bobba, Gharib,
  Marsden,
• Theory Parrilo, Carlson, Paganini, Lall,
  Barahona, DAndrea,
• Physics Mabuchi, Doherty, Marsden,
  Asimakapoulos,
• AfCS Simon, Sternberg, Arkin,
• Biology Csete,Yi, Borisuk, Bolouri, Kitano,
  Kurata, Khammash, El-Samad, Gross, Sauro, Hucka,
  Finney,
• Web/Internet Low, Effros, Zhu,Yu, Chandy,
  Willinger,
• Engineering CAD Ortiz, Murray, Schroder,
  Burdick, Barr,
• Disturbance ecology Moritz, Carlson, Robert,
• Power systems Verghese, Lesieutre,
• Finance Primbs, Yamada, Giannelli, Martinez,
• and casts of thousands

Caltech faculty
Other Caltech
Other
3
Collaboratorsand contributors(partial list)

• Turbulence Bamieh, Dahleh, Bobba,
• Theory Carlson, Parrilo (ETHZ), .
• Quantum Physics Mabuchi, Doherty,

Caltech faculty
Other Caltech
UCSB faculty
4
For more details

• Next week see website for links

www.cds.caltech.edu/doyle www.aut.ee.ethz.ch/par
rilo
Funding AFOSR MURI Uncertainty Management in
Complex Systems
5
Dedicated to Mohammed Dahleh
6
Outline

• Concentrate on 3 of many persistent mysteries
  in the foundations of theoretical physics
• Ubiquity of power laws (Carlson)
• Coherent structures in shear flow turbulence
  (Bamieh)
• Quantum entanglement (Parrilo)
• Describe a new, unifying conceptual framework
  plus math tools for complex multiscale physics
• Compare the beginning of a new physics circa
  2000 with the origins of robust control circa
  1980.
• Prospects for the future of controls and physics

7
Topics skipped today

• Other related problems Origin of dissipation and
  entropy, quantum measurement and
  quantum/classical transition
• Much work involving control of turbulence,
  quantum systems, etc (e.g. Speyer, Kim,
  Cortellezi, Bewley, Burns, King, Krstic, )
• Related multiscale problems in networking
  protocols (Low, Paganini,) and biological
  regulatory networks (Khammash, El Samad, Yi,)
  (See talks later today.)

8
Caveats

• Not an historical account
• Not a scholarly treatment
• Just the tip of the iceberg
• Lots of details are available in papers and
  online
• See website next week (URL on the last slide)
• All of this has appeared or will appear outside
  the controls literature

9
Thanks to Mory Gharib Jerry Marsden Brian Farrell
Turbulence in shear flows
Kumar Bobba, Bassam Bamieh
wings
channels
Turbulence is the graveyard of theories. Hans
Liepmann Caltech
pipes
10
Chaos and turbulence

• The orthodox view
• Adjusting 1 parameter (Reynolds number) leads to
  a bifurcation cascade (to chaos?)
• Turbulence transition is a bifurcation
• Turbulent flows are perhaps chaotic, certainly
  intrinsically a nonlinear phenomena
• There are certainly many situations where this
  view is useful.
• (But many people believe there is much more to
  the story.)

11
velocity
high
low
equilibrium
periodic
chaotic
12
random pipe
13
bifurcation
laminar
flow (average speed)
turbulent
pressure (drop)
14
Random pipes are like bluff bodies.
15
flow
Typical flow
Transition
pressure
16
wings
Streamline
channels
pipes
17
theory
laminar
log(flow)
experiment
turbulent
Random pipe
log(pressure)
18
log(flow)
Random pipe
log(Re)
19
Reynolds number

• Dimensionless constant
• Key determinant of qualitative flow
  characteristics

20
Average flow speed

• For generic flows
• Geometry plus R determines qualitative flow
  behavior
• Assume throughout that geometry and nominal
  velocity are fixed
• Vary viscosity, and hence R

21
This transition is extremely delicate (and
controversial).
Random pipe
It can be promoted (or delayed!) with tiny
perturbations.
log(Re)
22
Transition to turbulence is promoted (occurs at
lower speeds) by
Surface roughness Inlet distortions Vibrations The
rmodynamic fluctuations? Non-Newtonian effects?
23
None of which makes much difference for random
pipes.
Random pipe
24
Shark skin delays transition to turbulence
25
log(flow)
It can be reduced with small amounts of polymers.
log(pressure)
26
HOT
log(flow)
random
log(pressure)
27
streamlined
flow
HOT
HOT turbulence? Robust, yet fragile?
random
pressure drop

• Through streamlined design
• High throughput
• Robust to bifurcation transition (Reynolds
  number)
• Yet fragile to small perturbations
• Which are irrelevant for more generic flows

28
Flow direction
Viewed from below through clear wall.
29
Flow direction
Viewed from below through clear wall.
30
streamwise
Couette flow
31
(No Transcript)
32
(No Transcript)
33
spanwise
Couette flow
34
high-speed region
From Kline
35
high-speed region
y
flow
position
z
x
36
3d/3c Nonlinear NS
37
3d/3c Linear NS
3d/3c Nonlinear NS
Linearize
3d/3c Linear NS
y
v
flow
flow
position
velocity
z
u
w
x
3 components
3 dimensions
38
3d/3c Linear NS
y
v
flow
flow
position
velocity
z
u
w
x
3 components
3 dimensions
39
streamwise
The mystery.
Thm The first instabilities are spanwise
constant.
All observed flows are largely streamwise
constant.
40
Thm The first instabilities are spanwise
constant.
41
Thm The first instabilities are spanwise
constant.
This is as different as two flows can be.
42
3d/3c Linear NS

• Linearized Navier-Stokes
• Stable for all Reynolds numbers R
• Orthodox wisdom transition must be an inherently
  nonlinear phenomena
• Experimentally no evidence for an attractor or
  subcritical bifurcations
• Theoretically no evidence for
• The mystery deepens.

43
3d/3c Linear NS
Forcing

• Mathematically
• External disturbances
• Initial conditions
• Unmodeled dynamics

• Physically
• Wall roughness
• Acoustics
• Thermo fluctuations
• NonNewtonian
• Upstream disturbances

44
3d/3c Linear NS
Forcing
energy
(Bamieh and Dahleh)
t
45
t
46
The predicted flows are robustly and strongly
streamwise constant.
y
flow
Consistent with experimental evidence.
z
x
47
3d/3c Nonlinear NS
3d/3c Linear NS
Linearize
Stable for all R.
y
flow
z
x
2d/3c Linear NS
48
3d/3c Nonlinear NS
3d/3c Linear NS
Linearize
Stable for all R.
y
flow
z
x
2d/3c LNS
2d/3c NLNS
Linearize
49

• 2d/3c NLNS solutions to 3d/3c NLNS for streamwise
  constant initial conditions
• 2d/3c NLNS has 3 velocity components depending on
  2 (spanwise) spatial variables

3d/3c NLNS
2d/3c NLNS
y
flow
z
x
50
3d/3c NLNS
Thm 2d/3c NLNS
Globally stable for all R.
2d/3c NLNS
Proof can rescale equations to be independent of
R!
51

• High gain, low rank operator
• Implications for
• Model reduction
• Computation
• Control

3d/3c Linear NS
Globally stable for all R.
2d/3c NLNS
Linearize
2d/3c LNS
52
The predicted flows are robustly and strongly
streamwise constant.
y
flow
z
x
Consistent with experimental evidence.
53
2d/3c
54
Worst-case amplification is streamwise constant
(2d/3c). (Bamieh and Dahleh)
?
2d/3c
3d/3c
55
Robustness of shear flows
Fragile
Viscosity
Everything else
Robust
56
Robustness is a conserved quantity?
Fragile
Random
Viscosity
Everything else
Robust
57
Lessons learnedTransition and turbulence

• Be skeptical of orthodox explanations of
  persistent mysteries.
• Listen to the experimentalists.
• Singular values are as important as eigenvalues.
• Interconnection is as important as state.
• Robustness is a conserved quantity.

58
Lessons learnedRobust control

• Be skeptical of orthodox explanations of
  persistent mysteries.
• Listen to the experimentalists.
• Singular values are as important as eigenvalues.
• Interconnection is as important as state.
• Robustness is a conserved quantity.

59
Lessons learnedRobust control
logS
yet fragile
?
Robust
60
streamlined pipes
flow
HOT turbulence? Robust, yet fragile?
HOT
random pipes
pressure drop

• Through streamlined design
• High throughput
• Robust to bifurcation transition (Reynolds
  number)
• Yet fragile to small perturbations
• Which are irrelevant for more generic flows
• Turbulence is a robustness problem.

61
Transition to turbulence is promoted (occurs at
lower speeds) by
Surface roughness Inlet distortions Vibrations The
rmodynamic fluctuations? Non-Newtonian effects?
62
Universal
HOT
log(thru-put)
log(demand)
63
Highly Optimized Tolerance (HOT)(Jean Carlson,
Physics, UCSB)

• Complex systems in biology, ecology, technology,
  sociology, economics,
• are driven by design or evolution to
  high-performance states which are also tolerant
  to uncertainty in the environment and components.
• This leads to specialized, modular, hierarchical
  structures, often with enormous hidden
  complexity,
• with new sensitivities to unknown or neglected
  perturbations and design flaws.
• Robust, yet fragile!

64
Robust, yet fragile

• Robust to uncertainties
• that are common,
• the system was designed for, or
• has evolved to handle,
• yet fragile otherwise
• This is the most important feature of complex
  systems (the essence of HOT).

65
Persistent mystery 2

• The ubiquity of power laws in natural and human
  systems
• Orthodox theories
• Phase transitions and critical phenomena
• Self-organized criticality (SOC)
• Edge of chaos (EOC)
• Single largest topic in physics literature for
  the last decade
• New alternative HOT
• Already a sizeable HOT literature, so this will
  be very brief and schematic

66
6
Data compression (Huffman)
WWW files Mbytes (Crovella)
5
4
Cumulative
3
Frequency
Forest fires 1000 km2 (Malamud)
2
1
0
-1
-6
-5
-4
-3
-2
-1
0
1
2
Decimated data Log (base 10)
Size of events
67
18 Sep 1998
Forest Fires An Example of Self-Organized
Critical Behavior Bruce D. Malamud, Gleb Morein,
Donald L. Turcotte
4 data sets
68
6
Web files
5
Codewords
4
Cumulative
3
Frequency
Fires
2
1
0
-1
-6
-5
-4
-3
-2
-1
0
1
2
Size of events
Log (base 10)
69
6
gt1e5 files
Data compression (Huffman)
WWW files Mbytes (Crovella)
5
4
gt4e3 fires
Cumulative
3
Frequency
Forest fires 1000 km2 (Malamud)
2
1
0
-1
-6
-5
-4
-3
-2
-1
0
1
2
Decimated data Log (base 10)
Size of events
70
20th Centurys 100 largest disasters worldwide
2
10
Technological (10B)
Natural (100B)
1
10
US Power outages (10M of customers)
0
10
-2
-1
0
10
10
10
71
20th Centurys 100 largest disasters worldwide
2
10
1
10
0
10
-2
-1
0
10
10
10
72
2
10
Log(Cumulative frequency)
1
10
Log(rank)
0
10
-2
-1
0
10
10
10
Log(size)
73
100
80
Technological (10B)
rank
60
Natural (100B)
40
20
0
0
2
4
6
8
10
12
14
size
74
2
10
Log(rank)
1
10
0
10
-2
-1
0
10
10
10
Log(size)
75
20th Centurys 100 largest disasters worldwide
2
10
Technological (10B)
Natural (100B)
1
10
US Power outages (10M of customers)
0
10
-2
-1
0
10
10
10
76
6
Data compression
WWW files Mbytes
5
4
Cumulative
3
Frequency
Forest fires 1000 km2
2
1
0
-1
-6
-5
-4
-3
-2
-1
0
1
2
Decimated data Log (base 10)
Size of events
77
6
Data compression
WWW files Mbytes
5
exponential
4
-1
Cumulative
3
Frequency
Forest fires 1000 km2
2
-1/2
1
0
-1
-6
-5
-4
-3
-2
-1
0
1
2
Size of events
78
6
Data compression
WWW files Mbytes
5
exponential
4
Cumulative
All events are close in size.
3
Frequency
Forest fires 1000 km2
2
1
0
-1
-6
-5
-4
-3
-2
-1
0
1
2
Size of events
79
6
Data compression
WWW files Mbytes
5
4
-1
Cumulative
3
Frequency
Forest fires 1000 km2
2
-1/2
1
0
-1
-6
-5
-4
-3
-2
-1
0
1
2
Size of events
80
6
Most files are small
Data compression
WWW files Mbytes
5
4
-1
Cumulative
3
Frequency
Forest fires 1000 km2
Most fires are small
2
-1/2
1
0
-1
-6
-5
-4
-3
-2
-1
0
1
2
Size of events
81
6
Data compression
WWW files Mbytes
Robust
5
4
-1
Cumulative
3
Frequency
Forest fires 1000 km2
2
-1/2
1
Yet Fragile
0
-1
-6
-5
-4
-3
-2
-1
0
1
2
Size of events
82
Large scale phenomena is extremely non-Gaussian

• The microscopic world is largely exponential
• The laboratory world is largely Gaussian because
  of the central limit theorem
• The large scale phenomena has heavy tails (fat
  tails) and power laws

83
Orthodox summary

• Necessity Power laws iff system is at
  criticality.
• Universality Statistics dont depend on details
  of system or model
• Conclusion Power laws suggest criticality, and
  details dont matter
• Using even extremely simplified models is
  justified

84
Claimed examples of EOC/SOC and related mechanisms

• Internet traffic and topology
• Biological and ecological networks
• Evolution and extinction
• Earthquakes and forest fires
• Finance and economics
• Social and political systems
• There is an enormous literature in premier
  journals.

yield
None of these claims hold up under careful
scrutiny.
85
Orthodoxy problems

• Necessity Only applies to random systems
• Universality All predictions are extremely poor
  for real world data
• The conjecture of criticality is refuted by the
  very data used to support it!
• Sufficiently sloppy statistics can hide almost
  anything.

86
The HOT view of power laws

• Engineers design (and evolution selects) for
  systems with certain typical properties
• Optimized for average (mean) behavior
• Optimizing the mean often (but not always) yields
  high variance and heavy tails
• Power laws arise from heavy tails when there is
  enough aggregate data
• One symptom of robust, yet fragile

87
Exponential
Log(rank)
Log(size)
88
HOT and fat tails?

• Surprisingly good explanation of statistics with
  extremely simple models.
• But statistics are of secondary importance
• Not mere curve fitting, but new insights, and new
  insights lead to new designs
• Consistent with more complex models
• Understanding ? design

89
A HOT forest fire abstraction
Fire suppression mechanisms must stop a 1-d front.
Optimal strategies must tradeoff resources with
risk.
90
A toy website model( 1-d grid HOT design)
document
91
Optimize 0-dimensional cuts in a 1-dimensional
document
links files
92
Source coding for data compression
(simplest optimal design theory in engineering)
93
Generalized coding problems
Data compression
Optimizing d-1 dimensional cuts in d dimensional
spaces.
Web
94
PLR optimization
Minimize expected loss
95
d-dimensional
li volume enclosed ri barrier density
pi Probability of event
Resource/loss relationship
96
PLR optimization
? 0 data compression ? 1 web layout ?
2 forest fires
? dimension
97
Minimize average cost using standard Lagrange
multipliers
Leads to optimal solutions for resource
allocations and the relationship between the
event probabilities and sizes.
With optimal cost
98
Data
6
DC
5
WWW
4
3
FF
2
1
0
-1
-6
-5
-4
-3
-2
-1
0
1
2
99
Data Model
6
DC
5
WWW
4
3
FF
2
1
0
-1
-6
-5
-4
-3
-2
-1
0
1
2
100
18 Sep 1998
Forest Fires An Example of Self-Organized
Critical Behavior Bruce D. Malamud, Gleb Morein,
Donald L. Turcotte
4 data sets
101
Data Model/Theory
6
DC
5
WWW
4
3
2
1
Forest fire
0
-1
-6
-5
-4
-3
-2
-1
0
1
2
102
2
10
-1/2
1
10
0
10
-2
-1
0
1
2
3
4
10
10
10
10
10
10
10
Exponents are way off
103
California geographyfurther irresponsible
speculation

• Rugged terrain, mountains, deserts
• Fractal dimension ? ? 1?
• Dry Santa Ana winds drive large (? 1-d) fires

104
Data HOT Model/Theory
6
5
California brushfires
4
3
FF (national) d 2
2
1
0
-1
-6
-5
-4
-3
-2
-1
0
1
2
105
Data HOTSOC
6
5
4
3
2
1
0
-1
-6
-5
-4
-3
-2
-1
0
1
2
106
Critical/SOC exponents are way off
Data ? gt .5
SOC ? lt .15
107
HOT
SOC and HOT have very different power laws.
d1
SOC
d1

• HOT ? decreases with dimension.
• SOC?? increases with dimension.

108

• HOT yields compact events of nontrivial size.
• SOC has infinitesimal, fractal events.

HOT
SOC
large
infinitesimal
size
109
SOC and HOT are extremely different.
HOT
SOC
110
SOC and HOT are extremely different.
HOT
SOC
111
Summary

• Power laws are ubiquitous, but not surprising
• HOT may be a unifying perspective for many
• Criticality SOC is an interesting and extreme
  special case
• but very rare in the lab, and even much rarer
  still outside it.
• Viewing a system as HOT is just the beginning.

112
The real work is

• New Internet protocol design
• Forest fire suppression, ecosystem management
• Analysis of biological regulatory networks
• Convergent networking protocols
• etc

113
Forest fires details
Hfire state of the art detailed simulation
Intensity Frequency Extent
114
Los Padres National Forest
Max Moritz and Jean Carlson
115
Red human ignitions (near roads)
Yellow lightning (at high altitudes in ponderosa
pines)
Brown chaperal Pink Pinon Juniper
Ignition and vegetation patterns in Los Padres
National Forest
116
Model Data
117
More persistent mysteries

• Lots of mysteries at the foundations of
  statistical and quantum mechanics
• Macro dissipation and entropy versus micro
  reversibility
• Quantum measurement
• Quantum/classical transition and decoherence
• Progress on various aspects, but story incomplete
• Focus hot topic in QM testing entanglement
• Bonus! Not a controversial result!

118
Entangled Quantum States(Doherty, Parrilo,
Spedalieri 2001)

• Entangled states are one of the most important
  distinguishing features of quantum physics.
• Bell inequalities hidden variable theories must
  be non-local.
• Teleportation entanglement classical
  communication.
• Quantum computing some computational problems
  may have lower complexity if entangled states are
  available.

How to determine whether or not a given state is
entangled ?
119

• QM state described by psd Hermitian matrices ?
• States of multipartite systems are described by
  operators on the tensor product of vector spaces
• Product states
• each system is in a definite state
• Separable states
• a convex combination of product states.
• Entangled states those that cannot be written as
  a convex combination of product states.

120
Decision problem find a decomposition of r as a
convex combination of product states or prove
that no such decomposition exists.
(Hahn-Banach Theorem)
Z is an entanglement witness,a generalization
of Bells inequalities
Hard!
121
First Relaxation
Restrict attention to a special type of Z
The bihermitian form Z is a sum of squared
magnitudes.
122
First Relaxation

• Equivalent to known condition
• Peres-Horodecki Criterion, 1996
• Known as PPT (Positive Partial Transpose)
• Exact in low dimensions
• Counterexamples in higher dimensions

If minimum is less than zero, r is entangled
123
Further relaxations
Broaden the class of allowed Z to those for which
is a sum of squared magnitudes.
Also a semidefinite program.
Strictly stronger than PPT.
Can directly generate a whole hierarchy of tests.
124
Second Relaxation
minimize
subject to
If the minimum is less than zero then r is
entangled. Detects all the non-PPT entangled
states tried
125
Quantum entanglement and Robust control
126
Quantum entanglement and Robust control
127
Higher order relaxations

• Nested family of SDPs
• Necessary Guaranteed to converge to true answer
• No uniform bound (or PNP)
• Tighter tests for entanglement
• Improved upper bounds in robust control
• Special cases of general approach
• All of this is the work of Pablo Parrilo (PhD,
  Caltech, 2000, now Professor at ETHZ)
• My contribution I kept out of his way.

128
A sample of applications

• Nonlinear dynamical systems
• Lyapunov function computation
• Bendixson-Dulac criterion
• Robust bifurcation analysis
• Nonlinear robustness analysis
• Continuous and combinatorial optimization
• Polynomial global optimization
• Graph problems e.g. Max cut
• Problems with mixed continuous/discrete vars.

In general, any semialgebraic problem.
129
Sums of squares (SOS)
A sufficient condition for nonnegativity

• Convex condition (Shor, 1987)
• Efficiently checked using SDP (Parrilo). Write

where z is a vector of monomials. Expanding and
equating sides, obtain linear constraints among
the Qij. Finding a PSD Q subject to these
conditions is exactly a semidefinite program
(LMI).
130
Nested families of SOS (Parrilo)
Exhausts co-NP!!
131
Stronger µ upper bounds

• Structured singular value µ is NP-hard
• Standard µ upper bound can be interpreted
• As a computational scheme.
• As an intrinsic robustness analysis question
  (time-varying uncertainty).
• As the first step in a hierarchy of convex
  relaxations.
• For the four-block Morton Doyle counterexample
• Standard upper bound 1
• Second relaxation 0.895
• Exact µ value 0.8723

132
Continuous Global Optimization

• Polynomial functions NP-hard problem.
• A simple relaxation (Shor) find the maximum
  ?such that f(x) ? is a sum of squares.
• Lower bound on the global optimum.
• Solvable using SDP, in polynomial time.
• A concise proof of nonnegativity.
• Surprisingly effective (Parrilo Sturmfels 2001).

133

• Much faster than exact algebraic methods (QE,GB,
  etc.).
• Provides a certified lower bound.
• If exact, can recover an optimal feasible point.
• Surprisingly effective
• In more than 10,000 random problems, always the
  correct solution
• Bad examples do exist (otherwise NPco-NP), but
  rare.
• Variations of the Motzkin polynomial.
• Reductions of hard problems.
• None could be found using random search

134
Finding Lyapunov functions

• Ubiquitous, fundamental problem
• Algorithmic LMI solution

Convex, but still NP hard.
Test using SOS and SDP.
After optimization coefficients of V.
A Lyapunov function V, that proves stability.
135
Example
Given
Propose
After optimization coefficients of V.
A Lyapunov function V, that proves stability.
136
Conclusion a certificate of global stability
137
More general framework

• A model co-NP problem
• Check emptiness of semialgebraic sets.
• Obtain LMI sufficient conditions.
• Can be made arbitrarily tight, with more
  computation.
• Polynomial time checkable certificates.

138
Semialgebraic Sets

• Semialgebraic finite number of polynomial
  equalities and inequalities.
• Continuous, discrete, or mixture of variables.
• Is a given semialgebraic set empty?
• Feasibility of polynomial equations NP-hard
• Search for bounded-complexity emptiness proofs,
  using SDP. (Parrilo 2000)

139
Positivstellensatz (Real Nullstellensatz)
if and only if

• Stengle, 1974
• Generalizes Hilberts Nullstellensatz and LP
  duality
• Infeasibility certificates of polynomial
  equations over the real field.
• Parrilo Bounded degree solutions computed via
  SDP!
• ? Nested family of polytime relaxations for
  quadratics, the first level is the S-procedure

140
Combinatorial optimization MAX CUT
Partition the nodes in two subsets
To maximize the number of edges between the two
subsets.
Hard combinatorial problem (NP-complete).
Compute upper bounds using convex relaxations.
141
Standard semidefinite relaxation
Dual problems
This is just a first step. We can do better! The
new tools provide higher order relaxations.

• Tighter bounds are obtained.
• Never worse than the standard relaxation.
• In some cases (n-cycle, Petersen graph),
  provably better.
• Still polynomial time.

142
MAX CUT on the Petersen graph
The standard SDP upper bound 12.5 Second
relaxation bound 12. The improved bound is
exact. A corresponding coloring.
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Summary

• Single framework with substantial advances in
• Testing entanglement
• MaxCut
• Global continuous optimization
• Finding Lyapunov functions for nonlinear systems
• Improved robustness analysis upper bounds
• Many other applications
• This is just the tip of a big iceberg

144
Nested relaxations and SDP
145

• Huge breakthroughs
• but also a natural culmination of more than 2
  decades of research in robust control.
• Initial applications focus has been CS and
  physics,
• but substantial promise for persistent
  mysteries in controls and dynamical systems
• Completely changes the possibilities for
• robust hybrid/nonlinear control
• interactions with CS and physics

146

• Unique opportunities for controls community
• Resolve old difficulties within controls
• Unify and integrate fragmented disciplines within
• Unify and integrate without comms and CS
• Impact on physics and biology
• Unique capabilities of controls community
• New tools, but built on robust control machinery
• Unique talent and training

147
Controls will be the physics of the 21st
Century. (Larry Ho)

• Two interpretations
• Metaphorical
• Literal

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Metaphorical

• Physics has been the foundation of science and
  technology
• New science and technology
• Ubiquitous, embedded networking
• Integrated controls, comms, computing
• Postgenomics biology
• Global ecosystems management
• Etc. etc
• Controls will be the new foundations of science
  and technology

149
Literal

• Physics has many persistent, unresolved problems
  at its foundations
• New mathematics built on robust control will
  resolve these problems
• Redefine not only the foundations of physics, but
  also fundamentally rethink all of science and
  technology
• Towards a truly rigorous foundation for science

150
Lessons learnedRobust control Physics

• Dont assume the experts are right (including
  me).
• Listen to the experimentalists.

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For more details

• Almost nothing so far in controls literatures
• Lots on HOT vs. SOC in physics literature
• A few papers on HOT turbulence
• Parrilo Thesis and papers available online
• Next week see website for links

www.cds.caltech.edu/doyle www.aut.ee.ethz.ch/par
rilo
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For more details

• ACC workshop
• IFAC workshop?
• Both will include physics, biology, and networking

www.cds.caltech.edu/doyle www.aut.ee.ethz.ch/par
rilo
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Two great abstractions in science and technology

• Separate systems from physical substrate
• Systems The physical details dont matter
• Dont sweat the small stuff
• Reductionists The physics are all that matters
• Its all small stuff

• Separate systems engineering into control,
  communications, and computing
• Theory
• Applications

154
Zen Dont sweat the small stuff, and its
all small stuff
155
Two great abstractions

• Separate systems
• from physical substrate
• into control, communications, and computing
• Facilitated massive, wildly successful, and
  explosive growth in both mathematical theory and
  technology
• but creating a new Tower of Babel where even the
  experts do not read papers or understand systems
  outside their subspecialty.

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Biology and advanced technology

• Biology
• Integrates control, communications, computing
• Into distributed control systems
• Built at the molecular level
• Advanced technologies will do the same
• We need new theory and math, plus unprecedented
  connection between systems and devices
• Two challenges for greater integration
• Unified theory of systems
• Multiscale from devices to systems

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Bonus!

• Unified systems theory helps resolve
  fundamental unresolved problems at the
  foundations of physics
• Ubiquity of power laws (statistical mechanics)
• Shear flow turbulence (fluid dynamics)
• Macro dissipation and thermodynamics from micro
  reversible dynamics (statistical mechanics)
• Quantum-classical transition
• Quantum entanglement, measurement
• Thus the new mathematics for a unified theory of
  systems is directly relevant to multiscale
  physics
• The two challenges are connected.

158
Recent progress in related areas

• Coherent control/communications theory of TCP/IP
  networks (Low)
• Generalized source coding (data compression and
  web layout)
• Robust, scalable TCP
• Insights into protocol stack design, separation
  theory
• Deepening understanding of biological regulatory
  strategies
• Results are partial, but very encouraging