Universal laws and architectures: Theory and lessons from flows, brains, hearts, cells, grids, nets, bugs, bodies, planes, docs, fire, fashion, earthquakes, turbulence, music, buildings, cities, art, running, throwing, Synesthesia, spacecraft, statistical mechanics John Doyle 道陽 Jean-Lou Chameau Professor Control and Dynamical Systems, EE, & BioE Ca # 1 tech

Universal laws and architectures: Theory and lessons from flows, brains, hearts, cells, grids, nets, bugs, bodies, planes, docs, fire, fashion, earthquakes, music, buildings, cities, art running, throwing, Synesthesia, spacecraft, statistical mechanics and zombies John Doyle 道陽 Jean-Lou Chameau Professor Control and Dynamical Systems, EE, & BioE Ca # 1 tech

Outline (two extremes) Part 1: Intro to control Much simpler than Bassam or Mihailo or Tom Aim for maximum accessibility to general audience Trying out new material for video series, looking for feedback Refer to related work but skip details (see pubs) Part 2: Latest theory Distributed, delayed comms, localized, scalable Applicable to internet, smartgrid, neuro, cells, and turbulence?

Efficiency/instability/layers/feedback New efficiencies but also instability (and/or amplification) Needs new distributed/layered/complex/active control Money/finance/lobbyists/etc Industrialization Society/agriculture/weapons/etc Bipedalism Maternal care Warm blood Flight Mitochondria Oxygen Translation (ribosomes) Glycolysis Major transitions

Let’s take some data

Fast Why? Mechanism Tradeoff Slow Architecture Speed Flexibility Robustness Virtualization Diversity Fast

Fast Why? Mechanism Tradeoff Slow Architecture Speed Flexibility Bacteria Biofilms Ants Development Regeneration Cancer Internet Vision Brains Turbulence Slow Architecture Speed Flexibility Robustness Virtualization Diversity Fast

Efficiency/instability/layers/feedback New efficiencies but instability (and/or amplification) Needs distributed/layered/complex/active control Money/finance/lobbyists/etc Industrialization Society/agriculture Tools/weapons Bipedalism Maternal care Warm blood Flight Mitochondria Oxygen Translation (ribosomes) Glycolysis

Laws as Tradeoffs efficient Function= Locomotion fragile robust efficient costly

Cartoon of early walking Cartoon of modern top parasite Cartoon of early walking Can’t fall Slow, inefficient

Tradeoffs >2x fragile 4x robust efficient costly

bike Learning walk crawl fragile . robust efficient costly

Universal laws and architectures efficient Our heroes Universal laws and architectures fragile Evolution Complexity Architecture Impossible (law) Ideal robust efficient wasteful

Actual fragile Ideal robust efficient wasteful expensive

Universal laws Impossible (law) robust efficient Actual fragile Ideal wasteful expensive

Engineering and medicine Actual fragile Impossible (law) Ideal robust efficient wasteful expensive

Impossible (law) robust efficient The risk Actual fragile Ideal wasteful expensive

Toy example of universals fragile Just add a bike? robust efficient costly

Toy example of universals: Universal laws and architectures Robust efficiency Learning, evolution, design, environment Learn fragile robust efficient costly

Sustainable  robust + efficient accessible accountable accurate adaptable administrable affordable auditable autonomy available credible process capable compatible composable configurable correctness customizable debugable degradable determinable demonstrable dependable deployable discoverable distributable durable effective evolvable extensible fail transparent fast fault-tolerant fidelity flexible inspectable installable Integrity interchangeable interoperable learnable maintainable manageable mobile modifiable modular nomadic operable orthogonality portable precision predictable producible provable recoverable relevant reliable repeatable reproducible resilient responsive reusable safety scalable seamless self-sustainable serviceable supportable securable simple stable standards survivable tailorable testable timely traceable ubiquitous understandable upgradable usable fragile Crash? efficient efficient robust sustainable efficient costly Energy robust

Sustainable  robust + efficient accessible accountable accurate adaptable administrable affordable auditable autonomy available credible process capable compatible composable configurable correctness customizable debugable degradable determinable demonstrable dependable deployable discoverable distributable durable effective evolvable extensible fail transparent fast fault-tolerant fidelity flexible inspectable installable Integrity interchangeable interoperable learnable maintainable manageable mobile modifiable modular nomadic operable orthogonality portable precision predictable producible provable recoverable relevant reliable repeatable reproducible resilient responsive reusable safety scalable seamless self-sustainable serviceable supportable securable simple stable standards survivable tailorable testable timely traceable ubiquitous understandable upgradable usable efficient efficient sustainable robust

Sustainable  robust + efficient accessible accountable accurate adaptable administrable affordable auditable autonomy available credible process capable compatible composable configurable correctness customizable debugable degradable determinable demonstrable dependable deployable discoverable distributable durable effective evolvable extensible fail transparent fast fault-tolerant fidelity flexible inspectable installable Integrity interchangeable interoperable learnable maintainable manageable mobile modifiable modular nomadic operable orthogonality portable precision predictable producible provable recoverable relevant reliable repeatable reproducible resilient responsive reusable safety scalable seamless self-sustainable serviceable supportable securable simple stable standards survivable tailorable testable timely traceable ubiquitous understandable upgradable usable fragile Crash? efficient efficient robust sustainable efficient costly Energy robust

efficient Universal laws and architectures fragile Crash? robust wasteful fragile efficient robust Ideal Impossible (law) Architecture Flexibly achieve what is possible efficient costly Energy Universal laws and architectures

U Theorems+ {case study} Architecture Impossible (law) Universal laws Words and definitions wasteful fragile efficient robust Ideal Impossible (law) Architecture Flexibly achieve what is possible Universal laws and architectures

U Theorems+ {case study} Architecture Impossible (law) robust Brains Bugs (microbes, ants) Medical physiology Nets/Grids (cyberphys) Theorems+ U {case study} Words and definitions Lots of aerospace Wildfire ecology Earthquakes Physics: turbulence, stat mech (QM?) “Toy”: Lego clothing, fashion Buildings, cities Synesthesia wasteful fragile efficient robust Ideal Impossible (law) Architecture Flexibly achieve what is possible Fundamentals!

U Theorems+ {case study} Brains Bugs (microbes, ants) Medical physiology Nets/Grids (cyberphys) Theorems+ U {case study} Words and definitions Lots of aerospace Wildfire ecology Earthquakes Physics: turbulence, stat mech (QM?) “Toy”: Lego clothing, fashion Buildings, cities Synesthesia Fundamentals! turbulence

U Theorems+ {case study} Brains Bugs (microbes, ants) Medical physiology Nets/Grids (cyberphys) Turbulence Theorems+ U {case study} Words and definitions Lots of aerospace Wildfire ecology Earthquakes Physics: stat mech (QM?) “Toy”: Lego clothing, fashion Buildings, cities Synesthesia Fundamentals!

~1980 Starting point 2012 Lots of aerospace Precursors in 1940s Wildfire ecology Earthquakes Physics: turbulence, stat mech (QM?) “Toy”: Lego clothing, fashion Buildings, cities Synesthesia Precursors in 1940s

Since ~2000 Focus today: Neuroscience Cell biology (esp. bacteria) Brains Bugs (microbes, ants) Medical physiology Nets/Grids (cyberphys) Turbulence Focus today: Neuroscience + People care + Live demos Cell biology (esp. bacteria) + Perfection  Some people care Medical physiology (esp. HRV) + People care, somewhat familiar - Live demos difficult Internet (of everything) (& Cyber-Phys) + Understand the details (and now theory) - Flawed designs (that we can fix) Everything you’ve read is wrong (in science)* Since ~2000 * In high impact “journals”

Chiang, Low, Calderbank, and Doyle Starting point Chiang, Low, Calderbank, and Doyle

Cell biology (esp. bacteria) Brains Bugs (microbes, ants) Medical physiology Nets/Grids (cyberphys) Turbulence Focus today: Neuroscience + People care + Live demos Cell biology (esp. bacteria) + Perfection  Some people care Medical physiology (esp. HRV) + People care, somewhat familiar - Live demos difficult Internet (of everything) (& Cyber-Phys) + Understand the details - Flawed designs Everything you’ve read is wrong (in science)* * In high impact “journals”

Cell biology (esp. bacteria) Focus today: Neuroscience + People care + Live demos Cell biology (esp. bacteria) + Perfection  Some people care Medical physiology (esp. HRV) + People care, somewhat familiar - Live demos difficult Internet (of everything) (& Cyber-Phys) + Understand the details - Flawed designs Everything you’ve read is wrong (in science)* * Mostly high impact “journals”

robust efficient A convenient cartoon fragile Function= Movement costly

A convenient cartoon demo fragile robust efficient costly up down

Simplified inverted pendulum y l length (COM) g gravity  l linearize

Gravity (-g) is destabilizing Gravity (+g) is stabilizing Universal laws? Law #1 : Mechanics (Newton) Law #2 : Gravity (Galileo) Gravity (-g) is destabilizing Gravity (+g) is stabilizing oscillates unstable

Gravity (-g) is destabilizing Gravity (+g) is stabilizing Universal laws? Law #1 : Mechanics (Newton) Law #2 : Gravity (Galileo) Gravity (-g) is destabilizing Gravity (+g) is stabilizing Same laws, different consequences.

crash fragile stable Theory & Data robust up down

crash, details unpredictable fragile Stable, predictable robust up down OK, boring so far, but…

crash, details unpredictable Stabilize with active feedback control? crash, details unpredictable fragile Easier to control than predict? robust OK, boring so far, but…

Stabilize with active feedback control? (Sense, decide, act) eye vision Control Act

harder? hard easy easy easier? down

n noise e error eye Law #3 : Vision/light

N noise E error eye vision slow delay Control Act

v y l length (to COM) g gravity v control (acceleration)  l x Simplified inverted pendulum y l length (to COM) g gravity v control (acceleration)  l v x Act

Laplace transform Linearize ±

N E Amplification (noise to error) theorem: Entropy rate Energy (L2) eye vision delay Control Act

Amplification (noise to error) theorem: Entropy rate Energy (L2) Fragility two ways (~ Bode* and Zames): * With key help from Freudenberg and Seron et al

Universal laws Mechanics+ Gravity + Light + Amplification (noise to error) theorem: Entropy rate Energy (L2) Universal laws Mechanics+ Gravity + Light + With Yoke Peng Leong

Proof? error Max modulus C + noise P

fragility 0.2 0.4 0.6 0.8 1 2 4 6 8 10 Fragile Length, m Shorter

Also exponential in delay! 0.2 0.4 0.6 0.8 1 2 4 6 8 10 linear Fragile 10 Length, m .1 1 .5 .2 2 loglog Fragile Also exponential in delay!

10 8 Harder 6 Hard 4 2 Theory 0.2 0.4 0.6 0.8 1 Length, m

10 8 Harder 6 Hard 4 2 easy Theory & Data 0.2 0.4 0.6 0.8 1 Length, m

l length l g gravity Essential constraint (“law”): 0.2 0.4 0.6 0.8 1 2 10 Fragile l length g gravity l Essential constraint (“law”):

Entropy rate Energy (L2) Intuition state Before you can react time

Amplification is more important than instability. Bassam (& Brian, Beverley, Dennice, …) says But no analytic formulas Amplification is more important than instability. Stable Unstable Caution state Before you can react time

Transients more than asymptotics. But no analytic formulas Amplification more important than instability. Stable Unstable Transients more than asymptotics. state Before you can react time

10 8 6 4 2 easy 0.2 0.4 0.6 0.8 1 Harder Hard Fragility to gravity (up) length (+noise) 2 easy 0.2 0.4 0.6 0.8 1 Robust to mass gravity (down) Length, m

A convenient cartoon demo crash fragile harder hard easy robust short long “efficient” “costly”

Simpler but Same laws easy crash fragile harder hard robust short long “efficient” “costly”

Law #1 : Mechanics Law #2 : Gravity Law #3 : Light/vision Law #4 : crash fragile harder hard robust short long

“Waterbed effect” Oscillations amplify robust See glyco-oscillations paper

??? hard harder

??? harder

Simple analytic formulas Unstable zeros

Proof? error C + noise P

100 hardest! 10 Theory 2 .1 .2 .5 1 Length, m

100 hard hardest! 10 2 .1 .2 .5 1 Length, m

hardest! hard harder Unstable zero Unstable pole What is sensed matters. hardest! hard harder Unstable pole Unstable zero

hardest!

hardest! Theory & data crash crash fragile harder hard robust short long

Gratuitously fragile fragile robust short long

Gratuitously fragile fragile Look up & shorten robust short long

Actual fragile Ideal robust efficient wasteful expensive

Universal laws Impossible (law) robust efficient Actual fragile Ideal wasteful expensive

Engineering and medicine Actual fragile Impossible (law) Ideal robust efficient wasteful expensive

Impossible (law) robust efficient The risk Actual fragile Ideal wasteful expensive

fragile robust short long

noise Recap eye vision delay Control Act fragile robust short long

Recap noise fragile Fragile to Up Length lo (sense) Length l Noise eye vision delay Control Act fragile Fragile to Up Length lo (sense) Length l Noise robust short long

noise Robust to mass down fragile Fragile to Up Length lo (sense) eye vision Robust to mass down delay Control Act fragile Fragile to Up Length lo (sense) Length l Noise robust short long

Robust to mass down Fragile to Up Length lo (sense) Length l Noise Medial direction Close one eye Stand one leg Alcohol Age … fragile robust long short

Efficiency/instability/layers/feedback New efficiencies but instabilities Needs distributed/layered/complex/active control Money/finance/lobbyists/etc Industrialization Society/agriculture/weapons/etc Bipedalism Maternal care Warm blood Flight Mitochondria Oxygen Translation (ribosomes) Glycolysis (2011 Science) How universal? Very.

Cell biology (esp. bacteria) Brains Bugs (microbes, ants) Medical physiology Nets/Grids (cyberphys) Focus today: Neuroscience + People care + Live demos Cell biology (esp. bacteria) + Perfection  Some people care Medical physiology (esp. HRV) + People care, somewhat familiar - Live demos difficult Internet (of everything) (& Cyber-Phys) + Understand the details - Flawed designs Everything you’ve read is wrong (in science)* * Mostly high impact “journals”

UG biochem, math, control theory Chandra, Buzi, and Doyle Insight Accessible Verifiable

Efficient = Metabolic overhead to make enzymes Robust Efficient Energy Supply Robust to  in supply and demand Efficient = Metabolic overhead to make enzymes

Efficient = Metabolic overhead to make enzymes Robust Efficient Energy Supply fragile 1 10 too fragile Robust to  in supply and demand complex 10 -1 1 10 10 10 expensive Efficient = Metabolic overhead to make enzymes

Efficiency is domain specific Robust efficiency 10 -1 1 too fragile complex No tradeoff expensive fragile 10 100 .1 1 .5 .2 2 fragile Efficiency is domain specific

Robust/fragile is more universal Robust efficiency 10 -1 1 too fragile complex No tradeoff expensive fragile 10 100 .1 1 .5 .2 2 fragile Robust/fragile is more universal Efficiency is domain specific

Robust/fragile is more universal Efficiency is domain specific Brains Bugs (microbes, ants) Medical physiology Nets/Grids (cyberphys) Focus today: Neuroscience + People care + Live demos Cell biology (esp. bacteria) + Perfection  Some people care Medical physiology (esp. HRV) + People care, somewhat familiar - Live demos difficult Internet (of everything) (& Cyber-Phys) + Understand the details - Flawed designs Everything you’ve read is wrong (in science)* Robust/fragile is more universal Efficiency is domain specific * Mostly high impact “journals”

Health  Complexity  Chaos/Fractals Li, Cruz, Chien, Sojoudi, Recht, Stone, Csete, Bahmiller, Doyle Robust efficiency and actuator saturation explain healthy heart rate control and variability Proc. Nat. Acad. Sci. PLUS 2014 Most popular/cited story? Health  Complexity  Chaos/Fractals wrong

Li, Cruz, Chien, Sojoudi, Recht, Stone, Csete, Bahmiller, Doyle Robust efficiency and actuator saturation explain healthy heart rate control and variability Proc. Nat. Acad. Sci. PLUS 2014 Mechanistic physiology + rigorous math and stats

HRV, homeostasis, and robust efficiency controls errors heart rate ventilation vasodilation coagulation inflammation digestion storage … O2 BP pH Glucose Energy store Blood volume … Mechanistic physiology energy breath trauma heart beat infection sensor external disturbances internal noise

Low Healthy variability? errors Brain O2 O2 High mean BP Low variability O2 BP pH Glucose Energy store Blood volume … Brain BP Mid mean Low variability Low

Low High Healthy variability? errors O2 BP pH Glucose Energy store Blood volume … Low energy trauma infection external disturbances High

Low High High Healthy variability? controls errors heart rate O2 ventilation vasodilation coagulation inflammation digestion storage … O2 BP pH Glucose Energy store Blood volume … Low High energy trauma infection external disturbances High

Low High High Healthy variability? controls errors heart rate O2 ventilation vasodilation coagulation inflammation digestion storage … O2 BP pH Glucose Energy store Blood volume … Low High energy breath trauma heart beat infection sensor external disturbances High internal noise

Universals Robust efficiency and actuator saturation explain healthy heart rate control and variability Challenge Mechanistic + rigorous math and stats + easily reproducible experiments+ accessible

Most “physical” laws are domain specific controls external disturbances heart rate ventilation vasodilation coagulation inflammation digestion storage … errors O2 BP pH Glucose Energy store Blood volume internal noise High Low Plumbing and chemistry Most “physical” laws are domain specific 10 -1 1 too fragile complex No tradeoff expensive fragile 10 100 .1 1 .2 2 Law #1 Mechanics Law #2 Gravity Law #3 Light Law #1 Chemistry Law #2 Autocatalysis Law #3 Allostery long

Efficiency is domain specific controls external disturbances heart rate ventilation vasodilation coagulation inflammation digestion storage … errors O2 BP pH Glucose Energy store Blood volume internal noise High Low Robust efficiency 10 -1 1 too fragile complex No tradeoff expensive fragile 10 100 .1 1 .5 .2 2 Efficiency is domain specific

Robust/fragile is more universal controls external disturbances heart rate ventilation vasodilation coagulation inflammation digestion storage … errors O2 BP pH Glucose Energy store Blood volume internal noise High Low Robust efficiency Robust/fragile is more universal 10 -1 1 too fragile complex No tradeoff expensive fragile 10 100 .1 1 .2 2 long

Robust/fragile is very universal controls external disturbances heart rate ventilation vasodilation coagulation inflammation digestion storage … errors O2 BP pH Glucose Energy store Blood volume internal noise High Low robust efficient costly Robust/fragile is very universal 10 100 .1 1 .2 2 10 -1 1 too fragile complex No tradeoff expensive fragile long

Oscillations are common side effects. amplify 10 100 .1 1 .2 2 10 -1 1 too fragile complex No tradeoff expensive fragile long

Universal Not efficient wasteful Domain specific Diverse

Universal laws Fragility is more “universal” fragile Tradeoffs are more “universal” Impossible (law) robust efficient wasteful Domain specific Diverse

Universal laws fragile Impossible (law) robust efficient wasteful Fragility is more “universal” fragile Tradeoffs are more “universal” Impossible (law) robust efficient wasteful Good theory must “plug in” domain specifics Domain specific Diverse

Laws and architectures Simplify essentials and universals Simpler live demos and experiments Undergrad math, bio, neuro, tech only (Skip lots of details) N>1! eye vision Act delay Control noise error slow Slow Architecture? Law? Fast Flexible Inflexible

+ noise vision gain Object motion eye Cortex Head motion slow Highly fast slow Highly evolved (hidden) architecture Act AOS delay VOR gain Error Tune gain Cerebellum Act

Understand this picture. noise Cortex Object motion eye vision + Head motion fast slow Act AOS delay VOR gain Error Tune gain Understand this picture. Cerebellum slowest Act AOS = Accessory Optical system

Universal laws and architectures: Theory and lessons from nets, grids, brains, bugs, planes, docs, fire, fashion, art, turbulence, music, buildings, cities, earthquakes, bodies, running, throwing, Synesthesia, spacecraft, statistical mechanics wasteful fragile efficient robust Ideal Impossible (law) Architecture

Doyle, Csete, PNAS, JULY 25 2011 For more info Most accessible No math References

Robust vision w/motion Object motion Self motion Motion Vision

Fast Why? Mechanism Tradeoff Slow Architecture Speed Flexibility Robustness Virtualization Diversity Fast

Fast Why? Mechanism Tradeoff Slow Architecture Speed Flexibility Bacteria Biofilms Ants Development Regeneration Cancer Internet Vision Brains Turbulence Slow Architecture Speed Flexibility Robustness Virtualization Diversity Fast

Controlling functionality (bacteria) Why? Mechanism Tradeoff Slow Cheap HGT Architecture Virtualization Diversity Speed Flexibility Robustness Transcription/ Translation Fast Costly Protein

Layered architecture Slow Cheap HGT Apps Architecture Virtualization Diversity Speed Flexibility Robustness Trans* OS Fast Costly Protein HW

Tradeoff Why? Mechanism Tradeoff Slow Cheap HGT Trans* Trans* Protein Fast Costly Flexible Inflexible General Special

Tradeoff Why? Mechanism Tradeoff Slow Cheap Apps OS OS HW HW HW Fast Costly Flexible Inflexible General Special

Tradeoff Why? Mechanism Tradeoff Slow Cheap Apps OS OS HW HW HW Fast Costly Flexible Inflexible General Special

Tradeoff Why? Mechanism Tradeoff Slow Cheap Apps OS HW Fast Costly Flexible Inflexible General Special

Universal HGT Slow Cheap Apps Trans* OS Protein HW Fast Costly Flexible Inflexible General Special

Universal HGT Slow Apps Trans* OS Protein HW Fast Flexible Inflexible

Horizontal App Transfer Diversity App App App App App App App App HGT App App Slow Apps Trans* OS Protein HW Fast Flexible Inflexible

Horizontal App Transfer Horizontal Hardware Transfer Universal App App App App App App App App App HGT App App Slow Apps Trans* OS Protein HW HW Fast HW Horizontal Hardware Transfer HW HW Flexible Inflexible HW

Horizontal App Transfer Horizontal Hardware Transfer Future “Internet of Everything”? App App App HGT App App Slow Apps OS HW HW Fast HW Horizontal Hardware Transfer HW HW Flexible Inflexible HW

What you can look forward to. FaceWorld Siri 3.0 Glass 3.0

The zombie/vampire apocalypse is here… Fossil fuel

Horizontal App Transfer Horizontal Hardware Transfer Virtualization App App App App App App App App HGT App App Slow Apps Trans* OS Protein HW HW Fast HW Horizontal Hardware Transfer HW HW Flexible Inflexible HW

Horizontal Gene Transfer Horizontal Hardware Transfer Virtualization Gene Gene Gene Gene Gene Gene Gene Gene HGT Gene Gene Slow Trans* Protein HW HW Fast HW Horizontal Hardware Transfer HW HW Flexible Inflexible HW

Horizontal App Transfer Horizontal Hardware Transfer Hijacking App App App App App App App App HGT App App Slow Virus Apps Trans* OS Protein HW HW Fast HW Horizontal Hardware Transfer HW HW Flexible Inflexible HW

Where function is controlled HGT Slow Cheap Apps Trans* OS Protein HW Fast Costly Flexible Inflexible General Special

Biofilms HGT Apps Trans* OS Protein HW Initiation, development in to spatially-structured population, cellular differentiation, biofilm-level reproduction (dispersers) HGT Apps Trans* OS Intercellular communication, chemical gradients, mechanical forces, geometry Protein HW Cells

Initiation, invasion, metastasis Cancer Initiation, development in to spatially-structured population, cellular differentiation, biofilm-level reproduction (dispersers) Initiation, invasion, metastasis Intercellular communication, chemical gradients, electrical gradients, mechanical forces Intercellular communication, chemical gradients, mechanical forces, geometry Cells Cells

Fast Why? Mechanism Tradeoff Slow Architecture Speed Flexibility Bacteria Biofilms Ants Development Regeneration Cancer Internet Vision Brains Turbulence Slow Architecture Speed Flexibility Robustness Virtualization Diversity Fast

Fast Why? Mechanism Tradeoff Slow Architecture Speed Flexibility Robustness Virtualization Diversity Fast

Why? Mechanism Tradeoff Slow vision VOR Fast Thanks to Partha Mitra

Fast Flexible Mechanism Vestibular Ocular Reflex (VOR) Tradeoff Slow vision Tradeoff VOR Fast Flexible Inflexible

eye vision slow Act delay Slow vision Fast Flexible Inflexible

fast Fast Flexible eye vision slow Act delay Slow vision VOR Inflexible

fast Fast Flexible eye Vestibular Ocular Reflex (VOR) Does not use “vision”? fast Act Vestibular Ocular Reflex (VOR) Slow VOR Fast Flexible Inflexible

It works in the dark or with eyes closed, but can’t easily tell. fast Act Slow VOR Fast Flexible Inflexible

fast Fast Flexible eye vision slow Act delay Slow vision VOR Inflexible

Layering Feedback Fast Flexible eye vision slow Act Highly evolved (hidden) architecture delay Slow vision Illusion Fast VOR Flexible Inflexible

What components can build from neural hardware. Slow vision Fast VOR Flexible Inflexible

Slow vision Fast VOR Flexible Inflexible

System is “tuned” to a specific environment + noise Cortex System is “tuned” to a specific environment eye vision Object + Head fast slow Act AOS delay VOR gain Error Tune gain slowest Cerebellum Slow vision Act Tuned What good architecture allows. Fast VOR Flexible Inflexible

Temporarily drop this tradeoff picture. Terminology? Tuned? Illusion? Architecture? Temporarily drop this tradeoff picture. Slow vision Tuned What good architecture allows. Fast VOR Flexible Inflexible

System is “tuned” to a specific environment + noise Cortex System is “tuned” to a specific environment eye vision Object + Head fast slow Act AOS delay VOR gain Error Tune gain slowest Cerebellum And focus on mechanism Act Tuned What good architecture allows.

What is the next most important missing piece? Error Cortex Object motion eye vision + Head motion Act delay VOR slow fast Summary so far. What is the next most important missing piece?

These signals must “match” Error Cortex Object motion eye vision + Head motion Act delay VOR slow fast These signals must “match” What is the next most important missing piece?

The VOR gain must be tuned to match the visual feedback loop. Error Cortex Object motion eye vision + Head motion fast slow Act delay VOR gain Tune gain? The VOR gain must be tuned to match the visual feedback loop.

+ fast eye vision Cortex slow gain Cerebellum Error Object motion Head motion fast slow Act delay VOR gain AOS Tune gain Error Cerebellum AOS = Accessory Optical system

Needs “feedback” tuning This fast “forward” path Error Cortex Object motion eye vision + Head motion slow Needs “feedback” tuning Act delay VOR gain AOS This fast “forward” path Tune gain Error Via AOS and cerebellum (not cortex) Cerebellum AOS = Accessory Optical system

Cortex Slow Reflex Fast Flexible Inflexible + Cerebellum fast eye vision Act slow delay VOR fast Object motion Head motion Cerebellum Error + Tune gain gain AOS Cortex Slow Cerebellum Fast Reflex Flexible Inflexible

Cortex Slow vision Special case VOR Fast Flexible Inflex Slow Fast Cerebellum Fast Reflex Flexible Inflexible

Where function is controlled HGT Apps Slow Trans* Cortex OS Protein Cerebellum HW Reflex Fast Flexible Inflexible

Virtualization Cortex HGT Apps Slow Trans* OS Protein HW Illusion Cerebellum HW Illusion Reflex Fast Flexible Inflexible

Horizontal Meme Transfer Horizontal Tool Transfer Slow Cortex Cerebellum Reflex Fast Horizontal Tool Transfer Flexible Inflexible

Horizontal Cortex Horizontal Meme Transfer Slow Illusion Reflex Fast HGT meme meme meme HGT meme meme Slow Cortex Cerebellum Illusion Reflex Fast Horizontal Tool Transfer Flexible Inflexible

Virtualization Cortex HGT Apps Slow Trans* OS Protein HW Illusion Cerebellum HW Illusion Reflex Fast Flexible Inflexible

Virus Bad Meme Transfer Hijacking? Cortex HGT Apps Slow Trans* OS Protein Cerebellum HW Reflex Fast Flexible Inflexible

+ noise vision gain Object motion eye Cortex Distributed control Head motion fast slow Act AOS delay VOR gain Error Tune gain Cerebellum slowest Delays everywhere Act AOS = Accessory Optical system

+ slowest noise vision slower gain Object motion eye Cortex direct,fast Head motion Act slower AOS delay VOR gain feedbacks Error Tune gain Cerebellum slowest Heterogeneous delays Act

Common pattern direct,fast Slow feedbacks Tuned Fast Flexible Inflexible

Control of heat shock in rpoH Control of heat shock in E. Coli  mRNA   DnaK Other operons El-Samad, Kurata, Doyle, Gross, Khammash (2005), Surviving Heat Shock: Control Strategies for Robustness and Performance. PNAS (8): FEB 22, 2005  DnaK DnaK RNAP ftsH Lon  RNAP DnaK FtsH Lon

Control of heat shock in direct,fast rpoH Control of heat shock in E. Coli  mRNA   DnaK Other operons feedbacks El-Samad, Kurata, Doyle, Gross, Khammash (2005), Surviving Heat Shock: Control Strategies for Robustness and Performance. PNAS (8): FEB 22, 2005  DnaK DnaK RNAP ftsH Lon  RNAP DnaK FtsH Lon

+ noise vision gain Object motion eye Cortex Distributed control Head motion fast slow Act AOS delay VOR gain Error Tune gain Cerebellum slowest Delays everywhere Act AOS = Accessory Optical system

Heterogeneous delays everywhere noise Cortex Object motion eye vision + Head motion fast slower Act AOS delay VOR gain Error Tune gain Cerebellum slowest Heterogeneous delays everywhere Act

10 100 .1 1 .5 .2 2 Slower noise error Slow Fast delay Speed  1/

delay Slower noise error Fast Slow 10 100 .1 1 .5 .2 2 Speed  1/ robust short

10 100 .1 1 .5 .2 2 noise error delay robust short

delay Short Fragile Speed  1/ Slow  Fragile Length lo noise error 10 100 .1 1 .5 .2 2 Speed  1/ Slow  Fragile Length lo noise error Length l delay Speed  1/ Length lo Length l

delay Robust to Fragile to mass Up down Length l Instability Length lo (sense) Noise Medial direction Close one eye Stand one leg Alcohol Age … Instability fragile Sensors/ actuators robust Delay delay short long

Physics of Fluids (2011) y y x z z x high-speed 3D coupling region Flow x z upflow high-speed region downflow low speed streak Blunted turbulent velocity profile Laminar Turbulent 3D coupling

What I remember about turbulence Bassam Brian Beverley Dennice Bassam Brian Beverley Dennice What I remember about turbulence

Turbulent Laminar Streamline Laminar fragile Transition Turbulent robust efficient wasteful

Turbulent z x y Laminar Laminar fragile Transition Turbulent robust Flow Laminar Laminar fragile Transition Turbulent Fundamentals! robust efficient wasteful

Control? Turbulent Laminar wasteful fragile Laminar Turbulent Bassam Turbulent Laminar wasteful fragile Laminar Turbulent efficient robust Control? Sharks Dolphins

Passive and active control? Massive sensing/actuation? Distributed? Turbulent Passive and active control? Massive sensing/actuation? Distributed? Sparse comms Delays Localized? Time and space Scalable synthesis computation Scalable implementation Laminar Laminar fragile Control? Sharks Dolphins Turbulent robust efficient wasteful

References http://www.cds.caltech.edu/~yw4ng Y.-S. Wang, N. Matni, S. You, and J. C. Doyle, “Localized Distributed State Feedback Control with Communication Delays,” ACC, 2014. Y.-S. Wang, N. Matni, and J. C. Doyle, “Localized LQR Optimal Control,” CDC, 2014. Y.-S. Wang and N. Matni, “Localized Distributed Optimal Control with Output Feedback and Communication Delays,” Allerton, 2014. In the figure, we use unstable plant. For the math, we use stable plant. QI framework, use Q to convexify the problem. If QI, then Q \in S <=> K \in S. 182

Large-Scale Systems Smart grid, Internet, wireless sensor network, biological systems,…etc. Tradeoffs between Efficiency (E), Robustness (R), Scalability (S) Mainstream: (E), (R), (S) are done in a serial and ad-hoc manner 183

Large-Scale Systems Control theory deal with the transient of the system – essential for robustness Traditional control theory: fundamental limits on the tradeoff between (E) and (R), NO (S) Localized control theory: fundamental limits on the tradeoff between (E), (R), and (S) 184

Large-Scale Systems Add more applications 185

Interconnected Systems Plant Interaction

Open-loop Disturbance

Open-loop State Deviation

Open-loop Propagation

Open-loop Propagation

Open-loop Propagation Space

Space-Time Diagram Space Time

Open-loop Space Marginally Stable Time

Closed-loop Different controller architectures Controller

Idealized Centralized Control Sensing / Actuation delay: 1 Sensing / Actuating

Idealized Centralized Control State / Control State Space Time

Idealized Centralized Control State Space + Global Optimal ‒ Infinite Comm Speed ‒ Global Comm ‒ Global Model / Design Time

Distributed Control Information Sharing with Delay

Idealized Centralized Control State Space + Global Optimal ‒ Infinite Comm Speed ‒ Global Comm ‒ Global Model / Design Time

Distributed Optimal H2(Lamperski, Doyle 2013) Control Control State Space + Near Global Optimal + Finite Comm Speed ‒ Global Comm ‒ Global Model / Design Comm speed: Inf Global optimal Time

Collect all info to compute About QI framework Controller Collect all info to compute local control action

Localized Distributed Control

Localized Distributed Control Sensing / actuation delay: 1 Comm speed: 2 (compared to plant speed) Slightly stronger than QI 206

Localized Distributed Control Basic idea

Localized Distributed Control Basic idea State deviation

Localized Distributed Control Basic idea activate propagate

Localized Distributed Control Basic idea Two steps further

Localized Distributed Control Basic idea Two steps further

Localized Distributed Control Basic idea Localized!

Localized Distributed Control Basic idea Localized FIR

Distributed Optimal H2(Lamperski, Doyle 2013) Control Control State Space + Near Global Optimal + Finite Comm Speed ‒ Global Comm ‒ Global Model / Design Comm speed: Inf Global optimal Time

Localized Distributed Control State Space + Near Global Optimal + Finite Comm Speed + Local Comm + Local Model / Design + Localized closed-loop Time

Space-Time Region Finite Impulse Response (FIR) Space-Time Region (state) Localized Region Space Time

Space-Time Region Control Region Constraints Space State Region Time

State Feedback Global Plant Model

State Feedback Global Plant Model Local Plant Model

State Feedback Localizability Generalization of controllability Controllability Matrix

State Feedback Localizability Local Feasibility Test (controllability in a space-time region) State Region Constraint Control Region Constraint (Boundary is zero) (Communication delay)

State Feedback Localizability Localizable: All local feasibility tests are feasible Linear constraint for localized optimization (LQR) State Region Constraint Control Region Constraint (Boundary is zero) (Communication delay)

Localized Implementation Now, we have localized closed-loop response. How to synthesize and implement the controller in a localized way? Recall the control space-time region

Space-Time Region Space Control Region Time

Space-Time Region Space Control Region Time

Space-Time Region Information Collection Space Time

Localized Synthesis Information Collection Space Localized synthesis by passing the feasibility solution locally Time

Localized Implementation Information Collection Space Localized implementation based on estimated disturbance Time

Localized Distributed Control Global Plant Model Localized Implementation

Comparison Scheme Synthesis Implementation Performance Centralized Global Inf comm Global info Optimal Completely Decentralized NP-hard Decentralized info Unknown Heuristic No guarantee Distributed QI comm ~Optimal Localized Distributed Localized (SF LQR) ~QI comm Local info (better in L0)

Summary Localizability is a generalization of controllability and observability in space-time regions. If localizable, we have Localized FIR closed loop (~global optimal) Localized implementation Localized synthesis (with decomposable cost) In the figure, we use unstable plant. For the math, we use stable plant. QI framework, use Q to convexify the problem. If QI, then Q \in S <=> K \in S. 240

Applications Disturbance localization Power network, transportation network, software-defined networking, structure design, resilience in network (under failure),… Optimal transient with practical control Ex: smart grid,… Scalable design / implementation Ex: energy-efficient wireless sensor network,… In the figure, we use unstable plant. For the math, we use stable plant. QI framework, use Q to convexify the problem. If QI, then Q \in S <=> K \in S. 241

References http://www.cds.caltech.edu/~yw4ng Y.-S. Wang, N. Matni, S. You, and J. C. Doyle, “Localized Distributed State Feedback Control with Communication Delays,” ACC, 2014. Y.-S. Wang, N. Matni, and J. C. Doyle, “Localized LQR Optimal Control,” CDC, 2014. Y.-S. Wang and N. Matni, “Localized Distributed Optimal Control with Output Feedback and Communication Delays,” Allerton, 2014. In the figure, we use unstable plant. For the math, we use stable plant. QI framework, use Q to convexify the problem. If QI, then Q \in S <=> K \in S. 242

Tradeoffs

Model Chain model with 24 nodes Marginally stable Equal penalty on state and control Equal magnitude for process / sensor noise

Design Factors 1. Actuator / Sensor density (centralized) 2. Communication speed (distributed) 3. Localization / FIR constraints (localized) In the figure, we use unstable plant. For the math, we use stable plant. QI framework, use Q to convexify the problem. If QI, then Q \in S <=> K \in S. 245

Actuator / Sensor Density In the figure, we use unstable plant. For the math, we use stable plant. QI framework, use Q to convexify the problem. If QI, then Q \in S <=> K \in S. 246

Communication Speed In the figure, we use unstable plant. For the math, we use stable plant. QI framework, use Q to convexify the problem. If QI, then Q \in S <=> K \in S. 247

Locality / FIR constraints d = 9, T = 30 In the figure, we use unstable plant. For the math, we use stable plant. QI framework, use Q to convexify the problem. If QI, then Q \in S <=> K \in S. 248

Comparison # Act. # Sen. Speed Local Time Obj. Normal Degrade 24 Inf Max(23) 6.9035 1 12 7.7017 1.1156 11.56% 8.0933 1.1723 5.09% 1.5 8.1494 1.1805 0.70% 9 30 8.1585 1.1818 0.11% In the figure, we use unstable plant. For the math, we use stable plant. QI framework, use Q to convexify the problem. If QI, then Q \in S <=> K \in S. 249

Large-Scale Example 1000 nodes, 250 actuators, 500 sensors Centralized v.s. Localized SF + Localized FC (suboptimal) Comparison Controller implementation Controller synthesis Closed loop performance In the figure, we use unstable plant. For the math, we use stable plant. QI framework, use Q to convexify the problem. If QI, then Q \in S <=> K \in S. 250

Controller Implementation Scheme Centralized Localized Comm. Speed Inf 1.5 LQR Locality Max (999) 8 Kalman Locality 4 Type Const. matrix FIR filters

Controller Synthesis Scheme Centralized Localized Comp. complexity Comp. time (parallel) 467 s 1.552 s Model Locality Max (999) 9 (LQR) 5(Kalman) Redesign Offline (global) Real time (local)

Closed Loop Performance Scheme Centralized Localized Affected Region Max(999) 13 Affected Time Inf 100 Normalized H2 1 1.02

Localized Distributed Control State Space + Near Global Optimal + Finite Comm Speed + Local Comm + Local Model / Design + Localized closed-loop Time

Idealized Centralized Control State Space + Global Optimal ‒ Infinite Comm Speed ‒ Global Comm ‒ Global Model / Design Time

Cheap but tight lower bound? State Centralized Space Time

More Extensions/Apps Apps: neuro, smartgrid, CPS, cells IMC/RHC, etc (all of centralized control theory) Cyber theory: Delay jitter (uncertainty) Cyber: Comms co-design (CDC student prize paper) Physical: Robustness (unmodeled dynamics, noise) Cyber-phys: System ID, ML, adaptive SDN (Software defined nets, OpenDaylight) Revisit “layering as optimization”? Poset causality (streamlining)? Quantization and network coding?