John Doyle 道陽 - PowerPoint Presentation

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

Outline (two extremes)Part 1: Intro to controlMuch simpler than Bassam or Mihailo or Tom Aim for maximum accessibility to general audienceTrying out new material for video series, looking for feedbackRefer to related work but skip details (see pubs) Part 2: Latest theoryDistributed, delayed comms, localized, scalableApplicable to internet, smartgrid, neuro, cells, and turbulence?

Efficiency/instability/layers/feedback Money/finance/lobbyists/etcIndustrializationSociety/agriculture/weapons/etc BipedalismMaternal careWarm bloodFlight MitochondriaOxygenTranslation (ribosomes)Glycolysis New efficiencies but also instability (and/or amplification)Needs new distributed/layered/complex/active control Major transitions

Let’s take some data

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

Fast Why? Mechanism Tradeoff Slow Bacteria Biofilms Ants Development Regeneration Cancer InternetVisionBrainsTurbulenceArchitectureSpeedFlexibilityRobustnessVirtualizationDiversity

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

costly fragile efficient robust Laws as Tradeoffs Function= Locomotion

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

costly fragile efficient robust Tradeoffs 4x >2x

crawl walk bike Learning costly fragile efficient robust

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

wasteful expensive fragile efficientrobust Actual Ideal

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

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

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

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

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

accessibleaccountableaccurate adaptableadministrable affordableauditableautonomy availablecredibleprocess capable compatiblecomposable configurable correctness customizable debugable degradable determinable demonstrabledependabledeployablediscoverable distributabledurableeffectiveevolvableextensiblefail transparentfastfault-tolerantfidelityflexibleinspectableinstallableIntegrityinterchangeableinteroperable 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 robust sustainable Sustainable  robust + efficient efficient costly fragile efficient robust Crash? Energy

accessibleaccountableaccurate adaptableadministrable affordableauditableautonomy availablecredibleprocess capable compatiblecomposable configurable correctness customizable debugable degradable determinable demonstrabledependabledeployablediscoverable distributabledurableeffectiveevolvableextensiblefail transparentfastfault-tolerantfidelityflexibleinspectableinstallableIntegrityinterchangeableinteroperable 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 robust sustainable Sustainable  robust + efficient efficient

accessibleaccountableaccurate adaptableadministrable affordableauditableautonomy availablecredibleprocess capable compatiblecomposable configurable correctness customizable debugable degradable determinable demonstrabledependabledeployablediscoverable distributabledurableeffectiveevolvableextensiblefail transparentfastfault-tolerantfidelityflexibleinspectableinstallableIntegrityinterchangeableinteroperable 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 robust sustainable Sustainable  robust + efficient efficient costly fragile efficient robust Crash? Energy

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

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

Lots of aerospace Wildfire ecologyEarthquakes Physics: turbulence, stat mech (QM?)“Toy”: Lego clothing, fashionBuildings, cities S y n e s t hesia{case study}UFundamentals! Brains Bugs (microbes, ants) Medical physiology Nets/Grids ( cyberphys ) Theorems+ Words and definitions wasteful fragile efficient robust Ideal Impossible (law) Architecture Flexibly achieve what is possible

Lots of aerospace Wildfire ecologyEarthquakes Physics: turbulence, stat mech (QM?)“Toy”: Legoclothing, fashionBuildings, cities S y n e s t hesia{case study}UFundamentals! Brains Bugs (microbes, ants) Medical physiology Nets/Grids ( cyberphys ) Theorems+ Words and definitions turbulence

{case study} U Fundamentals! Brains Bugs (microbes, ants) Medical physiology Nets/Grids ( cyberphys ) Turbulence Theorems+ Words and definitionsLots of aerospaceWildfire ecologyEarthquakes Physics: stat mech (QM?) “Toy”: Lego clothing, fashion Buildings, cities S y n e s t h e s i a

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

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)* * In high impact “journals” Brains Bugs (microbes, ants) Medical physiology Nets/Grids ( cyberphys ) Turbulence Since ~2000

Chiang, Low, Calderbank, and Doyle Starting point

Focus today: Neuroscience+ People care + Live demosCell 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 designsEverything you’ve read is wrong (in science)* * In high impact “journals” 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 designsEverything you’ve read is wrong (in science)* * Mostly high impact “journals”

A convenient cartoonFunction= Movement costly fragile efficient robust

costly fragile efficient robust up down A convenient cartoon demo

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

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

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

fragile robust up down stable crash Theory & Data

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

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

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

harder? hard easy easy down easier?

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

eye vision slow Act delay Control N noise E error

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

Linearize ± Laplace transform

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

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

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

P + noise error C Max modulus Proof?

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

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

0.2 0.4 0.6 0.8 1 2 4 6 8 10 0 Length, m Hard Harder Theory

0.2 0.4 0.6 0.8 1 2 4 6 8 10 0 Length, m Hard Harder Theory & Data easy

0.2 0.4 0.6 0.8 1 2 4 6 8 10 Fragile l l length g gravity Essential constraint (“law”):

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

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

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

0.2 0.4 0.6 0.8 1 2 4 6 8 10 0 easy Fragility to gravity (up) length (+noise) Robust to mass gravity (down) Length, m Hard Harder

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

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

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

“Waterbed effect” amplify robust

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

hard harder ???

harder ???

Unstable zeros Simple analytic formulas

P + noise error C Proof?

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

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

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

hardest!

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

fragile robust short long Gratuitously fragile

fragile robust short long Gratuitously fragile Look up & shorten

wasteful expensive fragile efficientrobust Actual Ideal

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

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

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

fragile robust short long

fragile robust short long eye vision Act delay Control noise Recap

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

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

Fragile toUp Length l o (sense)Length lNoise Medial directionClose one eye Stand one leg Alcohol Age … fragile robust shortlong Robust to mass down

Efficiency/instability/layers/feedbackMoney/finance/lobbyists/etcIndustrializationSociety/agriculture/weapons/etc BipedalismMaternal careWarm blood FlightMitochondriaOxygenTranslation (ribosomes)Glycolysis (2011 Science)New efficiencies but instabilities Needs distributed/layered/complex/active control How universal? Very.

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 designsEverything you’ve read is wrong (in science)* * Mostly high impact “journals” Brains Bugs (microbes, ants) Medical physiology Nets/Grids ( cyberphys )

Chandra, Buzi, and Doyle UG biochem, math, control theory Insight AccessibleVerifiable

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

10 -1 10 0 10 1 10 0 10 1 too fragile complex fragile expensive Efficient = Metabolic overhead to make enzymes Robust to  in supply and demand Robust Efficient Energy Supply

Robust efficiency 10 -1 10 0 10 1 10 0 10 1 too fragile complex No tradeoff expensive fragile 10 100 .1 1 .5 .2 2 fragile Efficiency is domain specific

Robust efficiency 10 -1 10 0 10 1 10 0 10 1 too fragile complex No tradeoff expensive fragile 10 100 .1 1 .5 .2 2 Robust/fragile is more universal fragile Efficiency is domain specific

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 designsEverything you’ve read is wrong (in science)* * Mostly high impact “journals” Brains Bugs (microbes, ants) Medical physiology Nets/Grids ( cyberphys ) Robust/fragile is more universal Efficiency is domain specific

Li, Cruz, Chien, Sojoudi, Recht, Stone, Csete, Bahmiller, DoyleRobust 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

Mechanistic physiology + rigorous math and stats 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

sensor controls external disturbances heart rate ventilation vasodilation coagulation inflammation digestion storage … errorsO2BPpHGlucoseEnergy storeBlood volume…infectiontraumaenergyHRV, homeostasis, and robust efficiencyinternal noiseheart beatbreath Mechanistic physiology

errors O2 BP pHGlucoseEnergy storeBlood volume… Low Brain O2 High mean Low variability Healthy variability? Brain BP Mid mean Low variability

external disturbances errors O2 BP pHGlucoseEnergy store Blood volume … infection trauma energy High LowHealthy variability?

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

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

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

10 100 .1 1 .2 2 10 -1 10 0 10 1 10 0 10 1 too fragile complex No tradeoff expensive fragile controls external disturbances heart rate ventilation vasodilation coagulation inflammation digestion storage … errors O2 BP pH Glucose Energy store Blood volume … internal noise High Low High Most “physical” laws are domain specific Plumbing and chemistry Law #1 Mechanics Law #2 Gravity Law #3 Light Law #1 Chemistry Law #2 Autocatalysis Law #3 Allostery long

10 -1 10 0 10 1 10 0 10 1 too fragile complex No tradeoff expensive fragile controls external disturbances heart rate ventilation vasodilation coagulation inflammation digestion storage … errors O2 BP pH Glucose Energy store Blood volume … internal noise High Low High Efficiency is domain specific Robust efficiency 10 100 .1 1 .5 .2 2

10 100 .1 1 .2 2 10 -1 10 0 10 1 10 0 10 1 too fragile complex No tradeoff expensive fragile controls external disturbances heart rate ventilation vasodilation coagulation inflammation digestion storage … errors O2 BP pH Glucose Energy store Blood volume … internal noise High Low High long Robust/fragile is more universal Robust efficiency

10 100 .1 1 .2 2 long 10 -1 10 0 10 1 10 0 10 1 too fragile complex No tradeoff expensive fragile controls external disturbances heart rate ventilation vasodilation coagulation inflammation digestion storage … errors O2 BP pH Glucose Energy store Blood volume … internal noise High Low High Robust/fragile is very universal costly fragile efficient robust

10 100 .1 1 .2 2 long 10 -1 10 0 10 1 10 0 10 1 too fragile complex No tradeoff expensive fragile amplify Oscillations Oscillations are common side effects.

Universal wasteful efficient Domain specific Diverse Not

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

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

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

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

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

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, S ynesthesia, spacecraft, statistical mechanicswastefulfragileefficientrobustIdeal Impossible (law) Architecture

Doyle, Csete, PNAS, JULY 25 2011 For more infoMost accessibleNo mathReferences

Robust vision w/motion Object motion Self motion Vision Motion

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

Fast Why? Mechanism Tradeoff Slow Bacteria Biofilms Ants Development Regeneration Cancer InternetVisionBrainsTurbulenceArchitectureSpeedFlexibilityRobustnessVirtualizationDiversity

FastCostly SlowCheap HGT Transcription/Translation Protein Why? Mechanism Tradeoff Architecture Virtualization Diversity SpeedFlexibilityRobustnessControlling functionality (bacteria)

FastCostly SlowCheap HGT Trans* ProteinLayered architecture Apps OS HW Architecture Virtualization Diversity SpeedFlexibilityRobustness

Fast Costly SlowCheap FlexibleInflexible General Special HGT Trans* Protein Trans* Protein ProteinTradeoffWhy?MechanismTradeoff

Fast Costly SlowCheap FlexibleInflexible General Special Apps OS HW OS HW HWTradeoffWhy?MechanismTradeoff

Fast Costly SlowCheap FlexibleInflexible General Special Apps OS HW OS HW HWTradeoffWhy?MechanismTradeoff

Fast Costly SlowCheap Flexible Inflexible General Special Apps OS HW Tradeoff Why?MechanismTradeoff

Fast Costly Slow Cheap Flexible Inflexible General Special Universal Apps OS HWHGTTrans*Protein

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

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

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

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

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

The zombie/vampire apocalypse is here… Fossil fuel

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

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

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

Fast Costly Slow Cheap Flexible Inflexible General Special Where function is controlled Apps OSHWHGTTrans*Protein

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

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

Fast Why? Mechanism Tradeoff Slow Bacteria Biofilms Ants Development Regeneration Cancer InternetVisionBrainsTurbulenceArchitectureSpeedFlexibilityRobustnessVirtualizationDiversity

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

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

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

Slow Flexible vision eye vision Act slow delay Fast Inflexible

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

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

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

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

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

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

vision VOR Slow Flexible Fast Inflexible

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

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

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

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

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

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

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

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

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

vision VOR Slow Flexible Fast Inflex Slow Flexible Fast Inflexible Cerebellum ReflexCortexSpecial case

Fast Slow Flexible Inflexible Where function is controlled Apps OS HW HGT Trans* ProteinCerebellumReflexCortex

Fast Slow Flexible Inflexible Apps OS HW HGT Trans* Protein Cerebellum ReflexCortexIllusionVirtualization

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

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

Fast Slow Flexible Inflexible Apps OS HW HGT Trans* Protein Cerebellum ReflexCortexIllusionVirtualization

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

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

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

feedbacks direct,fast Common pattern Slow Flexible Fast Inflexible Tuned

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

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

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

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

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

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

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

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

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

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

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

wasteful fragile Laminar Turbulent efficient robust Laminar Turbulent Transition Streamline

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

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

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

Referenceshttp://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.

Large-Scale SystemsSmart 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

Large-Scale SystemsControl 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)

Large-Scale Systems

Large Scale Systems How to design the controller?

Interconnected Systems Plant Interaction

Open-loop Disturbance

Open-loop State Deviation

Open-loop Propagation

Open-loop Propagation

Open-loop Space Propagation

Space-Time Diagram Space Time

Open-loop Space Time Marginally Stable

Closed-loopDifferent controller architectures Controller

Idealized Centralized ControlSensing / Actuation delay: 1 Sensing / Actuating

Idealized Centralized Control Space Time State State / Control

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

Completely Decentralized Control

Completely Decentralized ControlLimitation: No (hard) collaboration Heuristic: No global performance guaranteeOptimal: NP-hard to design / redesign

Distributed Control Information Sharing with Delay

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

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

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

Localized Distributed Control

Localized Distributed ControlSensing / actuation delay: 1Comm speed: 2 (compared to plant speed)

Localized Distributed ControlBasic idea

Localized Distributed ControlBasic idea State deviation

Localized Distributed ControlBasic idea activate propagate

Localized Distributed ControlBasic idea Two steps further

Localized Distributed ControlBasic idea Two steps further

Localized Distributed ControlBasic idea Localized!

Localized Distributed ControlBasic idea Localized FIR

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

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

Localized Distributed Control Space Time State Control Locality: 48 -> 3

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

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

Space-Time Region Space Time State Region Control Region Constraints

State Feedback Global Plant Model

State Feedback Local Plant Model Global Plant Model

State Feedback LocalizabilityGeneralization of controllability Controllability Matrix

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

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

Localized ImplementationNow, 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 Time Control Region

Space-Time Region Space Time Control Region

Space-Time Region Space Time Information Collection

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

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

Localized Distributed Control Global Plant Model Localized Implementation

Output FeedbackSystem dynamics

Output FeedbackSystem dynamics Closed loop transfer matrix

New Formulation Spatial Temporal Constraints

New Formulation Finite Dimensional Affinely Constrained Convex Program

New Formulation Generalization of Controllability

New Formulation Generalization of Observability

New Formulation Output Feedback Localizability

Comparison Scheme Synthesis Implementation Performance Centralized Global Inf comm Global info Optimal Completely Decentralized NP-hard Decentralized info Unknown Heuristic No guarantee Distributed Global QI comm Global info ~Optimal Localized Distributed Localized (SF LQR) ~QI comm Local info ~Optimal ( better in L 0 )

SummaryLocalizability is a generalization of controllability and observability in space-time regions. If localizable, we haveLocalized FIR closed loop (~global optimal) Localized implementationLocalized synthesis (with decomposable cost)

ApplicationsDisturbance 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 / implementationEx: energy-efficient wireless sensor network,…

Referenceshttp://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.

Tradeoffs

ModelChain model with 24 nodes Marginally stableEqual penalty on state and control Equal magnitude for process / sensor noise

Design Factors1. Actuator / Sensor density (centralized)2. Communication speed (distributed) 3. Localization / FIR constraints (localized)

Actuator / Sensor Density

Communication Speed

Locality / FIR constraints d = 9, T = 30

Comparison # Act. # Sen. Speed Local Time Obj. Normal Degrade 24 24 Inf Max(23) Inf 6.9035 1 12 24 Inf Max(23) Inf 7.7017 1.1156 11.56% 12 12 Inf Max(23) Inf 8.0933 1.1723 5.09% 12 12 1.5 Max(23) Inf 8.1494 1.1805 0.70% 12 12 1.5 9 30 8.1585 1.1818 0.11%

Large-Scale Example1000 nodes, 250 actuators, 500 sensors Centralized v.s. Localized SF + Localized FC (suboptimal)ComparisonController implementation Controller synthesisClosed loop performance

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

Controller Synthesis Scheme Centralized Localized Comp. complexity O(n 3 ) O(n) 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 Space Time State Control + Near Global Optimal + Finite Comm Speed + Local Comm + Local Model / Design + Localized closed-loop

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

Cheap but tight lower bound? Space Time State Centralized

More Extensions/AppsApps: 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, adaptiveSDN (Software defined nets, OpenDaylight) Revisit “layering as optimization”?Poset causality (streamlining)? Quantization and network coding?