Universal Laws And Architectures - University Of Pennsylvania

Universal Laws and ArchitecturesJohn DoyleJohn G Braun ProfessorControl and Dynamical Systems, BioEng, ElecEngCaltechPlus a cast of thousandsThird Year Review: October27, 2010ONR MURI: NexGeNetSci

layeredmultiscaleDoyleUniversal Lawsand ArchitecturesTheory First principles Rigorous math Algorithms ProofsDataAnalysis Correctstatistics Only as goodas underlyingdataLabNumericalExperiments Experiments Simulation Synthetic,clean data Stylized Controlled Clean,real worlddataFieldExercisesReal-WorldOperations Semi Controlled Messy,real worlddata Unpredictable After actionreports in lieuof data

Laws, laws, and architecture Conservation laws, constraints, hard limits– Important tradeoffs are between– Control, computation, communication, energy,materials, measurement– Existing theory is fragmented and incompatible– Continuing progress on unifications Power laws, data, models, high variability Architecture “constraints that deconstrain”– Expand “layering as optimization”– Include human in loop and physical action/control– Achieving hard limits

Triaged today Power laws, data, models, high variability– Estimating tails, MLE and WLS– High variability in markets Architecture– Dynamics in layered architectures– Case studies: TCP/IP, cell, brain, wildfire ecology, – Naming and addressing details– Beam forming details

IEEE TRANS ON SYSTEMS, MAN, AND CYBERNETICS,JULY 2010Alderson and Doyle

wastefulStandard system theories are severely limited ?Each focuses on one dimensionImportant tradeoffs are across these dimensionsNeed “clean slate” theoriesProgress is encouraging(Old mysteries are also being resolved)slow Thermodynamics (Carnot)Communications (Shannon)Control (Bode)Computation (Turing)fragile?

Most dimensions are robustnessCollapse for visualizationRobust Secure Scalable Evolvable Verifiable Maintainable Designable Fragile Not Unverifiable Frozen fragile

fragile

Conservation lawsfragile Important tradeoffs are across thesedimensions Speed vs efficiency vs robustness vs Robustness is most important forcomplexity Collapse efficiency dimensionswaste timewasteresources wasteful

Conservation laws?fragile?wasteful

? Badarchitectures?fragile?gap?Badtheory?wasteful

ConservationlawsfragileCase studiesSharpenhard boundswasteful

ArchitectureGood architecturesallow for effectivetradeoffsfragilewasteful

Complementaryapproachesfragile bad Find andfix bugsCase studiesSharpenhard boundswasteful

bad fragileFind andfix bugswasteful

Layered architecturesDiverse applicationsTCPIPMACSwitchMACMACPt to PtPt to PtPhysical

AppApplicationsRouterApp

AppApplicationsApp3.5 viewpoints on layered architecture: Operating systems Programming languages Control and dynamical systems Operations research, optimizationRouter Information theory

Naming and addressing Names to locate objects 2.5 ways to resolve a name1. Exhaustive search, table lookup2. Name gives hints Extra ½ is for indirection Address name that involves locations

Operating systems OS allocates and shares diverseresources among diverse applications “Strict layering” is crucial e.g. clearly separate– Application name space– Logical (virtual) name/address space– Physical (name/) address space Name resolution within applications Name/address translation across layers

Benefits of stricter layering“Black box” effects of stricter layering Portability of applications Security of physical address space Robustness to application crashes Scalability of virtual/real addressing Local variables and addresses Optimization/control by duality?

Problems with incomplete layering“Black box” benefits are lost Global variables? @ %*&! %@& Poor portability of applications Insecurity of physical address space Fragile to application crashes No scalability of virtual/real addressing Limits optimization/control by duality?

In programming:No global variablesAppuserDirectaccess tophysicalmemory?kernelIn operating systems:Don’t cross layers

AppApplicationsRouterApp

IPCAppAppDNSRobust? Secure Scalable Verifiable Evolvable Maintainable Designable IP addressesinterfaces notnodesGlobaland directaccess tophysicaladdress!

Naming and addressing need to be resolved within layer translated between layers not exposed outside of layerRelated issues DNS NATS Firewalls Multihoming Mobility Routing table size Overlays ApplicationTCPIPPhysical

ant

Meta-layering of cyber-phys NetworkcablePhysicalplant

ArchitectureGood architecturesallow for effectivetradeoffsfragilewasteful

ngthe physicalPhysicalplant

ArchitectureGood architecturesallow for effectivetradeoffsfragileCollapsingthe stack atthe edgesExploitingthe physicalwasteful

Programmable Antenna Design UsingConvex OptimizationLavaei, Babakhani,Hajimiri, and DoyleCaltechTheory: Lavaei, DoyleExperiment: Babakhani, Ali HajimiriQI

Papers by Lavaei, Babakhani, Hajimiri, and Doyle,"Design of Passively Controllable Smart Antennas for Wireless SensorNetworks," Submitted to IEEE Transactions on Automatic Control."Solving Large-Scale Hybrid Circuit-Antenna Problems," To appear inIEEE Transactions on Circuits and Systems I, 2010."'Passively Controllable Smart Antennas," to appear in IEEE GlobalCommunications Conference (GLOBECOM), Miami, Florida, 2010."Finding Globally Optimum Solutions in Antenna Optimization Problems,"in IEEE International Symposium on Antennas and Propagation,Toronto, Canada, 2010."Programmable Antenna Design Using Convex Optimization," in Math.Theory of Networks and Systems, Budapest,2010 (invited paper)."A Study of Near-Field Direct Antenna Modulation Systems Using ConvexOptimization," in American Control Conference, Baltimore, 2010."Solving Large-Scale Linear Circuit Problems via Convex Optimization,"in Proc. 48th IEEE Conf on Dec. and Control, Shanghai, China, 2009.33

Summary of results A passively controllable smart (PCS) antennathat can be implemented as an integrated circuitand be programmed in real time. Can be used for smart data transmission. For the first time, excellent beam-formingpatterns obtained with a small-sized antenna. The programming of the PCS antennaovercomes apparent intractability. Potentially completely changes what is possibleat wireless physical layer34

Complementaryapproaches bad fragileFind andfix bugsSharpenhardboundsCase studieswasteful

fragileSharpenhardboundsCase studies thatachieve boundswasteful

Theory plus biology case studyHard tradeoffs between Fragility (disturbance rejection) Metabolic overhead– Amount (of enzymes)– Complexity (of enzymes) Glycolytic oscillations Most ubiquitous and studied “circuit” in science orengineering New insights and experiments Resolves longstanding mysteries Biology component funded by NIH and Army ICB

Fragility (disturbance rejection) Metabolic overhead– Amount (of enzymes)– Complexity (of enzymes)Fragilitysimpleenzymehard limitcomplex enzymeEnzyme amount

Theorem1zz p ln S j 2d ln2 0z p z Fragilitylnz pz psimpleenzymecomplex enzymeEnzyme amount

1zz p ln S j 2d ln2 0z p z TheoremFragility (standard control theory) rigorous, first principles.Sensitivity Function21.50.2ln S j 0-0.2g 0, k 31Log S Time Simulation-0.40.5-0.60-0.5-10-0.8h 2h 3h 45Frequency-1100510Time

Theorem1zz p ln S j 2d ln2 0z p z z and p are functions of enzyme complexity and amount standard biochemistry models phenomenological first principles?simpleenzymecomplex enzymeEnzyme amount

1z lnS j 22 0 z 10z p ln d z p 1Biological architecturesachieve hard limits anduse complex enzymesand networksFragilityz pz pcomplex enzyme010 -110100k101Enzyme amount

ArchitectureGood architecturesallow for effectivetradeoffsFragilityAlternative biocircuitswith shared architecture“Conservationlaws”Metabolic overhead

ArchitectureGood architecturesallow for effectivetradeoffsfragilewasteful

Phenomenology1. Incorporate domain specifics2. First principles models

Fragilityhard limits General Rigorous First principlesimplecomplex?Plugging indomain detailsOverhead, waste Domain specific Ad hoc Phenomenological

Fragility General Rigorous First principle?Plugging indomain details Fundamental multiscale physics Start classically Foundations, origins of– noise– dissipation– amplificationOverhead, waste Domain specific Ad hoc Phenomenological

IEEE TRANS ON AUTOMATIC CONTROL,to appear, FEBRUARY, 2011Sandberg, Delvenne, and Doyle

Layers in hardwareSo well-known as to be taken for granted Digital abstraction and modularity Analog substrate is active and lossy Microscopic world is lossless Reconcile these in a clear and coherent way Exploit designable physical layer more

stepresponse s 1stepresponse s V(t)

stepresponse 10Amplitude1.5 s 1dissipative,lossy t1 e10.5000.5But the microscope world is lossless(energy is conserved).Where1 does dissipation1.52 come from?2.5Time (sec)

stepresponse s 1stepresponse ss s2 2kdissipative,lossyV(t)LosslessApproximate

LosslessApproximatestepresponses s2 2kstepresponse ss s2 2kV(t)LosslessApproximate

LosslessApproximatestepresponses s2 2kT 11.51Amplitude0.50-0.5n 10-1-1.500.511.5Time (sec)22.5

1.510.5n 1000-0.5-1-1.500.20.40.60.81T 11.510.50n 10-0.5-1-1.500.20.40.60.81

1.5n 41n 100.5000.20.4T 10.60.81Time (sec)stepresponse ss s2 2kV(t)LosslessApproximate

1.51Amplitude0.50-0.5n 10-1-1.500.511.522.5Time (sec)LosslessApproximates s2 2kstepresponse

Response to Initial Conditions1.51Amplitude0.50-0.5-1n 10-1.5-200.20.40.60.8Time (sec)randominitialconditionss s2 2k1

Response to Initial Conditions1.51Amplitude0.50-0.5-1n 10-1.5-200.20.40.60.81T 1Time (sec)Response to Initial Conditions0.80.60.4Amplitude0.20-0.2-0.4n 100-0.6-0.800.20.40.6Time (sec)0.81

1.51Dissipation0.50-0.5-1-1.500.20.40.60.81T 1Theorem: Fluctuation DissipationResponse to Initial 4-0.6-0.800.20.40.6Time (sec)0.81

Theorem: FluctuationDissipationTheorem: Linear passive ifflinear lossless approximationTheorem: Linear active needsnonlinear lossless approximation

Consequencesy (t )System y (t )Back action yˆ (t )Sense-Est.Sensor “noise”“Physical”implementatione(t )

Sensor at temp T Short interval (0,t)y (t )System y (t )Back actionE y 2 (t ) kTt O t 2 yˆ (t )Sense-Est.Sensor “noise”kT O 1 E e (t ) t2Theoreme(t )

y (t )System y (t )yˆ (t )Senseback-action y (t ) -Est.E y 2 (t ) kTkT O 1 E e (t ) t2errore(t )e (t )

y (t )System y (t ) yˆ (t )Sense-e (t )Est.kT O 1 E e (t ) t2Sensor “noise”kTE e (t ) t2errore(t )

y (t )SystemE y (t ) kT2back-action y (t )E y (t ) 2 kTtBack action y (t )Sense yˆ (t )-Est.e (t )

y (t )SystemE y (t ) kT2 y (t )back-action y (t ) yˆ (t )Sense-e (t )Est.kT O 1 E e (t ) t2Theorem:E y (t ) 2 y (t ) e(t ) kT O t kTtkTE e (t ) t2errore(t )

y (t )System y (t )back-action yˆ (t )Sense-e (t )Est. y (t ) y (t ) e(t ) kT O t Cold sensorsare betterand faster(but not cheaper)error e(t )

y (t )System y (t ) yˆ (t )Sensebackactionlarger tmore dataE y (t ) smaller tless data kTtkTE e (t ) tEst. y (t ) e(t ) kT22error-e (t )

y (t )System y (t )Sensebackaction yˆ (t )-e (t )Est.A transient and far-from-equilibriumupgrade of statistical mechanicsE y 2 (t ) y (t ) e(t ) kT O t kTtkTE e (t ) t2error

backactionA transient and far-from-equilibriumupgrade of statistical mechanics Estimation to control Efficiency of devices, enzymes Classical to quantumerror

103 1k xkrank k102unmixmix101010 -31010-210-1Power laws100

310 1k xkrank k210unmixmix110010 -310-2-11010-210010-110010

SoCalFaults.pdf

These are the closest toour assumptions: Coastal Chaparral large watersheds210 limited urban boundarymechanisticmodel4 2lpnf-w2 bigsur11012 3lpnf-nw010 210103104 Mix and unmixed fits well witha -.5 in body, Mix tail is deviating as expected105

These are the closest toour assumptions: Coastal Chaparral large watersheds210 limited urban boundarymix4 2lpnf-w2 bigsur11012 3lpnf-nw010 210103104 Mix and unmixed fits well witha -.5 in body, Mix tail is deviating as expected105

These are the closest toour assumptions: Coastal Chaparral large watersheds210 limited urban boundarymixmodel4 2lpnf-w2 bigsur11012 3lpnf-nw010 210103104 Mix and unmixed fits well witha -.5 in body, Mix tail is deviating as expected105