Jinkyu LeeSungkyunkwan University(SKKU)

ClosingtheGapbetweenStabilityandSchedulability:ANewTaskModelforCyber-Physicalsystems

Hoon SungChwa andKangG.ShinUniversityofMichigan

▪ Operationofphysicalsubsystem inaCPSismonitored&controlledbycyber/computational subsystem.▫ Examples:autonomousvehicles,medicaldevices,smartbuildings

Cyber-PhysicalSystems

Cyber-PhysicalSystemsFeedbackcontrolloop

Physical plant

Controllerreference

SensorActuatorstate

outputinput

Periodictaskmodel(T,C,D):Period,Worst-caseexecutiontime,Deadline

State-spacerepresentation

Real-timescheduling

Stability

Schedulability

PhysicalpartCyberpart Gap

• Stability• Mostphysicalsubsystemsaredesignedtotolerateoccasionalcontrolupdatemisses.• Trade-offbetween samplingrateand updatemisses

• Stability,controlperformance,resourceutilization

Motivation

Feedbackcontrolloop

Physical plant

Controller

SensorActuatorSampling

rate

Controlupdatemiss

▪ AdaptiveCruiseControl(ACC)▫ Goal:maintainasafedistance▫ Input:inter-vehicledistance(𝛿),velocity(∆𝑣)▫ Output:vehicleacceleration(𝑎)<speedcontrol>

▪ Periodic(feedback)controlloop▫ Samplingperiod:𝑇

CaseStudy:ADASsystem

▪ State-spacerepresentation

▪ Stabilityanalysis[Astrom andWittenmark 97]

CaseStudy:ADASsystem

𝑥 𝑘 + 1 = 𝐴𝑥 𝑘 + 𝐵𝑢(𝑘 − 𝑚 𝑘 )𝑢 𝑘 = −𝐾𝑥(𝑘)𝑥 𝑘 = 𝛿∆𝑣𝑎 T

𝑚 𝑘 : # of consecutive update misses at 𝑡5

Astrom andWittenmark.Computer-controlledsystems.Prentice-HallInc.,1997.

▪ Stabilityregion

Observation

▪ Stabilityregion

Observation

(100ms,3misses)

(40ms,10misses)

• Shorter samplingperiod->moretolerable consecutivecontrolupdatemisses

▪ Stabilityregion

Observation

• Shorter samplingperiod->moretolerable consecutivecontrolupdatemisses

• Shorterperiodallowingmoreupdatemisses->Stabilityguaranteewithmuchfewerresources

Whenm=0,171ms

Whenm=1,(1+1)140 = 280ms

Whenm=10,(10+1) 40 = 440ms

Effective control update period

(m:consecutivecontrolupdatemisses)

40ms

140ms

171ms

▪ Stabilityregion

Observation

▪ Controlperformance(standardquadraticperformanceindex)▫ Deviationfromthedesiredstate

▪ Controlperformancedegradesasboththesamplingperiodand#updatemissesincrease.

Observation

▪ Periodiccontroltaskbehaviorwithcontrolupdatemisses▫ Case1:controltaskwithperiodT,consecutivemisses2

▫ Case2:controltaskwithperiod3T,consecutivemisses0

Observation

▪ Therelationbetweensamplingperiod andupdatemissescanbeexploitedtoimprovebothcontrolperformance andresourceefficiency withoutlosingstability

▪ OurGoal

Implication

▪ Control-scheduleco-design▫ Optimalperiodassignmenttomaximizecontrolperformance▫ Onlineperiod-adjustmentschemes▫ Assumption:stricthardguaranteeofeverydeadline

▪ Fault-tolerantscheduling▫ Relaxationofstricthardreal-timeguarantees

▪ (m,k)-firmdeadline,skip-overmodel,weakly-hardtaskmodel▪ Allowoccasionalcontrolsignaldropsorskippingjobs

▫ Assumption:fixedorgiventaskperiods

StateoftheArt

Noconsiderationoninteractionbtw.taskperiod anddeadlinemisses

[Seto etal. 96][BiniandCervin 08][Xuetal. 15][Cervin etal. 04][Wuetal. 10][Aminifar etal. 12][Palopoli etal. 02][Khatib etal. 17]

[Cervin etal. 02][Martietal. 04][Castane etal. 06]

[Palopoli etal. 00][Branicky etal. 02][Kauer etal. 14][Goswami etal. 14][Soudbakhsh etal. 13][Majumdar etal. 11][Yoshimotoetal. 11]

OurApproach

NewCPStaskmodel

Newschedulingmechanism

• capturesthetrade-offbetweensamplingperiod andcontrolupdatemissesü Stability,controlperformance

• Determinestaskperiods andmanagedeadlinemissesü Improvescontrolperformancewithoutlosingstabilityü Utilizeslimitedresourcesefficiently

▪ Foreachcontroltask𝜏7

NewCPSTaskModel

(𝑇7, 𝐶7, 𝐷7)

Classicalreal-timetaskmodel

({(𝑚7, [𝑇7=7> 𝑚7 , 𝑇7=?@(𝑚7)])}, 𝐶7, 𝐷7)

NewCPStaskmodel

𝑚7:maximumtolerableconsecutivedeadlinemisses

Generalize

Stablepair

▪ Foragivensetofcontroltasks,▪ Step1[offlineparameterassignment]▫ Determine𝜏7: 𝑚7, 𝑇7, 𝐶7, 𝐷7 ({(𝑚7, [𝑇7=7> 𝑚7 , 𝑇7=?@(𝑚7)])}, 𝐶7, 𝐷7)

guaranteeingstability

▪ Step2[onlinestate-awarescheduling]▫ Generateactualschedulebydynamicallycontrollingdeadlinemisses(≤ 𝑚7)▫ Considerplantstatetomaximizecontrolperformancewithoutlosingstability

Problem

▪ Howtofindastable parameterassignment?

▪ Howtofindaperformance-optimal parameterassignmentamongstableparameterassignments?

OfflineParameterAssignment

▪ Howtofindastableparameterassignment?▫ Derivenecessaryconditions foratasksettobestable▪ Notionofcritical job

▫ Ajobissaidtobecritical,ifitisreleasedaftermissing𝑚7 consecutivejobdeadlines

▪ Ifallcriticaljobsareschedulable,thephysicalplantisstable

OfflineParameterAssignment

Time

𝐽7F 𝐽7G 𝐽7H 𝐽7I 𝐽7J 𝐽7K 𝐽7L 𝐽7M 𝐽7N

Criticaljob Jobrelease Deadlinemiss𝑇7

𝑚7 = 2

Stabilityofitsphysicalplant

Schedulabilityofacontroltask

▪ Howtofindastableparameterassignment?▫ Schedulability ofallcriticaljobs▪ Difficult todeterminetheschedulability▪ ∵ Criticaljobdynamicallychanges▪ ∵ Interferenceonacriticaljob varies

OfflineParameterAssignment

Time

𝐽7F 𝐽7G 𝐽7H 𝐽7I 𝐽7J 𝐽7K 𝐽7L 𝐽7M 𝐽7N

𝐽7F 𝐽7G 𝐽7H 𝐽7I 𝐽7J 𝐽7K 𝐽7L 𝐽7M 𝐽7N

miss miss miss miss

miss miss miss miss miss

Criticaljob

dependingonthescheduleofnon-criticaljobs

▪ Howtofindastableparameterassignment?▫ Assume astaticminimal jobschedule

▪ Onlycriticaljobsarescheduled

▫ Applyresponse-timeanalysis

OfflineParameterAssignment

Time

𝐽7F 𝐽7G 𝐽7H 𝐽7I 𝐽7J 𝐽7K 𝐽7L 𝐽7M 𝐽7N

𝑚7 + 1 ⋅ 𝑇7 = 3 ⋅ 𝑇7

Period

Deadline

𝑇7

▪ Howtofindaperformance-optimalparameterassignmentamongstableparameterassignments?▫ Optimizationproblem

▫ Exponentiallyincreasingsearchspace▪ Two-stepapproach

OfflineParameterAssignment

control performance index

stability region

schedulability of critical jobs

State-awareOnlineScheduling

▪ UponJOB-RELEASEorJOB-COMPLETION▫ Maintaintwotypesofqueue:readyqueueandwaitqueue▫ Checkthepossibilityofexecutingnon-criticaljobs

State-awareOnlineScheduling

▪ Howtoensuredeadlineguaranteesofallcriticaljobs?▫ Challenge

▪ Infinitenumber ofcriticaljobswillbereleasedinfuture▪ Synchronousreleaseisnolongerthecriticalinstant

▫ Ourapproach▪ Provethatsufficienttocheckonlyonecriticaljobthatwillbereleasedearliest▪ Developschedulability analysis

▪ Autonomousvehiclecontrolsystem▫ Adaptivecruisecontrol,lanekeepingcontrol,DC-servocontrol▫ 3controltasks+hardreal-timetasks

Evaluation

▪ Comparison

Evaluation

[Martietal. 04]

Ournewtaskmodel({(m,T)},C,D)

Traditionaltaskmodel(T,C,D)

Parameter assignment

Periodassignmentwithharddeadline

(m,T)assignment[Our-PA]

Online scheduling

State-awarescheduling

[Our-PA-SAS]

Critical-job-onlyscheduling[Our-PA]

Dynamic periodadjustmentunderEDF

[DPA-EDF]

Static periodassignmentunderRM[SPA-RM]

Martietal.Optimalstatefeedbackbasedresourceallocationforresource-constrainedcontroltasks.InRTSS,2004.

▪ Evaluationcriteria▫ Schedulingperformance(cyberpart)

▪ Thenumberoftasksetsschedulablebytheproposedtechnique

Evaluation

54%

39%Accommodatemorecontroltasks

withoutlosingstability

▪ Evaluationcriteria▫ Controlperformance(physicalpart)

▪ Cumulativeerrorfromdesiredstateforcontroltasks

Evaluation

32%

Summary

Static viewonstability

GAP

<Physicalpart> <Cyberpart>

Stability ofphysicalpart

Tolerable updatemisses Nodeadlinemissallowed

Identifykeyparameters andtheirrelationship

Propose anewtaskmodelthatcapturestherelationship

Improvebothcontrolperformance andresourceutilization

ReferenceSeto etal.Ontaskschedulability inreal-timecontrolsystems.InRTSS,1996.

BiniandCervin.Delay-awareperiodassignmentincontrolsystems.InRTSS,2008.

Xuetal.Exploitingjobresponse-timeinformationintheco-designofreal-timecontrolsystems.InRTCSA,2015.

Cervin etal.Thejittermarginanditsapplicationinthedesignofreal-timecontrolsystems.InRTCSA,2004.

Wuetal.Parameterselectionforreal-timecontrollersinresource-constrainedsystems.InIEEETransactionsonIndustrialInformatics, 2010.

Aminifar etal.Designinghigh-qualityembeddedcontrolsystemswithguaranteedstability.InRTSS,2012.

Palopoli etal.Synthesisofrobustcontrolsystemsunderresourceconstraints.InHSCC,2002.Khatib etal.Schedulingofembeddedcontrollersundertimingcontracts.InHSCC,2017.

Cervin etal.Feedback-feedforwardschedulingofcontroltasks.InReal-TimeSystems,2002.Martietal.Optimalstatefeedbackbasedresourceallocationforresource-constrainedcontroltasks.InRTSS,2004.

Castane etal.Resourcemanagementforcontroltasksbasedonthetransientdynamicsofclosed-loopsystems.InECRTS,2006.Palopoli etal.Real-timecontrolsystemanalysis:anintegratedapproach.InRTSS,2000.

Branicky etal.Schedulingandfeedbackco-designfornetworkedcontrolsystems.InCDC,2002.Kauer etal.Fault-tolerantcontrolsynthesisandverificationofdistributedembeddedsystems.InDATE,2014.

Goswami etal.Relaxingsignaldelayconstraintsindistributedembeddedcontrollers.InIEEETransactionsonControlSystemsTechnology,2014.Soudbakhsh etal.Co-designofcontrolandplatformwithdroppedsignals.InICCPS,2013.

Majumdar etal.Performance-awareschedulersynthesisforcontrolsystems.InEMSOFT,2011.

Yoshimotoetal.Optimalarbitrationofcontroltasksbyjobskippingincyber-physicalsystems.InICCPS,2011.

▪ Alinearsystemisasymptoticallystable ifalltrajectoriesconvergetotheorigin▫ Foranyinitialstate𝑥 𝑘S ,

Stability

𝑥 𝑘 → 0𝑎𝑠𝑘 → ∞

State-awareOnlineScheduling

▪ Whichnon-criticaljobtoexecute?▫ Considercurrentstateerrors

▪ Insteadystate,nobenefitbyexecutinganon-criticaljob▪ Intransientstate,controlperformanceimprovementbyquickreactiontoperturbation

▫ Chooseajobwiththelargesterrorfirst

Time

Transient SteadyOutpu

t

▪ Evaluationcriteria▫ Schedulingperformance(cyberpart)

▪ Thenumberoftasksetsschedulablewithoutlosingstability▫ Controlperformance(physicalpart)

▪ Thesumofperformancemeasuresforcontroltasks

▪ Tasksetgeneration▫ 3controltasks+hardreal-timetasks

Evaluation