Mixed H2/H∞ robust control approach for NCS with uncertainties and data dropouts

MixedH2/H∞robustcontrolapproachfor NCSwith uncertaintiesand datadropouts⋆ I.Jurado,M.G.Ortega and F.R.Rubio Departamento deIngenier´ıa deSistemasyAutom´atica EscuelaSuperiordeIngenieros,Universidad deSevilla Camino delosDescubrimientos s/n-41092 Sevilla(Spain) (e-mail: {ijurado,ortega,rubio}@cartuja.us.es). Abstract:Inthispaper,aRobustNetworkedControlSystem(RNCS)subject todatalosses constraintsisconsidered.Thesedatalossesaremodelledasanindependentsequence ofi.i.d. Bernoulli randomvariable.Thisrandomvariableisreplaced byanadditivenoiseplusa gain, whichisequaltothesuccessfultransmission probabilityinthefeedbackloop.Also,structural uncertaintiesinthemodeloftheplantare considered. Tocopewiththisproblem,amixedH2/H∞controltechniqueisproposedinthiswork.Inthis way,theH2approachisusedtostabilize theNCStakinginto account theprobabilityofdata dropouts,whiletheH∞approachisinchargeofmakingthe closed-loopsystemrobustenough againststructuraluncertaintiesofthenominalmodel. Keywords:Controlundercommunicationconstraints,controland estimationwith dataloss and networkedembeddedcontrolsystems. 1.INTRODUCTION Nowadays,controlsystemswhereinacommunication networkexitsaregettingimportance moreand more.Usually, the communication networkconnects some elementsofthe controlsystem.This kind ofsystemsand theircharacteristicsarewidelydescribedinHespanhaetal. (2007)and Zhangetal. (2001). Therearealotofstudiesintheliteratureabout themain problemsassociatedwithNetworkedControlSystems. Oneoftheseproblemsistherelatedwiththevariable delays inthedatatransmission(see,forexample,Guand Chen(2003)).Onewayto approachthisissueistoresort Lyapunov-Krasovskii functionals(see,forexample,Millan etal. (2010)and Yue etal. (2005)). Anotherimportant topictobestudiedinNCSsisthe network-induced dataloss.This kind ofproblemoccurs whenthe communicationchannel isnotabletotransmit thedata and itgetlost.Thismayoccurs,forinstance, duetocolissionsorlowSNR(signaltonoiseratio).There aredifferentsways todealwiththesekind ofNCSs.One wayistheuseofpredictive control, whichmakespossible tocalculatefuturemodel-based data and tousethemto computethe controlactions.Some examplesofnetwork controlbasedonMPCforlinearand non-linearsystems can befound inZhangetal. (2006),Millanetal. (2008) and inMu˜nozand Christofides(2008). AdifferentwaytodealwithNCSsubject todatadropouts constraintsconsistsinmodelingthedropoutsbymeans ofaswitchedsystem, i.e., aMarkovjumplinearsystem ⋆Theauthorswouldliketo acknowledgeMCyT(GrantDPI201019154.),and theEuropeanCommission(EC) (FeedNetBackProject, grantagreement223866),forfundingthiswork. (MJLS).Relatedwiththisapproach,Ling and Lemmon (2004)presentsaresultwhichshowsthat,foraspecific NCSarchitecturesubject todatadropoutsconstraints,the resultingMJLSisequivalent to a linearsystemwithan externalnoisesource.Thisnoisehastheparticularityof having a variance thatisproportionaltothevariance of anothersignalwithintheinitialcontrol loop.Thisresultis usedin Silvaetal. (2009) toshowthat there exitsasecond ordermomentsequivalence betweenthe consideredNCS and anauxiliarycontrolsystem.Inthisauxiliarycontrol system,theunreliable controlchannelhasbeenreplace by anadditivei.i.d.noise channelthathasaSignaltoNoise Ratio(SNR)constraint.Inthatpaper,theprobabilityof datalossesisafixedvaluethatisusedinthe control synthesis.Theobjectivein Silvaetal. (2009)istominimize the errorcovariance designingthe controllerviaYoula parametrization.However, inthatworkonlyaperfect LTInominalmodel isconsidered,and thereforerobust propertiesarenotguaranteed. Inthispaper,anNCSwhereinacommunicationchannel withadatadropouts source existsisconsidered,aswell as structuraluncertaintiesintheplant.Therefore,the maingoalofthisworkistofind arobustcontrollerfor theplantwith uncertaintiesand with datalossesinthe transmission;alsofinding out theminimalprobabilityof success inthetransmissionsuchthatmeansquarestability (MSS)and robustness propertiescan beguaranteed.A mixedH2/H∞controlapproachisproposedinsuchaway thatbothstructuraluncertaintiesintheplantand data lossescan betolerated. Theremainderofthepaperisorganizedasfollows:In Section2,abriefsummaryofthemixedH2/H∞controlproblemtheoryisexposed.In Section3the control problemtobesolvedispresented.Section4showsthe Proceedings of the 18th World Congress The International Federation of Automatic Control Milano (Italy) August 28 - September 2, 2011 978-3-902661-93-7/11/$20.00 © 2011 IFAC 13269 10.3182/20110828-6-IT-1002.02152 architectureofthe controlscheme.Section5includesthe obtainedresultswithanexample.Finally,Section6draws themainconclusionsofthepaper. 2.MIXEDH2/H∞CONTROLPROBLEM Inthis section,abriefmixedH2/H∞controlapproach isdescribed.Furtherinformationcan befound inZhou etal. (1996)and Doyle etal. (1994).The controlsystem describedinFigure1isconsidered,wherethegeneralized plantP(z)and the controllerC(z)arebothassumed tobereal-rationaland proper.Thesignalsinvolvedin thediagramarethefollowing:w′∈Rm1representsthe disturbance vector,u∈Rm2isthe control input,z∞∈ Rp1and z2∈Rp2arethe errorvectors,thefirstonefor themeasurementoftheH∞performance,and thesecond onefortheH2performance.Themeasurementsuppliedto the controllerisrepresented bym∈Rp3. P(z) C(z) Z Z mu w ∞ 2 Fig.1.MixedH2/H∞synthesis Thesynthesisproblemconsideredinthisapproachconsists in finding a suboptimalLTIcontrollerC(z) thatminimizes thefollowingmixedH2/H∞criterion: MinαkT∞k2 ∞+βkT2k2 2,(1) subject to: • kT∞k∞<γ0 • kT2k2<ν0 whereT∞(z)and T2(z)denotethe closed-looptransfer functionsfromw′toz∞and z2,respectively;and γ0, ν0∈R+. Aswill beshown,theminimizationofkT2k2impliesthe minimizationofthelowerbound ofthesuccess probability inthedatatransmission. Inordertofind outacontrollerbymeansofthiscontrol technique, itisnecessarytoput theoriginalsysteminto theformoftheblockdiagramshowninFigure1.Todo this,theoriginalsystemischangedwithalowerlinear fractionaltransformation. Inthiscase,T∞ischosentorepresentamixed-sensitivity H∞controlproblem,whichiswidelyexplainedin Skogestadand Postlethwaite(1996).Sotwoweightingfunctionsare chosen:Ws(z) toweight thesensitivityfunction S(z)and Wt(z) toweight the complementary sensitivity functionT(z).Theseweightingfunctionsallowtospecify therangeof frequenciesofrelevance forthe corresponding closed-looptransfermatrix.Asitis known,anappropriateshaping ofT(z)isdesirablefortrackingproblems, noiseattenuationand for robuststabilitywithrespect to multiplicativeoutputuncertainties.Ontheotherhand, aconvenientshaping ofS(z)will allowtoimprovethe performance ofthesystem.So,thisapproachisusefulto haveanappropriateperformance ontrackingproblems,as well asforthesystemrobustificationagainstnoisesand uncertainties. 3.PROBLEMDEFINITION ThispaperisfocusedonaRNCSwhereinthemain problemsaretheuncertaintiesinthemodeloftheplant and thepacketsdropouts.So,theaimistodesigna controllerthatstabilize asystemsubject tothesetwo problemstogether. Theuncertaintiesunderconsiderationwill berepresented bythefollowingequation: G∗(z)=G(z)(I+Wm(z)∆(z)), whereG∗(z)representsall thepossibleplants,G(z)is thenominalplantand Wm(z)∆(z)isthemultiplicative uncertainty,withk∆(z)k∞<1. Inthefollowingthewaytodealwiththeinformationlosses ispresented.Afterthat,amorerealistic caseisconsidered includingtheplantuncertainties. Thepacketsdropoutsimplythat thereisan unreliable channel inthefeedbackpath.This situationisillustrated inFigure2,whereG∗(z)istheplant transferfunction, C(z)isthe controller,risthereference and yistheplant output.Therelation betweenthe channel inputvand the channeloutputwis: w(k). =(1−dr(k))v(k),∀k∈N0,∀v(k)∈N,(2) wheredrmodelsdatalosses,sodr(k)∈{0,1}∀k∈N0. C(z)G(z) Wm ∆ + +y G*(z) rmu _ v 1-dr Fig.2.RNCSwith packetsdropouts Thenotionofstabilityusedforthis kind ofsystemsis describedinthefollowingdefinition. Definition1(Meansquarestability)Silvaetal. (2009)Considerasystemdescribed byx(k+1)= f(x(k),w(k)),wherek∈N0,f:Rn×Rm→Rn, x(k)∈Rnisthesystemstateat timeinstantk,x(0)=x0, wherex0isasecond order randomvariable,and theinput wisasecond orderwss process independentofx0.The systemis saidtobemeansquarestable(MSS)ifand only ifthere exitfiniteµ∈Rnand finiteM∈Rn×n,M≥0, suchthat lim k→∞ E{x(k)}=µ, lim k→∞ E{x(k)x(k)T}=M,(3) 18th IFAC World Congress (IFAC'11) Milano (Italy) August 28 - September 2, 2011 13270 regardless oftheinitialstatex0. C(z)G*(z) y rmu _ v q p vp Fig.3.RNCSwith packetsdropouts Theuncertaintieswill beincludedinthesystemgiven bythefollowingtheorem.Thisresultmakespossibleto changetheoriginalsysteminto anotherequivalentone. Theorem1.(Equivalence)Silvaetal. (2009),Ling and Lemmon(2004)ConsiderthefeedbackloopinFigures2 and 3.Itis supossedthatp∈(0,1)and Assumptions1 and 2fromSilvaetal. (2009)hold.Then: (1)Ifthefeedback systemdepictedinFigure2isMSS and thefeedback systeminFigure3isinternally stable,thenthestationaryPSDsofthe error(e. =r− y)and ofall thesignalsintheloopsarethesamein bothsituations. (2)ThenetworkedsysteminFigure2isMSS ifand only ifthefeedbackloopinFigure3isasymptotically stableand p 1−p>kTp(z)k2 2,(4) whereTp(z)isthetransferfunctionfromqtovpin Figure3,namely Tp(z). =−pG∗(z)C(z)(1+pG∗(z)C(z))−1.(5) Proof.Theproofgoesasthesamelinesastheproofsin Ling and Lemmon(2004). Asaconsequence ofTheorem1, itis knownthatstudying theMSS ofthesysteminFigure2isequivalent to achieve thestabilityofthesysteminFigure3while condition(4) holds.Thereby,theproblemcan beposedastofind a controllerC(z) thatstabilizesthesysteminFigure3 and satisfiesthe equation(4),takinginto account that the plantG(z)isthenominalplantmodeland that the closedloopsystem mustberobustagainst theuncertaintiesinthe plantmodel. Asbeforementioned,structuraluncertaintiesaregoingto be consideredinthemodeloftheplantG∗(z).Dueto thisfact,themixedsensitivityapproachwithintheH∞ scopeallowstoimposerobustperformance bymeansof appropriatedesignofweightingfunctions.In particular, itiswell knownthatrobuststabilitycan beimposed byweightingthe complementary sensitivityfunctionif structuralmultiplicativeuncertaintyisconsidered(Ortega and Rubio(2004),Ortega etal. (2006)),whileperformance can beimposed bymeansofareasonableweightonthe sensitivityfunction. Ontheotherhand, itisnecessarythatcondition(4)holds. Then,by solving anH2controlproblemitispossibleto find theminimalprobabilityofsuccess inthetransmission (p).Therefore,bymixingthesetwotechniques,amixed H2/H∞controlproblemisformulated,withthefollowingcostfunctiontominimize:αkT∞k2 ∞+βkT2k2 2,where kT∞k∞includes someweightingfunctionsto achievethe systemrobustificationand kT2k2will bekTp(z)k2,toimpose condition(4). Problem1ConsidertheRNCSinFigure2wherethe plantG(z)hasboundedstructuralmultiplicativeuncertainties.Then,theproblemconsistsin finding a robust controllerC(z),usingtheRNCSinFigure3,thatachieves thefollowingconditions simultaneously: •Minimize kT∞k∞to achievea good performance ontrackingproblemsand thesystemrobustification against theplantuncertainties. •Minimize kT2k2tocalculatetheminimalsuccessful probabilityofdatalossespossiblefortheNCS, imposingcondition(4),sothesystemsintheFigures2 and 3 are equivalents. 4.CONTROLLERDESIGN Inthis sectionthe controllersynthesiswill beperformed by meansofthedescribedmixedH2/H∞controltechnique. Someweightingtransferfunctionswill beintroducedin thesystemtodealwiththeuncertaintiesoftheplant model. TheaugmentedsystemisrepresentedinFigure4. TheweightingtransferfunctionsWs(z)and Wt(z)weight thesensitivityfunction(S(z)) and the complementary sensitivityfunction(T(z)),respectively.Theoutputsof theseweightingtransferfunctionsarethesignalszsand ztrespectively,and theyrepresent the componentsofthe vectorz∞inFigure1. C1(z)G*(z)y rm1 u1 _ v q p Wt(z) Ws(z) m2 u2 z2 zt zs C2(z)Vp _e Fig.4.RNCSand theweightingtransferfunctions Itisimportant tonotethat thesystemunderconsideration(Figure3), isanon-unitaryfeedback system.So, in ordertoeliminatethesteady state errors,atwo-degreesof-freedomcontrollerisproposed.Therefore,the controller will beformed bytwotransferfunctions,C1(z)and C2(z). Also,thesensitivityfunction(S(z)) and the complementary sensitivityfunction(T(z)) expressionswill change. These expressionswill be: S(z)=1+C1(z)G(z) (C2(z)p−1) 1+C1(z)G(z)C2(z)p 18th IFAC World Congress (IFAC'11) Milano (Italy) August 28 - September 2, 2011 13271 T(z)=C1(z)C2(z)G(z)p 1+C1(z)C2(z)G(z)p Thesensitivityfunction(S(z)) representsthetransfer functionfromthereference tothe errorsignal. The complementary sensitivityfunction(T(z)) dependsontheopenlooptransferfunctionofthesystem,whichis:L(z)= C1(z)C2(z)G(z)p,sothe controlsignalu2should bethe inputoftheweightingtransferfunctionWt(z),asitis representedinFigure4. Theobjectivesofthe controllerarethefollowing: (1)Minimize theH∞normofthe closedloopfromthe exogenousdisturbances vectortothevectorz∞. (2)Minimize theH2normofthe closedloopsignalfrom thatvectortothesignalz2. So,asmentioned before,themixedH2/H∞controlproblemwill besolvedtofind asuboptimalcontrollerwhich achievesatrade-offbetweentheminimumofthetwo normsunderconsideration.Tocarryout thesynthesis,the systeminFigure4hastobe expressed,bymeansofalower linearfractionaltransformation,asinFigure1.Itiseasy to see that,byidentifyingtheterms,thefollowingsequations hold: z∞=[zszt]T,w′=[rq]T, P(z)=     Ws(z)0|−Ws(z)G(z)0 0 0 |0Wks(z) 0 0 |pG(z)0 I0|0−I 0I|pG(z)0      Withrespect totheminimization problemin(1),T∞(z) and T2(z)are chosenasfollows: kT2(z)k2=kTp(z)k2 kT∞(z)k∞=   Ws(z)S(z) Wt(z)T(z)   ∞ Theparameterswill be choseninsuchawaythat the condition(4)holds.Thismeansthat: ν0=p 1−p At thispoint, it’sworthmentioningsome commentsin relationtothe choice oftheothersparameters.Itisinterestingtonotethat, ifthepriorityisto achievetheminimal possiblep, itisimportant to obtainacontrollerthat providesanH2normofT2(z)veryclosetoitsminimum. Then,forthiscase,theparameterβshould begreaterthan α.Onthe contrary, iftheinterestliesonachievingthebest performance and robustness againstnoisesand uncertainties, itisbettertochoosetheparameterαgreaterthan β.Thismeansthat theresultingcontrollerwill providea very small H∞normofT∞(z). Theprobabilityofsuccess inthetransmissionpisassumed tobefixedinthe controllersynthesis.Thisispossibleifthe networkrequirementsarewell-known.Inanycase, ifthe valueofpchanges,thestabilityofthe closed-loopsystem isguaranteedifpisgreaterthantheminimalprobability ofsuccess inthetransmissionobtained. 5.NUMERICALRESULTS Toillustratethemethodologyproposedinthispaper, this sectionshowstheobtainedresultswhenthe control strategyisappliedto a particularexample.Inthisexample thefollowingunstablenominalplantwill be considered: G(z)=z−0.5 z(z−1.1) Thesamplingtimewill betm=0.05s. 10−3 10−2 10−1 100101102 −20 −15 −10 −5 0 5 10 15 frecuency (rad/s) Wt , uncertainty (dB) Wt as uncertainty superior limit (dB) Uncertainty 1 Uncertainty 2 WT Fig.5.Uncertaintiesand Wt Totakeinto account theuncertaintiesintheplant,two non-nominalmodelshavebeenalsoconsidered.To obtain thesetwo othermodels,therealplantis supposedtohave unmodelled dynamics,so,highfrequencypolesareinclude. Also a percentageofuncertaintyinthemodelgain has beenconsidered.Fromthesetwosystemsand thenominal plant,themultiplicativeuncertaintiescan be computed. Thefrequencyresponseoftheseuncertaintieshavebeen plottedinFigure5. Fromthisestimationoftheuncertainty,theweighting transferfunctionWt(z)forthe complementary sensitivity functionisdesignedinsuchwaythatitsmodulusmust begreaterthanthemodulusoftheuncertaintiesforall frequency.ThefrequencyresponseofWt(z)hasbeenalso representedinFigure5. By solvingthemixedH2/H∞controlproblemforthis caseusingsomefunctionsoftheµ−AnalysisandSynthesis ToolboxforMatlaband considering a success probability p=0.7,arobustcontrollerisobtainedyieldingthe followingresults: kT∞k∞=0.8441,kT2k2=1.3615 18th IFAC World Congress (IFAC'11) Milano (Italy) August 28 - September 2, 2011 13272 10−3 10−2 10−1 100101102 −70 −60 −50 −40 −30 −20 −10 0 10 frequency (rad/s) gain (dB) Sensibility function and its weight Snominal WS −1 S1 S2 Fig.6.S(z)ofthenominalplantmodeland Ws(z) Thismeansthat thesystemcanaffordasuccess probabilitypequalto orgreaterthan0.65,to guarantee MSS and topreservethedemandedrobustness properties. 10−3 10−2 10−1 100101102 −80 −70 −60 −50 −40 −30 −20 −10 0 10 20 frequency (rad/s) gain (dB) Complementary sensibility function and its weight Tnominal WT −1 T1 T2 Fig.7.T(z)ofthenominalplantmodeland Wt(z) InFigure6thesensitivityfunctionsofthenominaland non-nominalplantsmodelsand theinverseoftheweightingtransferfunctionWs(z)arerepresented.Thisgraphic showshowall thesensitivityfunctions,ofthenominalsystemand systemswith uncertainties,arebelowtheinverse oftheweightingfunctionWs(z).Thisfactindicatesthat theoutputycanfollowthereference rforall theplant modelsunderconsideration,thatis,atrackingproblem can besolvedalthoughtheplantmodel isnotexactly known. Figure7representsthe complementary sensitivityfunctionsofthenominaland non-nominalplantsmodelsand theinverseoftheweightingtransferfunctionWt(z).From thisgraphicitispossibletosee thatall the complementary sensitivityfunctions,ofthenominalsystemand systems with uncertainties,arebelowtheinverseoftheweighting functionWt(z),sotheobtainedcontrollerisrobustagainst theuncertaintiesintheplantmodel. Tocorroboratetheseresults,somesimulationshavebeen carriedoutwiththeproposedexample.Figure8shows howthesystemfollowsthereference withasuccessful transmission probabilityp=0.7,whichisgreaterthanthe minimalpthatcan provideMSS and robustness properties forthis system.Thisgraphicrepresentstheoutputsof the closed-loopsystemwiththenominalplant,withthe plantwiththeuncertainties1 and withtheplantwith theuncertainties2.Theresultsarevery similarbecause therobustness ofthesystem.However,there existsome differencesbetweenthedifferentsoutputs.Forexample, theoutputwiththeuncertainties1hasanovershoot that isgreaterthantheovershootwhenthenominalmodel is used.Withrespect totheoutputwiththeuncertainties2, theovershootisreducedwithrespect theothercases,but thestationaryperformance isworse. 0 5 10 15 20 25 30 35 40 −6 −4 −2 0 2 4 6 Time, t Plant output, y Reference Nominal plant Plant 1 Plant 2 Fig.8.Simulationresultswith p =0.7 Theoutputsofthedifferentsystemsforavalueofp=0.9 areshowninFigure9.Inthiscase,theprobabilityofsuccess inthetransmission hasbeenincreased,althoughthe controllerusedinthesesimulationsistheone calculated forp=0.7.Obviously,theresultsarebetterthaninthe onespresentedinFigure8,but thedifferencesbetween theperformance withthedifferentsystemsisthesame asinthe caseofp=0.7.Also,therearesteady state errorsbecausethe controlleristhe calculatedforp=0.7 sothefeedbackisnon-unitary.Thesesteady state errors mightbeavoid bycalculatingthe controllerusingp=0.9, but theobjectiveistocomparetheresultswiththesame controller,supposingthatphave changedinthenetwork. Finally,Figure10 presentstheoutputsofall thesystems imposingp=0.4,whileusingthesame controllerasinthe precedings simulations.Obviously,theperformancesget worseforall thesystems,and inthe caseoftheplantwith theuncertainties1 and 2,the closed-loopsystembecomes unstable.So,withp=0.4,therobuststabilityislost. 18th IFAC World Congress (IFAC'11) Milano (Italy) August 28 - September 2, 2011 13273 0 5 10 15 20 25 30 35 40 −6 −4 −2 0 2 4 6 Time, t Plant output, y Reference Nominal plant Plant 1 Plant 2 Fig.9.Simulationresultswith p =0.90 0 5 10 15 20 25 30 35 40 −6 −4 −2 0 2 4 6 Time, t Plant output, y Reference Nominal plant Plant 1 Plant 2 Fig.10.Simulationresultswith p =0.40 6.CONCLUSIONS ThepaperhasfocusedonaNCSsubject todatadropouts constraints.In particular,control loopsforSISOLTI plants,wherethefeedbackpathcomprisesacommunicationchannelthatproducesdatalosses,are considered. This systemhasbeenstudiedasanequivalentonewherein theunreliable channelhasbeenreplaced byanadditive i.i.d.noise channel, plusa gain. Theobjectiveofthispaperhasbeenthesynthesisofa controllerthatavoidthemodeluncertaintiesand support thefailedtransmissions.Also,thelowerbound ofthe success probabilityinthetransmission hasbeenfound. Toperformthistask,amixedH2/H∞controlproblem hasbeen proposed.To obtainarobustcontroller,some functionshavebeenchosentoweightsomesensitivityfunctions.Moreover,fromthiscontrolproblem,theminimal successfultransmission probabilityisobtainedsuchthat MSS and robustness propertiesforthe closed-loopsystem areguaranteed. Finally,anexamplehasbeenexposedto obtainsome numericalresultsthatillustratethe closed-loopsystem performance.Thesesimulationresultscorroboratedthat robustperformance isachievedifthesuccessfulprobabilitytransmissionishigherthantheminimumcomputed, whilethedifferents systemsperformancesgetworse,until therobuststabilityislost,asthesuccessfulprobability transmission decreases. ACKNOWLEDGEMENTS Theauthorswouldliketo acknowledgeMCyT(Grant DPI2010-19154.),and theEuropeanCommission(EC) (FeedNetBackProject,grantagreement223866),forfundingthiswork. REFERENCES Doyle,J.C., Zhou,K., Glover,K., and Bodenheimer, B.(1994).Mixedh2and h∞performance objectives ii: optimalcontrol. IEEE TransactionsonAutomatic Control,39(8),1575–1587. Gu,K.and Chen,J.(2003).StabilityofTime-Delay Systems (ControlEngineering).Birkh¨auserBoston. Hespanha,J.P., Naghshtabrizi, P., and Xu,Y.(2007).A surveyofrecentresultsin networkedcontrolsystems. ProceedingsoftheIEEE,95(1),138–162. 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