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392Vol.39,No.220132ACTAAUTOMATICASINICAFebruary,201312,(Networkedcontrolsystems,NCSs)..,,:,;,;,;,.,,,,,,..,2013,39(2):101¡118DOI10.3724/SP.J.1004.2013.00101SurveyofRecentProgressinNetworkedControlSystemsYOUKe-You1XIELi-Hua2AbstractWiththerapiddevelopmentofsensing,informationprocessing,andcommunicationtechnologies,theresearchintheemergingareaofnetworkedcontrolsystems(NCS)hasattractedconsiderableattentionintheresearchcommunity.Thepurposeofthissurveyistoprovideareviewofstate-of-the-artofsuchresearch.Weparticularlydiscussvariousnetworkconditionsrequiredfordi®erentcontrolpurposes,suchastheminimumratecodingforstabilizabilityoflinearsystemsinthepresenceoftime-varyingchannelcapacity,thecriticalpacketlossrateforthestabilityoftheKalman¯lterwithintermittentobservations,networktopologyforcoordinationofnetworkedmulti-agentsystems,aswellasevent-drivensamplingforenergyandcommunicatione±ciency.Thecommongoalofdiscussiononthesetopicsistorevealthee®ectofthecommunicationnetworkontheoperationofthenetworkedsystems.KeywordsNetworkedcontrolsystems,linearsystems,datarate,packetloss,event-basedcontrol,consensusCitationKe-YouYou,Li-HuaXie.Surveyofrecentprogressinnetworkedcontrolsystems.ActaAutomaticaSinica,2013,39(2):101¡118(Networkedcontrolsystems,NCS),1.,.,NCS.NCS(Microelectromechanicalsystems,2012-10-312012-11-08ManuscriptreceivedOctober31,2012;acceptedNovember8,2012(61120106011)SupportedbyNationalNaturalScienceFoundationofChina(61120106011)RecommendedbyAcademicianHUANGLin1.100084,2.639798,1.DepartmentofAutomation,TsinghuaUniversity,Beijing100084,China2.EXQUISITUS,CentreforE-City,SchoolofElectricalandElectronicEngineering,NanyangTechnologicalUniversity,Singapore639798,SingaporeActaAutomaticaSinica,vol.39,no.2,pp.101¡118,2013.MEMS)[1],.,NCS..1NCSFig.1GeneralNCSarchitectureNCS..,,10239(Communicationdatarate)(Lossychannel).,[2]..1NCS.2NCS,NCS.3.,.,NCS,.4.,,..5,.6.,.7.,.8,.2NCS.,NCS.,NCS.NCSDeviceNet[3],Ethernet[4],FireWire[5].NCS..,,.NCS.,,104»106,BluetoothTMIEEE802.11(b)CAN[1].(),[6].,,,,.(),()[7]().,.,(),.,,,().,,.,(TCP)NCS,..NCS,.350,,[8][9].//.,.,[10].,,.,,.[11].,,.2:103.NCS.,.,(Controllerareanetwork,CAN)(RobertBosch)1983[12].PROFIBUS1987[13].,(Foundation¯eldbus)(DeviceNet).NCS..,CAN.,.,,,..,NCS.NCS.,.,.,,.,(Scalability).(Unmannedaerialvehicles,UAVs).,.,.,NCS...,.,.NCS.44.1NCS2.,n:xk+1=Axk+Buk(1),xk2Rn,uk2Rm,(A;B).2Fig.2QuantizedfeedbackcontrolNCS.,xk.,Qk:Rn!SkxkSksk,.,xk.^xk,.,(),,xk¡^xk6=0.,..,,Sk,;.,..,1956[14].[14],Kalman..,Kalman[14],(Limitcycles)(Chaos).,,[15¡16]..,.,.,,.[17].,.,.,,/10439.,..(Quantizationlevel),,,.,.,[18],½.,Q(¢):½=lim²!0+inf#Q[²]¡ln²,#Q[²]Q(¢)[²;1=²].[19],(Sectorboundmethod).,.,(Absolutestability)[20].,.,,(Practicalstability)[21],..[22¡25].Brockett[25],.,:?,[24;26¡30].,¹kQk,¹kSk.,dlog2¹ke.(R):R=limk!1inf1kkXi=1log2¹i/,,RnXi=1maxf0;log2j¸ijg=H(A)(2),¸1;¢¢¢;¸nA.RH(A),.,H(A),,.,[31].(),(Entropyrate)[32].,H(A),(Topologicalentropy)[33]..,.,,...,,..NCS.,,.,,[34¡41]..4.24.1.,sk..,.,.2005Tatikonda[34],.[34],H(A),[34].[40].,(Erasurechannel),2:105,.[41¡43].,,.,Gilbert-Elliott[44],[45].,°kk.°k=1,,°k=0,./(;F;P).,F¾-,PF.(Pf°k+1=jj°k=ig)i;j2S=1¡qqp1¡p#(3),S=f0;1g.,pq01..,pq.TCP[46],ACK.,.1.limk!1E[kxkk2]=0.,E[¢]P.1[37¡39].°k,p+q=1,(A=¸)E·j¸j222°kR¸1(4)(4).,.j¸j2.,22R,R().,j¸j222°kR,,.,°k=1.(4)Rlog2j¸j.R!1,pj¸j¡2.[47¡50].,,.NCS,{[31](4):E·jdet(Au)j2nu22°kRnu¸1(5),Au2Rnu£nuA.,A().A,.,.,.,A=diagfJ1;¢¢¢;Ju;Asg,AsA,JiA¸iJordan[51].,¸i,Ji=266664¸i1¸i...¸i377775(6)¸i=ai+bii,bi6=0,D(¸i)=aibi¡biai#,:Ji=266664D(¸i)ID(¸i)...D(¸i)377775(7)S=fu1;¢¢¢;usg½f1;¢¢¢;ug,J(S)=diagfJu1;¢¢¢;Jusg,:x(S)k+1=J(S)x(S)k+B(S)u(S)k(8),x(S)kJ(S)().,xk,10639x(S)k.nS=dim(x(S)k),:Ejdet(J(S))j2nS22°kRnS#1;8S½f1;¢¢¢;ug(9),,°k=1,(9)(2).,,.,(),.,\.,.,.,.,,.[37;39;52].,.,.,°k,..,.,k,.,.tkk.t1=inffkjk¸1;°k=1gt2=inffkjkt1;°k=1g...tj=inffkjktj¡1;°k=1g(10),ktk.,tkk.,°0=1t0=0.¿k=tk¡tk¡1,:xtk+1=A¿k+1xtk+eBeUtk(11),eB=[BAB¢¢¢A¿k+1¡1B],eUTk=[uTtk+1¡1¢¢¢uTtk].¿k.1[53].¿k,Pf¿1=ig=(1¡p;i=1pq(1¡q)i¡2;i1.,.2[39].,(A=¸)E·j¸j2¿k22R¸1(12),¿k=1,(12)(2).,p+q=1,(12)(4).,R,.(11),tkR.A¿k.(1),,.,.,.,,,H(A)[34;40¡41].,(Momentstabilization),[36;54].,,.,,Como[55],.[56],,.,,.,.,,{.,[18¡19],,.,,[22].LQRH1[19],,.2:107[57¡62].5,/.,.,..[46;50;63¡72],[47¡48;73¡77]..,:(xk+1=Axk+wkyk=Cxk+vk(13),xk2Rnyk2Rm.wk2Rnvk2Rm,Q0R0.C,rank(C)=m·n.x0^x0P00.,wk;vkx0.yk,3.,.,°kyk.°k.,k,:zk=f°kyk;°kg3Fig.3Networkedestimationcon¯guration,Sinopoli[50](Minimummean-squareerror,MMSE).,,,.,Zk=fz1;¢¢¢;zkgk.MMSE^xkjk=E[xkjZk]^xk+1jk=E[xk+1jZk].Pkjk=E[(xk¡^xkjk)(xk¡^xkjk)TjZk]Pk+1jk=E[(xk+1¡^xk+1jk)(xk+1¡^xk+1jk)TjZk].[50],:^xkjk=^xkjk¡1+°kKk(yk¡C^xkjk¡1)(14)Pkjk=Pkjk¡1¡°kKkCPkjk¡1(15),Kk=Pkjk¡1CT(CPkjk¡1CT+R)¡1.,,^xk+1jk=A^xkjk;Pk+1jk=APkjkAT+Q^x0j¡1=¹x0,P0j¡1=P0.,.,.Pk=Pkjk¡1,PkPk+1=APkAT+Q¡°kAPkCT(CPkCT+R)¡1CPkAT(16),Pk.(16)Pk,Pk.[75],P(Pk·M)(PkM).Pk.,,,[75].[77].,[72].,,.,Pk,:supk2NE[Pk]11,°k.[78],k2N°k=1.(C;A).°k,(16).,°kPk.°k=0,(16).A,.,°k=1(C;A),.Pk,°k.,.,°k,p=1¡E[°k].,,,Pk.1¹Pk2N,E[Pk]·¹P.10839,?.3[46;50].(A;Q1=2),(C;A),A,pc2(0;1):1)pc·p·1,9P0¸0,limk!1E[Pk]=1;2)0·ppc8P0¸0,supk2NE[Pk]·MP0.,