Robuston oc in upervisor Controof Discrete-Event Systems un,er Partial Observation
Anooshiravan Saboori, Shahin Hashtrudi Zad · 2005
Robust control ofdiscrete events systems havebeenstudied byresearchers. [5]assumesthattheexactmodelofthe Control ofsystems withmodelling uncertainties orvarying plantisnotknown, howeveritisamonga finite setof dynamics isa omplex problem. Oneoftheapproaches to possibilities andfinds necessary andsufficient onditions for dealwithmodelling uncertainty isrobust control inwhichthe theexistence ofa solution fortherobust control problem, control system isdesigned toworkforafamily ofplants.assuming acommondesign specification forallpossible plant Asanexample ofrobust control problem, wemayconsider models. [7]generalizes theresults in[5]byconsidering fault tolerance andrecovery problems. Here, theplant (undernondeterministic generators. [4]considers maximizing theset control) maydevelop afailure andasaresult, itsbehavior ofplants which, undersupervision, satisfy therequirements (model) maychange. Inthis case, thecontrol system maybe oftherobust control problem. [10] generalizes therobust designed sothat itenforces thedesign specifications duringcontrol problem proposed in[4]byadding themaximally thenormal operation andafter thefailure. Theplant modelpermissiveness requirement andalsobyconsidering partial anddesign specifications before andafter failure areingeneral observation. [10]assumes thespecifications areprefix-closed different. Thustheproblem ofcontrol andsupervision inplants languages. In[1], theframework of[5]isgeneralized by subject tofailure canberegarded asarobust control problem. assuming aseparate specification foreachofthepossible plant Forinstance, consider asimple manufacturing plant consisting models. Nonblocking property isconsidered here. However, all oftwomachines MACHI1andMACH2,andabuffer. Each oftheevents areassumed tobeobservable. machine canperform twotypes ofoperation A andB.Inthe normal modeofoperation, MACHI1takes aworkpiece from Inthispaper, we extend theresults of[1](forcontrol aninput conveyor, performs operation A ontheworkpiece and withfullobservation) tothecaseofcontrol underpartial deposits itinthebuffer. MACH2takes aworkpiece fromthe observation. We managetocharacterize thesolutions ofthe buffer, performs operation B onit, anddeposits theworkpiece robust control problem andobtain necessary andsufficient onanoutput conveyor. Thedesign specifications fornormalconditions fortheexistence ofsolution fortherobust control operation arethat thesystem should benonblocking andthatproblem. Thedetails ofourworkarediscussed in[9]. thebuffer should notoverflow orunderflow. IfMACH2 breaks down,since MACH2 isbroken, MACH1 hastodoboth Thispaper isorganized asfollows. Section IIcovers prelimoperationls Aanld B.Therecovery specifications areasfollows, manares fromn supervisory control theory. Setionl IIIdiscusses MACHEIl should first comuplete thewolrkpiece itishalndlilng (ifmnodelklilng alnd plroblemn folrmulatioln. Iln Sectioln IV,wesolLve