CODIAGNOSABILITY OF NETWORKED DISCRETE EVENT SYSTEMS WITH TIMING STRUCTURE. Gustavo da Silva Viana

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1 CODIAGNOSABILITY OF NETWORKED DISCRETE EVENT SYSTEMS WITH TIMING STRUCTURE Gustvo d Silv Vin Tese de Doutordo presentd o Progrm de Pós-grdução em Engenhri Elétri, COPPE, d Universidde Federl do Rio de Jneiro, omo prte dos requisitos neessários à otenção do título de Doutor em Engenhri Elétri. Orientdor: João Crlos dos Sntos Bsilio Rio de Jneiro Fevereiro de 2018

2 CODIAGNOSABILITY OF NETWORKED DISCRETE EVENT SYSTEMS WITH TIMING STRUCTURE Gustvo d Silv Vin TESE SUBMETIDA AO CORPO DOCENTE DO INSTITUTO ALBERTO LUIZ COIMBRA DE PÓS-GRADUAÇÃO E PESQUISA DE ENGENHARIA (COPPE) DA UNIVERSIDADE FEDERAL DO RIO DE JANEIRO COMO PARTE DOS REQUISITOS NECESSÁRIOS PARA A OBTENÇÃO DO GRAU DE DOUTOR EM CIÊNCIAS EM ENGENHARIA ELÉTRICA. Exmind por: Prof. João Crlos dos Sntos Bsilio, Ph.D. Prof. Lilin Kwkmi Crvlho, D.S. Prof. Antônio Edurdo Crrilho d Cunh, D.Eng. Prof. Crlos Andrey Mi, D.S. Prof. José Reinldo Silv, D.S. RIO DE JANEIRO, RJ BRASIL FEVEREIRO DE 2018

3 Vin, Gustvo d Silv Codignosility of Networked Disrete Event Systems with Timing Struture/Gustvo d Silv Vin. Rio de Jneiro: UFRJ/COPPE, XIV, 147 p.: il.; 29, 7m. Orientdor: João Crlos dos Sntos Bsilio Tese (doutordo) UFRJ/COPPE/Progrm de Engenhri Elétri, Referênis Biliográfis: p Disrete event systems. 2. Networked systems. 3. Fult dignosis. I. Bsilio, João Crlos dos Sntos. II. Universidde Federl do Rio de Jneiro, COPPE, Progrm de Engenhri Elétri. III. Título. iii

4 Thus fr the Lord hs helped us. (1 Smuel 7:12) iv

5 Aknowledgments First, I will give thnks to you, Lord, with ll my hert; I will tell of ll your wonderful deeds. I thnk my mother nd grndmother for my edution, ptiene nd the support every time. I ould not hve hieved my D.S. degree without them. I deeply thnk my dvisor João Crlos Bsilio for your ptiene nd dedition to teh me. I would like to thnk Prof. Lilin Kwkmi Crvlho for the support nd the help during my postgrdute ourses. A speil thnk to my friend Mros Viniius for our nie disussions regrding our dotorl theses. I thnk the friends of Lortory of Control nd Automtion (LCA), speilly, Prof. Mros Viente Moreir, Felipe Crl, Crlos Edurdo, Antonio Gonzlez, Ingrid Antunes, Rphel Brelos, Alexndre Gomes, Julino Freire, Púlio Lim, Tigo Frnç nd Wesley Silveir. I thnk the Ntionl Counil for Sientifi nd Tehnologil Development (CNPq) for the finnil support. v

6 Resumo d Tese presentd à COPPE/UFRJ omo prte dos requisitos neessários pr otenção do gru de Doutor em Ciênis (D.S.) CODIAGNOSTICABILIDADE DE SISTEMAS A EVENTOS DISCRETOS EM REDE COM ESTRUTURA TEMPORIZADA Gustvo d Silv Vin Fevereiro/2018 Orientdor: João Crlos dos Sntos Bsilio Progrm: Engenhri Elétri Consider-se, neste trlho, o prolem d odignostiilidde de sistems disretos de eventos em rede om estrutur de temporizção (NDESWTS) sujeitos trsos e perds de oservções de eventos entre os lois de medição e dignostidores lois e, pr esse propósito, present-se um novo modelo om temporizção que represent o omportmento dinâmio d plnt om se no onheimento prévio do tempo mínimo de dispro pr d trnsição e dos trsos máximos nos nis de omunição que onetm LM e DL. Em seguid, onverte-se o modelo temporizdo em um não temporizdo e diion-se possíveis perds intermitentes de potes n rede de omunição. Com se nesse modelo não temporizdo, ondições neessáris e sufiientes pr odignosilidde de NDESWTS são presentds e dois testes pr su verifição são propostos: um utilizndo dignostidores e outro que utiliz verifidores. Um outro tópio de pesquis orddo neste trlho é o álulo d τ-odignostiilidde (tempo máximo pr dignostir um oorrêni de flh) e K-odignostiilidde (número máximo de eventos pr dignostir um oorrêni de flh) tmém usndo dignostidores e verifidores. vi

7 Astrt of Thesis presented to COPPE/UFRJ s prtil fulfillment of the requirements for the degree of Dotor of Siene (D.S.) CODIAGNOSABILITY OF NETWORKED DISCRETE EVENT SYSTEMS WITH TIMING STRUCTURE Gustvo d Silv Vin Advisor: João Crlos dos Sntos Bsilio Ferury/2018 Deprtment: Eletril Engineering We ddress, in this work, the prolem of odignosility of networked disrete event systems with timing struture (NDESWTS) sujet to delys nd loss of oservtions of events etween the mesurement sites (MS) nd lol dignosers (LD). To this end, we first introdue new timed model tht represents the dynmi ehvior of the plnt sed on the, priori, knowledge of the miniml firing time for eh trnsition of the plnt nd on the mximl delys in the ommunition hnnels tht onnet MS nd LD. We then onvert this timed model into n equivlent untimed one, nd dd possile intermittent pket loss in the ommunition network. Bsed on this untimed model, we present neessry nd suffiient onditions for NDESWTS odignosility nd propose two tests for its verifition: one tht deploys dignosers nd nother one tht uses verifiers. Another topi ddressed in this work is the omputtion of τ-odignosility (mximl time to dignose filure ourrene) nd K-odignosility (mximl numer of event ourrenes neessry to dignose filure). To this end, we propose two tests: (i) one test sed on dignoser-like tht does not require usul ssumptions on lnguge liveness nd nonexistene of unoservle yles nd (ii) nother one sed on the extended verifier tht shows not only the miguous pths ut lso those pths tht led to lnguge dignosis. vii

8 Contents List of Figures List of Tles x xiv 1 Introdution Filure Dignosis nd Computtion of τ- nd K-Codignosility Disrete Event Systems Sujet to Communition Delys nd Losses Contriutions of the Thesis Thesis Orgniztion Fundmentls of Disrete Event Systems nd Filure Dignosis Disrete Event Systems Lnguges Opertions on Lnguges Automt Opertions on Automt Nondeterministi Automt Deterministi Automt With Unoservle Events Strongly Conneted Components Disrete Event Systems Sujet to Loss of Oservtions Filure Dignosis of Disrete Event Systems Centrlized Dignosis Deentrlized Dignosis Conluding Remrks viii

9 3 Codignosility of Disrete Event Systems Revisited: A New Neessry nd Suffiient Condition nd Its Applitions A New Dignoser-Bsed Test for Codignosility Verifition Extending Verifiers to Show All Dignosis Pths Applition of the Proposed Approh to τ- nd K-Codignosility Anlysis Brief Review on Weighted Automton τ-codignosility Anlysis K-Codignosility Anlysis Conluding Remrks Codignosility of Networked Disrete Event Systems With Timing Struture Prolem Formultion Modeling of NDESWTS An Equivlent Untimed Model of NDESWTS Sujet to Communition Delys Only An Equivlent Untimed Model of NDESWTS Sujet to Communition Delys nd Intermittent Loss of Oservtions NDESWTS Codignosility NDESWTS Dignoser NDESWTS Verifier Conluding Remrks Conlusion 135 Biliogrphy 138 ix

10 List of Figures 1.1 Comprison mong different networked DES in the literture regrding the lotion of the ommunition hnnels sujet to delys, the numer of ommunition hnnels of ommunition delys (nd dely effets), nd the formlism used to mesure ommunition delys Automton G 1 of Exmple Automton G (); A(G) (); CoA(G) (), nd; T rim(g) (d) Automton G 2 of Exmple Automton G 1 G 2 of Exmple Automton G 1 G 2 of Exmple Automton G nd of Exmple Automton G of Exmple Automton Os(G, Σ o ) of Exmple Automton G of Exmple 2.9 (); utomton G of Exmple 2.9 () Lel utomton A l Automt G (); G l () nd Dignoser utomton G d () of Exmple Automt G () nd G d () of Exmple Automton G of Exmple Automton G d of Exmple Coordinted deentrlized rhiteture Automton G of Exmple Automt G d1 (); G d2 (); nd G d () of Exmple Automton G test = G d1 G d2 G d of Exmple Automton A N x

11 2.20 Automt G () nd G N () of Exmple Automt G l () nd G F () of Exmple Automt G N,1 () nd G N,2 () of Exmple Automton G V of Exmple Automt G (); G l () nd Dignoser utomton G d () of Exmple 2.10, whih re onsidered gin in Exmple Automton G s of Exmple Automt G () nd G d () of Exmple 2.11, whih re onsidered gin in Exmple Automton G s of Exmple Automton G of Exmple 2.12 onsidered gin in Exmple Automton G d of Exmple 2.12 (without hidden yles) Automton G s Plnt G (); dignoser G d1, for Σ o1 = {, } () nd dignoser utomton G d2, for Σ o2 = {, } () of Exmple Dignoser utomt G s1 = G d1 G l of Exmple Dignoser utomt G s2 = G d2 G l of Exmple Dignoser utomton G 2 s = G d1 G d2 G l of Exmple Plnt G of Exmple 3.4, whih is onsidered gin in Exmple Automt G N,1 (); G N,2 () nd G F (); of Exmple Automt G V (); nd G V T () of Exmple Weighted utomton G Weighted utomton G Weighted utomton G 1 fter topologil ordering Zero-weight yle utomton G 2 () nd yli time-weighted utomton G 3 () Weighted utomt: G d1 (); G d2 (); G l () nd Gs 2 (d) Weighted utomton G df of Exmple Weighted utomton G Vf Weighted utomton G df of Exmple Weighted utomton G Vf of Exmple xi

12 4.1 NDESWTS rhiteture NDESWTS = (G, t min, T ) for Exmple 4.1: ommunition dely struture () nd utomton G with miniml time funtion t min () Time line fter ourrene of events nd, in tre s 1 = σ f p, where p N Time line fter ourrene of event nd two events, in tre s 2 = q, where q N NDESWTS = (G, t min, T ) for Exmple 4.1, where ommunition dely struture () nd utomton G with miniml time funtion t min (), whih is onsidered gin in Exmple Exmple of stte of utomton G i NDESWTS = (G, t min, T ) for Exmples 4.1 nd 4.2, where ommunition dely struture () nd utomton G with miniml time funtion t min (), whih is onsidered gin in Exmple Exmple of utomton G 1 of Exmple NDESWTS = (G, t min, T ) for Exmples , where ommunition dely struture () nd utomton G with miniml time funtion t min (), whih is onsidered gin in Exmple Exmple of utomton G 1 of Exmple Automton G l1 of Exmple Automton G d1 of Exmple Automton G s1 of Exmple Automton G l 1 of Exmple Automton G d 1 of Exmple A pth of utomton G s 1 of Exmple 4.5 tht ontins strongly onneted omponent where x d is unertin nd x l is n Y-leled stte Hypothetil tres of G s1 (); G s2 () nd G s1 G s2 () NDESWTS = (G, t min, T ) for Exmple 4.6: ommunition dely struture () nd utomton G with miniml time funtion t min () Automton G 1 of Exmple Automton G 2 of Exmple xii

13 4.21 Automton G 1 of Exmple Automton G 2 of Exmple Automton G l 1 of Exmple Automton G l 2 of Exmple Automton G d 1 of Exmple Automton G d 2 of Exmple Pths tht reh strongly onneted omponents with mrked sttes in G s 1 of Exmple 4.6, where s 11, s 12 L(G s1 ) Pths tht reh strongly onneted omponents with mrked sttes in G s 2 of Exmple 4.6, where s 21, s 22 L(G s2 ) Pths tht reh strongly onneted omponents with mrked sttes of G NET s of Exmple 4.6, where s NET1, s NET2 L(G NET s ) Automton G 1,ρ of Exmple Automton G 1,F of Exmple Automton G 2,ρ of Exmple Automton G 2,F of Exmple Pth of V 1 with yli pth l 1 () nd pth of V 2 with yli pth l 2 () Pth of V with yle pth l Exmple xiii

14 List of Tles 3.1 Step 4 of Algorithm 3.4 to Exmple Computtionl omplexity of Algorithm Computtionl omplexity of Algorithm Renming sttes of G 1 nd G 2 of Exmple Computtionl omplexity of Algorithm Computtionl omplexity of Algorithm xiv

15 Chpter 1 Introdution In reent yers, new hllenges to mke prodution proesses more effiient, utonomous nd ustomizle hve led to new industril revolution. A new onept of industry, lled Industry 4.0 [1, 2], hs emerged nd is urrently dopted to denominte the urrent trend of utomtion nd dt exhnge in mnufturing tehnologies y reting smrt ftory [3]. One of the fundmentls of Industry 4.0 is the Cyer-Physil systems (CPS) [4 7]. CPS n e regrded s mehnism tht is ontrolled or monitored y omputer-sed lgorithms, tightly integrted with the Internet nd its users. Exmples of CPS inlude smrt grid, utonomous utomoile systems, proess ontrol systems, rootis systems nd mnufturing systems. An importnt lss of Cyer-Physil systems is lled Disrete Event Systems (DES) [8 12], whih re event-driven dynmi systems, with disrete stte spes. Suh systems rise in vriety of ontexts rnging from omputer opertion systems to the ontrol nd monitoring of lrge sle omplex proesses. Severl prolems in the literture hve een solved y using DES modeling tools; mong them, we mention: supervisory ontrol [8, 11, 13], opity [14, 15], detetility [16], prognosis [17], filure dignosis [18 22], nd mny other topis. In order to supply the demnd for interonneted devies, ommunition networks re more widely used in engineering systems [23, 24], sine devies re usully positioned fr wy from eh other in distriuted system. Although there re enefits, the use of ommunition networks hve introdued prolems suh s ommunition delys nd loss of informtion [25,26]. Time delys ome from om- 1

16 puttion time required for oding physil signls, ommunition proessing nd network trffi time, while losses of informtion ome minly from the limited memory in the devies, network trffi ongestion in the network nd drop out pkets. In order to del with these prolems, some relevnt theoretil pprohes hve een onsidered in the literture, regrding supervisory ontrol [27 39] nd filure dignosis [40 43] of networked disrete event systems. We ddress, in this thesis, the prolem of filure dignosis of DES sujet to delys nd losses in the trnsmission of oserved events from mesurement sites (MS) to lol dignosers (LD). Suh filure dignosis prolem is referred, in the literture to s odignosility of networked disrete event systems [42, 43]. In ddition, we revisit the odignosility of disrete event system prolem in order to provide some ontriutions s follows. The verifition of dignosility of disrete event systems y using dignoser proposed y SAMPATH et l. [19] nd the verifition of deentrlized dignosility (odignosility) of disrete event systems y using dignoser DEBOUK et l. [21] hve some drwks, sine the uthors ssume lnguge liveness nd nonexistene of unoservle yles of sttes onneted with unoservle events only. To overome these limittions, we propose new lgorithm to hek odignosility y hnging the dignoser struture so s to onsider oth oservle nd unoservle events, therefore, removing the ssumptions imposed in [19, 21]. Regrding odignosility verifition of disrete event systems y using verifiers [44 47], MOREIRA et l. [47] proposed verifier whose lnguge stops just efore the lnguge eomes dignosle. As onsequene, the event tht removes the miguity is not shown in the verifier. We propose here n lgorithm to extend the verifier utomton proposed in [47] to show the omplete pths tht led to the filure dignosis. As n pplition of these lgorithms, we ompute y mens of weighted utomton formlism [48, 49] the mximum time tht the dignosis system tkes to detet the filure ourrene (τ-odignosility) nd the mximum numer of events tht our fter the filure ourrene until the dignosis system eomes sure of the filure ourrene (K-odignosility). 2

17 1.1 Filure Dignosis nd Computtion of τ- nd K-Codignosility Filure detetion nd isoltion hs reeived lot of ttention in reent yers nd hs eome well-estlished re of reserh [18 22,44 47,50 56]. A filure is defined to e ny devition of system from its norml or intended ehvior. Dignosis is the proess of deteting n normlity in the system ehvior nd isolting the use or the soure of this normlity. Filures in industril systems ould rise from severl soures suh s design errors, equipment mlfuntions, opertor mistkes, nd so on. In the design of filure dignosis system for DES, the first step is to hek whether the lnguge generted y n utomton is dignosle, i.e., whether the system is le to dignose the filure ourrene in finite numer of events ourrenes. Severl pprohes hve een proposed in the DES literture to hek this property using dignoser or verifier. A dignoser is n utomton whose sttes re sets formed with the sttes of the utomton tht models the plnt together with lels tht indite if the tre ourred so fr possesses or not the fult event. An dvntge of dignosers is tht they n e used for oth on-line nd off-line purposes. Verifiers hve een proposed in [44 47], nd re, widely speking, otined y performing prllel omposition etween the filure system ehvior nd the system ehvior without filure. The disdvntge of verifiers is tht they re suitle only off-line verifition purposes. It is well known tht dignosers hve, in the worst se, exponentil omplexity in the plnt stte-spe s opposed to verifiers tht hve polynomil omputtionl omplexity in the numer of the sttes of the utomton tht genertes the lnguge [44 47]. However, it hs een reently onjetured in [57], sed on experimentl evidenes, tht the dignosers uilt in ordne with [19] hve stte size Θ(n 0.77 log k+0.63 ), on the verge, where k (resp. n) is the numer of events (resp. sttes) of the plnt utomton. This result is enourging in the sense tht it mkes dignosers vile tool for dignosility nlysis s well. However, dignosility nlysis using dignosers still requires the serh for yles whih hs omputtion omplexity worse thn exponentil [58], s opposed to dignosility nlysis using verifiers tht requires the serh for strongly onneted 3

18 omponents, whih is liner in the numer of utomton trnsitions [59, 60]. Although the dignosis of filure is n importnt issue regrding sfety of industril utomtion systems, it is lso importnt to know how long the dignosis system tkes to detet the filure ourrene (τ-odignosility), or, in the ontext of disrete event system models, how mny events must our fter the ourrene of the filure event in order for the dignosis system to e sure of its ourrene (K-odignosility). In order to ddress these onerns, we need to nlyze the dignoser hrteristis. Notie tht the dignoser proposed y [19] provides informtion on the filure ourrene sed solely on oservle events, i.e., those events whose ourrene n e reorded y sensors. Therefore, when dignosers re used offline to predit the time spent to dignose the filure, it is not possile to tke into ount the time intervl etween ourrenes of oservle events tht hve unoservle events in-etween. Another spet regrding dignosis is tht liveness nd nonexistene of unoservle yles in the plnt utomton re tully ssumed for oth dignosility nd odignosility verifition using SAMPATH et l. s nd DEBOUK et l. s dignosers. For this reson, K-dignosility ws defined y [19] nd [22] s the numer of oservle events tht must our fter the filure ourrene in order for the dignoser to e sure out the filure ourrene. We remove here ll of these ssumptions nd propose dignoser-sed test tht lso tkes into ount unoservle events nd does not require the serh for yles, ut for strongly onneted omponents. In this thesis, we hnge the dignoser struture so s to onsider oth oservle nd unoservle events. The min dvntges of the pproh proposed here re s follows: (i) dignosility verifition eomes prtiulr se of odignosility verifition s opposed to [19] nd [21], whih requires two different tests for dignosility nd odignosility; (ii) it does not require the usul ssumptions on lnguge liveness nd non-existene of yles of sttes onneted with unoservle events [19,21,54]; (iii) it is sed on the serh for strongly onneted omponents, s opposed to yles in the usul tests using dignosers [19,21,54] ; (iv) we n ddress τ-odignosility y dding weights ssoited with trnsitions of the utomton, forming, therefore, the so-lled weighted utomton. It is worth remrking tht weighted utomt hve only een employed for performne mesure 4

19 in the ontext of supervisory ontrol of disrete event system. Thus, the pproh proposed here redues to the step ounting y repling ll trnsition weights with unity weight, nd therefore, K-odignosility nlysis eomes prtiulr se of τ-odignosility. We now present rief omprison etween the methods proposed here to ompute τ- nd K-odignosility nd those found in the literture. QIU nd KUMAR proposed in [45] n lgorithm to ompute the mximum dely of odignosility using verifier, lso proposed in [45]. However, the proposed pproh nnot e extended to τ-odignosility sine the vlue of K is omputed y dding 1 to the longest tre of the verifier deployed in [45] euse the next event, i.e., the event tht removes the miguity is not shown in the verifier; therefore it is not possile to tke into ount its time in the omputtion of τ-odignosility. TOMOLA et l. [61] proposed n lgorithm for the omputtion of the dely ound for roust disjuntive deentrlized dignosis sed on the lgorithm for the omputtion of the dely ound in the non-roust se using the verifier utomton proposed in [47]. Like the strtegy developed in [45], the extension to τ-dignosility is not strightforwrd. YOO nd GARCIA [62] proposed n lgorithm to ompute K-dignosility (referred there to s fult detetion dely) using verifier similr to F i -verifier proposed in [46], whih n hve yles, ut those yles hve zero weight. As in the previous ppers, it is not ler how to extend the pproh proposed in [62] to K- nd τ-odignosility. VIANA et l. [63] proposed n lgorithm to ompute τ-dignosility, whih is prtiulr se using of the dignoser developed in this work for odignosility, nd ompute the mximum time for filure dignosis y using mx-plus mtrix representtion for the time-weighted utomt [49]. The omputtionl omplexity of the pproh proposed in [63] is, however, worse thn oth methods presented here. More reently K- nd τ-dignosility were ddressed y BASILE et l. [64] for leled Timed Petri nets, using the entrlized dignoser proposed in [19]. As onsequene: (i) it is, in the worst se, exponentil in the rdinlity of the stte spe of the system model; (ii) it requires the usul ssumptions on lnguge liveness 5

20 nd nonexistene of unoservle yles of sttes onneted with unoservle events only; (iii) it is sed on the serh for yles, nd; (iv) K-dignosility is defined tking into ount oservle events only [22]. An importnt work on τ- nd K-odignosility ws presented y CASSEZ [65], in whih the uthor pprohes the deentrlized filure dignosis prolem for disrete event systems modeled y finite utomt (FA) nd, timed systems modeled y timed utomt (TA) [66]. For FA (resp. TA), he omputes the mximum numer of steps (resp. the mximum dely), oth denoted s, tht re neessry for the detetion of the filure ourrene. As fr s τ-odignosility is onerned, the pproh presented here is lso different from [65, 67, 68]. In [67], Wonhm s timed disrete event model [69] is deployed, nd sixth order polynomil lgorithm in the size of the stte spe of the utomton tht models the plnt ws proposed to verify nd ompute the mximum dely for filure dignosis, wheres in [65, 68], dignosility is defined using Alur & Dill timed utomton model [66,70]. Here, we pproh τ-odignosility y using weighted utomt, whih nnot e inluded in the lss of timed utomt, lthough they rry informtion on the mximum time etween event ourrenes, whih mkes them suitle to e used s performne index. Therefore, in this regrd, the work developed here nd CASSEZ s work re inomprle. Regrding K-odignosility nlysis, the omputtionl omplexity of the lgorithm proposed y CASSEZ in [65] depends on the omplexity of the verifier utomton used, nd on the omplexity of performing the serh for the longest filure tre, whih is qudrti in the numer of trnsitions of the verifier, sine inry serh is used. Here, we propose polynomil time lgorithm sed on n extension of the verifier utomton presented in [47], whih hs the smllest omputtionl omplexity mong ll verifiers presented in the literture [71], nd whose serh lgorithm is liner in the numer of trnsitions of the verifier; therefore, the lgorithm proposed here to ompute K-odignosility is more effiient thn tht proposed in [65]. A omprison etween the omputtionl omplexity of the lgorithm proposed in [65] nd the lgorithm proposed in this thesis is presented in Chpter 3. 6

21 1.2 Disrete Event Systems Sujet to Communition Delys nd Losses Most of the works in the re of filure dignosis of DES ssume tht ll informtion is sent to the dignoser in semless nd immedite mnner [19,21]. However, due to the omplexity of the plnts, dignosers re often implemented in distriuted wy nd, onsequently, with the development of network tehnology, it hs eome more nd more ommon in industry, ommunition system implementtions y using shred ommunition networks [34]. In dignosis systems sed on ommunition networks, the intense dt trffi in ommunition hnnels, or the long distne etween mesurement sites nd dignosers, my dely the informtion ommunited through the hnnel. Thus, the dignoser n oserve events with some dely fter its ourrene, nd lso, when multiple ommunition hnnels re deployed, in order different from their ourrene in the plnt; thus, eing led to mke wrong deisions regrding filure ourrene. In ddition, in the sending of informtion, losses my our. The prolem of filure dignosis of DES with delys in ommunition networks ws first ddressed y DEBOUK et l. [40] nd QIU nd KUMAR [41]. However, the prolem ddressed in this work is different from [40, 41]. First, the prolem of deentrlized filure dignosis proposed in [40] is sujet to ommunition delys etween lol dignosers nd the oordintor, under Protools 1 nd 2 of [21]. A key feture of Protool 1 studied in [21] is the following: under the ssumption tht ll ommunited messges re reeived in the orret order y the oordintor, the oordintor is ple of trking the stte of the system s well s entrlized dignoser, even though it does not hve ny knowledge of dynmis of the system. Protool 2 studied in [21] is the following: if the system hs no filure miguous tres (Definition 18 in [21]), nd if the ommunited messges re reeived in the orret order y the oordintor, the oordintor n identify extly the sme filure types s the entrlized dignoser even when the ommunition etween lol sites nd the oordintion is not ontinuous. In [40], it is ssumed tht the events reeived y the oordintor n e oserved in different order from the originl order of ourrene; however, no dely etween the mesurement sites nd 7

22 the dignoser. Here we onsider Protool 3 of [21], sine we del with ommunition delys etween the mesurement sites nd the lol dignosers. Finite delys in the ommunition etween lol dignosers nd oordintor re not ssumed here sine they do not ffet the dignosis deision. The prolem proposed in this work is lso different from the so-lled distriuted dignosis sheme proposed in [41], where eh lol dignoser n exhnge informtion with the other lol dignosers to infer the filure event ourrene. In ddition, in [41] the ommunition dely etween two lol dignosers is onsidered equl, nd it is ssumed tht there is no dely etween the mesurement sites nd dignosers. The prolem of DES sujet to unrelile oservtions of events ws ddressed in [54] nd [61] (in the ontext of filure dignosis) without onsidering ommunition networks. In this work, we model the loss of oservtion sed on the tehnique proposed y CARVALHO et l. in [54] In [42, 43], the definition of network odignosility of DES sujet to event ommunition delys ws introdued, where the onept of step [33, 35] ws used to mesure ommunition delys, i.e., k N steps ounts for the ourrene of, t most, k events until the informtion of the event exeuted y the plnt rrives t the lol dignoser. In this thesis, we propose new pproh lled networked disrete event systems with timing struture (NDESWTS) y dding two prmeters to the utomton tht models the system ehvior s follows: (i) the mximl time ommunition delys etween the distriuted mesurement sites in the plnt nd the lol dignosers; (ii) miniml time funtion tht is ssoited with eh plnt utomton trnsition, whih orresponds to the miniml time the system must remin in the stte efore the trnsition n fire. Regrding the modeling of the oservtion of the events y lol dignoser sujet to dely nd losses, NUNES et l. [42, 43] rried out it in two steps s follows: in first step, n utomton tht model the effets of the delys is proposed; in the seond step, the utomton tht models the oservtion of the events y lol dignoser is omputed y performing the prllel omposition etween the utomton otined in the previous step nd the utomton tht models the plnt. In this thesis, we propose n lgorithm to onsider the models the oservtion of the events y lol dignoser sujet to dely nd losses without this intermedite step. To this end, we onvert the 8

23 new timed model tht represents the dynmi system ehvior of the plnt into n untimed one, nd dd possile intermittent pket loss in the ommunition network. We hek odignosility of NDESWTS proposed here y developing two lgorithms: one sed on dignosers nd nother sed on verifiers. We remrk tht the Timed Disrete Event System (TDES) model proposed y BRANDIN nd WONHAM in [69], tht introdues one dditionl event lled tik to represent tik of glol lok, ould lso e used. The uthors in [72 74] hve ddressed untimed model to del with ommunition delys y introduing tik events in the plnt to represent lok yle. The min limittion of tht pproh is when the system hs fr prt temporl hrteristis sine due to the fst system ehvior, the tik will e ssoited with smll time intervl, nd, s onsequene, the orresponding untimed model my hve lrge numer of sttes to represent slow dynmis in the model. Regrding models to represent time informtion, timed utomt [65, 66, 68, 70] ould lso e n option to model the time informtion. Timed utomt provide wy to model the ehvior of rel-time systems over time y using stte-trnsition grphs with timing onstrints using finitely mny rel-vlued loks. However, the ost to otin the ehvior of rel-time systems over time mkes this formlism more omplited to model nd nlyze. Indeed, the onstrution of region grph to reognize untimed lnguge of timed utomt is O( L ft( X ) 2 X K X ), where L is the numer of lotions (sttes), X is the numer of loks, K is the lrge onstnt used in timed utomt, nd f t( X ) denotes the ftoril of the rdinlity of X [65]. Thus, the doption of this formlism implies unneessry omputtionl effort to the gol of this work. It is importnt to remrk tht the prolem of ommunition delys hs lso een ddressed in the ontext of supervisory ontrol of DES y [27, 30, 32, 33, 35], for the monolithi se, nd y PARK nd CHO [31], nd [34] for the deentrlized nd distriuted se. In the forementioned works, it is ssumed tht there is only one ommunition hnnel etween the plnt nd supervisor, nd, thus, no hnge in the order of event oservtions y the supervisor ours. Sine odignosility is not time ritil, i.e., the dignoser n detet the fult fter n ritrrily lrge numer of event ourrenes, ounded ommunition delys tht nnot hnge the order of event oservtion re not importnt in the ontext of filure dignosis. We 9

24 here onsider deentrlized dignosis of NDESWTS ssuming tht ommunition delys n e lrge enough tht it n modify the order of oservtion of the events reeived y the lol dignosers. Still in the ontext of supervisory ontrol, TRI- PAKIS [28] nd SADID et l. [29] ssume tht ommunition delys my hnge the order of event oservtion. One importnt restrition of these pprohes is tht the sme dely upper ound is ssumed for ll ommunition hnnels. In ddition, SADID et l. restrits the prolem to those systems whose utomton models hve no loops of ommunition events (events tht re sujet to ommunition delys) in the originl system. None of these ssumptions re mde here. 1.3 Contriutions of the Thesis In this thesis, we ddress the prolem of odignosility of networked disrete event systems with timing struture (NDESWTS) sujet to delys nd losses of oservtions of events etween the mesurement sites (MS) nd lol dignosers (LD). We introdue new timed model tht represents the dynmi system ehvior of the plnt sed on the, priori, knowledge of the miniml firing time for eh trnsition of the plnt nd on the mximl delys in the event oservtion fter it is reorded in the MS. In order to void using the onept of step [33,42,43] or the TDES [69], we model the onsequenes of ommunition delys of the oservtions reeived y the lol dignoser y diretly pplying the time informtion. To this end, we onvert this timed model in n untimed one, nd dd possile intermittent pket loss in the ommunition network. Bsed on this untimed model, we present neessry nd suffiient onditions for NDESWTS odignosility nd propose two tests for its verifition: one tht deploys dignosers nd nother one tht uses verifiers. NDESWTS model proposed here is suffiiently generl to ddress prolems of other reserh res suh s supervisory ontrol of networked disrete event systems [38, 39]. In order to estlish omprison etween the pproh presented here nd others previously presented in the literture, we shown in Figure 1.1 the min differenes etween the pproh presented here nd previous works regrding the lotion of the ommunition hnnels sujet to delys, the numer of ommu- 10

25 Lotion of ommunition hnnels sujet to delys Communition etween Plnt nd Dignosers/Agents Communition etween Agents Communition etween Coordintor nd Dignosers This work [27,30-32,33-37,38,39,42,43,72,74] [28,29,41,73] [40] Numer of ommunition hnnels nd ommunition dely ounds Severl ommunition hnnels with different dely ounds Severl ommunition hnnels with the sme dely ound Single ommunition hnnel Events my e oserved in different order of their ourrenes This work [38,39,42,43] Events my e oserved in different order of their ourrenes Events re oserved in the sme order of their ourrenes [28,29,40,41,73] [27,30-32,33-37,72,74] Formlism used to mesure ommunition delys Timing Struture Step pproh TDES pproh Unounded dely This work [29-39,42,43] [72-74] [27,28] Figure 1.1: Comprison mong different networked DES in the literture regrding the lotion of the ommunition hnnels sujet to delys, the numer of ommunition hnnels of ommunition delys (nd dely effets), nd the formlism used to mesure ommunition delys. nition hnnels nd ommunition delys ounds, nd the formlism used to mesure ommunition delys. Another reserh topi ddressed in this work is the omputtion of τ- odignosility (mximl time to dignose filure ourrene) nd K- odignosility (mximl numer of events to dignose filure ourrene). To this end, we propose two tests: (i) one test sed on dignoser-like utomton tht does not require usul ssumptions on lnguge liveness nd nonexistene of unoservle yles nd (ii) nother one sed on the extended verifier tht shows not only the miguous pths ut lso those pths tht led to lnguge dignosis. 11

26 1.4 Thesis Orgniztion The orgniztion of this dotorl thesis is summrized s follows. In Chpter 2, we present review of DES theory nd rief introdution on filure dignosis of DES. In Chpter 3, we revisit the odignosility of disrete event systems prolem nd propose two new verifition lgorithms: (i) the first lgorithm sed on dignoser-like utomton tht does not require the usul ssumptions on lnguge liveness nd nonexistene of yles of sttes onneted with unoservle events; (ii) nd n extended verifier developed to show not only the miguous pths ut lso those pths tht led to lnguge dignosis. As n pplition, we ddress τ- nd K- odignosility prolems. In Chpter 4, we ddress the filure dignosis prolem of networked disrete event systems with timing struture (NDESWTS), nd, to this end, we formlly define NDESWTS nd propose n equivlent untimed model. Susequently, we present neessry nd suffiient onditions for odignosility of NDESWTS nd propose two tests to its verifition: the first one sed on dignosers, nd seond one, sed on verifiers. Finlly, in Chpter 5, we onlude the thesis nd point out potentil future diretions. 12

27 Chpter 2 Fundmentls of Disrete Event Systems nd Filure Dignosis In this hpter, we present the neessry kground on Disrete Event Systems (DES), nd on filure dignosis of DES. The theoretil foundtions of DES presented in Setion 2.1 re sed on [11]. The struture of the hpter is s follows. In Setion 2.1, the min formlisms for DES re presented. In Setion 2.2, we present model for DES sujet to intermittent loss of oservtions. The min onepts ssoited with filure dignosis re presented in Setion 2.3. Finlly, we drw some onlusions in Setion Disrete Event Systems In reent yers, the growth of omputer tehnology hs led to the propgtion of lss of highly omplex dynmil systems, with the distint ttriute tht their ehvior is determined y the synhronous ourrene of ertin events. Suh systems re lled Disrete Event Systems (DES). DES re dynmil systems with disrete stte-spes nd event-triggered dynmis. An event my e identified with speifi tken tion, or my e viewed s spontneous ourrene ditted y nture or, still, the result of severl onditions whih re ll suddenly met. Exmples of events re the eginning nd ending of tsk, the rrivl of lient to queue or the reeption of messge in ommunition system. The ourrene of n event uses, in generl, n internl hnge in 13

28 the system, whih my or my not mnifest itself to n externl oserver. In ddition, hnge n e used y the ourrene of n event internl to the system itself, suh s the termintion of n tivity or timing. In ny se, these hnges re hrterized y eing rupt nd instntneous, i.e., y pereiving n event ourrene, the system rets immeditely, ommodting itself to new sitution where it remins until new event ours. In this wy, the simple pssing of time is not enough to ensure tht the system evolves; for this, it is neessry tht events our. The system ehvior in the DES frmework is, therefore, y sequenes of events. All sequenes of the events tht n e generted y given DES desrie the lnguge of this system, whih is defined over set of events (lphet) of the system. Thus, we strt the review of DES theory with the onept of lnguge Lnguges One forml wy to study the logil ehvior of DES is sed on the theories of lnguge nd utomt. The strting point is the ft tht ny DES hs n ssoited event set Σ. We will ssume tht Σ is finite. The event set Σ is the lphet nd the sequenes re the words of lnguge. In the literture, the sequenes of lnguge re lso lled tres or strings; however, the term tre will e used throughout this thesis. The length of tre s is the numer of events it ontins nd will e denoted y s. The word tht does not ontin events is lled the empty tre, nd is denoted y ε, i.e., ε = 0. Definition 2.1 (Lnguge) A lnguge defined over n event set Σ is set of tres with finite length formed y events of Σ. Exmple 2.1 Let Σ = {,, } e set of events. As n exmple, we my then define, over Σ, the lnguge L 1 = {ε, } onsists of only two tres; or the lnguge L 2 = {,, } tht ontins three tres. Let us denote y Σ the set of ll finite tres formed with events Σ, inluding the empty tre ε. Σ is lso referred to s the Kleene-losure of Σ. Notie tht the set Σ is ountle, ut infinite, sine it ontin tres of ritrrily long length. For exmple, if Σ = {,, } then: Σ = {ε,,,,,,,,,,,,,,...}. 14

29 The si proess of forming lnguge is ontention. The ontention of two tres of events results in tre formed with the events of first one immeditely followed y the events of the seond one. For instne, tre formed from events in Σ = {,, }, n e formed y the ontention of tre with event, nd tre is otined from the ontention of events nd. The empty tre is the identity element of ontention, i.e., sε = εs = s, for every tre s. Before presenting the opertions on lnguges, we need to define some terminology out tres. Let us onsider tre s ritrrily prtitioned s s = tuv, where t, u, v Σ. We sy tht t, u nd v re sutre of s, in prtiulr, sutre t is prefix of s, wheres sutre v is suffix of s. Notie tht, ε nd s re oth sutre, prefixes nd suffixes of s Opertions on Lnguges The usul set opertions, suh s union, intersetion, differene, nd omplement with respet to Σ, re pplile to lnguges sine lnguges re sets. In ddition, the following opertions n e defined for lnguges: ontention, Kleene-losure, prefix-losure, post-lnguge nd nturl projetion. Contention Let L, L Σ, then the ontention etween two lnguges is the set of the ontentions of ll tres in L with ll tres in L. Forml definition is provided s follows. L L := {s = s s Σ : (s L ) (s L )}. (2.1) Kleene-losure The Kleene-losure of lnguge is the set of ll possile tres formed y the ontention of ll tres of this lnguge. Formlly, if L Σ then Kleene-losure is defined s: L := {ε} L LL LLL... (2.2) 15

30 Prefix-losure Another importnt opertion is the prefix losure of lnguge L, whih onsists of ll prefixes of ll tres in L. A tre t Σ is prefix of tre s Σ if there exists tre v Σ suh tht tv = s, nd thus, oth s nd ε re prefixes of s. Formlly, we n define prefix-losure s follows. L := {s Σ : ( t Σ )[st L]}. (2.3) L is sid to e prefix-losed if L = L. Thus lnguge L is prefix-losed if ll prefixes of every tre in L re lso n element of L. Post-lnguge Let L Σ nd s L. Then the post-lnguge of L fter s, denoted y L/s, is the lnguge L/s := {t Σ : st L}. (2.4) By definition, L/s = if s / L. Projetion Another type of opertion performed on tres nd lnguges is the so-lled nturl projetion, or simply projetion, denoted y P. This opertion tkes tre formed from the lrger event set Σ nd erses the events in it tht do not elong to the smller event set Σ s. Formlly, the projetion P : Σ Σ s n e defined s follows. P (ε) := ε, (2.5) e, if e Σ s, P (e) = ε, otherwise, (2.6) P (se) := P (s)p (e), s Σ, e Σ. (2.7) We will lso e working with the orresponding inverse mp, P 1 : Σ s 2 Σ, defined s the following. P 1 (t) := {s Σ : P (s) = t}. (2.8) 16

31 The projetion P nd its inverse P 1 re extended to lnguges y simply pplying them to ll the tres in the lnguge. For L Σ, P (L) = {t Σ s : ( s L)[P (s) = t]}. (2.9) For L s Σ s, P 1 (L s ) : {s Σ : ( t L s )[P (s) = t]}. (2.10) In order to illustrte the onepts of this susetion, onsider the following exmple. Exmple 2.2 Let us onsider gin the set of events Σ = {,, } nd lnguges L 1 = {ε, } nd lnguge L 2 = {,, }. Sine L 1 = {ε, } nd L 2 = {ε,,,, }, L 1 = L 1 nd L 2 L 2. Consequently, L 1 is prefix-losed nd L 2 is not prefix-losed. In ddition, we n see tht: L 1 = {ε,,,,...} L 1 L 2 = {,,,,, } L 2 L 1 = {,,,,, } L 2 / = {ε, } If we define projetion P : Σ Σ s suh tht Σ s = {, }, then: P () = {} P 1 (ε) = {} P 1 () = {} {}{} {}{} P (L 2 ) = {, } P 1 (L 1 ) = {{}, {} {}{} } Automt Automt re devies tht re ple of representing lnguge y using stte trnsition struture, i.e., y speifying whih events n our t eh stte of the system. They re n intuitive nd nturl desription of disrete event system. The modeling formlism of utomt is frmework for representing nd mnipulting lnguges nd solving prolems tht pertin to the logil ehvior of DES. Automt re useful model for mny kinds of hrdwre nd softwre: (i) softwre 17

32 for designing nd heking ehvior of digitl iruits; (ii) the lexil nlyzer of typil ompiler; (iii) softwre for snning lrge odies of text; (iv) softwre for verifying systems suh s ommunition protools or protools for seure exhnge of informtion. In ddition, in the literture, utomton model is lssil tool to del with the prolem we will ddress in this thesis, the so-lled filure dignosis prolem. Mthemtilly, we n define Deterministi utomton s follows. Definition 2.2 A deterministi finite-stte utomton G is six-tuple G = (X, Σ, f, Γ, x 0, X m ), (2.11) where X is the set of sttes, Σ is the set of events, f : X Σ X is the prtil trnsition funtion suh tht f(x, σ) = z, mens tht there is trnsition leled y event σ tht tkes G from stte x to stte z. Γ : X 2 Σ is the set of tive events, tht is, x X, Γ(x) = {σ Σ : f(x, σ)!}, with! mening tht f(x, σ) is defined, x 0 is the initil stte nd X m is the set of mrked sttes. Regrding the set of mrked sttes, proper seletion of whih sttes to mrk is modeling issue tht depends on the prolem of interest. By designting ertin sttes s mrked, we my, for instne, e reording tht the system, upon entering these sttes, hs ompleted some opertion or tsk. Notie tht Definition 2.11 does not impose tht the set of sttes X must e finite. However, in this thesis, we del with finite set of sttes X only; thus, the term finite-stte deterministi utomton will e repled with utomton for short. To understnd extly dynmi evolution of n utomton, ssume tht n utomton is in stte x n when n event σ ours. Then, utomton G moves to the stte x n+1 instntneously. This dynmi is hrterized y the stte trnsition funtion s follows: x n+1 = f(x n, σ) suh tht σ Γ(x n ). It is onvenient to represent grphilly n utomton whose stte set X is finite y mens of its stte trnsition digrm. The stte trnsition digrm of n utomton is direted grph whose nodes represent sttes nd the rs (leled) etween nodes re used to represent the trnsition funtion f : If f(x n, σ) = x n+1, then n r leled y σ is drwn from x n to x n+1. A speil nottion is used to identify the initil nd mrked sttes. The initil stte is identified y n rrow pointing into it nd mrked sttes re differentited y mens of doule irle or ox. From the stte 18

33 trnsition digrm of n utomton, it is possile to infer some informtion out its elements, s shown in following exmple. Exmple 2.3 Consider the stte trnsition digrm of utomton G 1 depited in Figure 2.1. From this piture, it n e onluded tht the set of sttes of G 1 is X = {x 0, x 1, x 2 }, the initil stte is x 0 nd the set of mrked sttes is X m = {x 0, x 2 }. Notie tht the sets of tive events for eh stte of G 1 re Γ(x 0 ) = {, }, Γ(x 1 ) = {, } nd Γ(x 2 ) = {,, }. The trnsition funtion is given s follows: f(x 0, ) = x 0, f(x 0, ) = x 2, f(x 2, ) = x 2, f(x 2, ) = f(x 2, ) = x 1, f(x 1, ) = x 1 nd f(x 1, ) = x 0. x 2, x 0 x 1 Figure 2.1: Automton G 1 of Exmple 2.3. For the ske of onveniene, the trnsition funtion f of n utomton is extended from domin X Σ to domin X Σ s follows: f(x, ε) = x nd f(x, sσ) = f(f(x, s), σ), x X, s Σ nd σ Σ suh tht f(x, s) = z nd f(z, σ) re oth defined. Thus, we n define the lnguges generted nd mrked y n utomton s follows. Definition 2.3 (Generted nd mrked lnguges) The lnguge generted y utomton G is defined s L(G) := {s Σ : f(x 0, s)!} nd the lnguge mrked y utomton G is defined s L m (G) := {s L(G) : f(x 0, s) X m }. The lnguge L(G) ontins the tres tht n e followed long the stte trnsition digrm of G, strting t the initil stte; the tre orresponding to pth is the ontention of the event lels of the trnsitions omposing the pth. The seond lnguge represented y G, L m (G), is the suset of L(G) onsisting only of the tres s for whih f(x 0, s) X m, tht is, these tres orrespond to pths 19

34 tht end t mrked stte in the stte trnsition digrm. Lnguges L(G) nd L m (G) stisfy the following inlusion reltion. L m (G) L m (G) L(G), (2.12) Opertions on Automt In order to exmine DES modeled y utomt, we need to define set of opertions tht ppropritely modify their stte trnsition digrm sed on well-defined riteri. The opertions tht modify single utomton re lled unry opertions nd re defined s follows. Unry opertions Aessile Prt A stte x X of n utomton G is essile if s Σ suh tht f(x 0, s) = x. Otherwise, x is non-essile stte. The essile prt opertion removes ll non-essile sttes of n utomton G, nd is defined s follows. A(G) := (X, Σ, f, Γ, x 0, X,m ), (2.13) where X = {x X : ( s Σ)[f(x 0, s) = x]}, X,m = X m X, f = f X Σ X, nd Γ = Γ X X, where f = f X Σ X nd Γ = Γ X X mens tht f nd Γ re restrited to X, respetively. Notie tht, the A opertion does not hnge the lnguges generted nd mrked y the utomton. Coessile Prt A stte x X of n utomton G is oessile if s Σ suh tht f(x, s) X m. Otherwise, x is non-oessile stte. The oessile prt opertion exludes ll non-oessile sttes of n utomton G, nd is defined s follows: CoA(G) := (X o, Σ, f o, Γ, x 0,o, X m ), (2.14) where X o = {x X : ( s Σ)[f(x, s) X m ]}, f o = f Xo Σ Xo, nd Γ o = Γ Xo Xo. Notie tht, the CoA opertion n ffet the lnguge generted y the originl utomton, ut it does not hnge the mrked lnguge. 20