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cTyn K DIoba[bHbIM MotreJIfiM gxaHuri H AalrHbrx. Hannwre oKc[eproB no3Bonfl'er noMHMo npolleAyp pacno3HaBaHHE, onrpacnrxH lr npHH flT/fl, peureHali TaI{X(e CTpoI{Tb: npoqeAypbl BbrfiBJreHEfl Henporl{BopetrHBbrx lHaurni, Hcnonb3yfr trI4HAMI{qecKUMeHtloulHecff rp}mnbr sKcneproB; co3[aBarb 3KcneprHbre MotreJrH uupa6orrcH petueHllfi wn pa3HbIX rsraccoB npo6ner"rlrrx curyaqufr; MOII€JIlIDo3erh

nro6r-re

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. rroilrn^n!, iisi-r i piijii{Soijilftiiofo

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BaHHoro npr{HffTuffperueHnfi; trocrnrarb 6onruefi o6unocru, wo no3Bonffer pearlu3oBaTbpa3nHqllbleMeTotrbIpelIIeHH.a3atraq.KporraeToro, B TaKoM KonrreKTHBe ecrb BogMo)r(Hocrb$oprrrurn3auHn lBflsr MexAy sKcuepraMu r{ nocrpoeHHfl Ha sroft ocHoBe craHA,aprHbrxcpeAcrB KoMMyrfi*"uH. c noMOIUbIO sTHX CPeACTBOprallr{3oBbrBarorpa3nHqHbrepexl{Mbr naanrvro4eficrBHff - or flBHoro o6pauleHnff opfloro 3r{cnepra K IpyroMy Ao HeffBrroro c6pnrr\eHur, KorAa aApecar onpeAerraercg no peanueyenaofiHM eynrqlffi. Hanutote MHox(ecrBa3a,qaq,uoAenefr H 3HilHI{ecnoco6a Hx Hctlonb3oBa'I{.g B Tex ITJIIIt'tHblxcHTyaqHtx arlpa6orKn H npHHfiTHfipeureHnfino3BoJrflerpa3paborarr eEHHbrecpe[crBa om{caHr{fi,a*ofi uHsoprraauur{H opraHn3arlnro HX aBToMarl{qecKoroHcnonb3oBaJfl'I/,n cucreuofi. B rcaqecrBeTaKHxcpeAcrB npr{MeHaIor cPeAcrBa nHHrBHcrr{qecrcofiu nporpartrrtruofi noA.qepxKn: .fl3brKr{ onpeAenennfi noruqecrcofi Mo&erruauasld (flO3) H Malnmynnponaruax :neMeHraMH norHqecKofi proAenH sHaru{fi (.tIM3) H HX nporpaMMHbre npoqeccopbl. Onpegene:rHe3HaHld npegnoJraraerBBeAeHHe HoBbrxrnnoB nHeoprrraLu{H' TaKHx, ICaK MoAenb' 3a,qaqa.MaHHrryrIHpoBaHHe 3HaHI{ffMHoc;{oBblBaercfl Ha nnaHHpoBaHHI'I npoqeccoB noHcKa peureHni s rnobanbrrofi MoAenr{ MexaHH3Marlenenorara}rnff [15, 17, lg, 20, ?!"*tt fi nyreM HcuoJrb3oBilHr{fi

2 3 , 2 4 ,2 7 1 .

MHoroo6pa:tHeJlorHqecK[x rroAenef, [axHbrx (M.[), B cr{creMax}npaBneHnx 6agauu l'*Hblx (cyrD frBnflercf,,o6tern'Hof, gaxouor.pro"tr,n pa3Burrrr reopHrr rr npaRrer paruco6parne grreMeHToBAarrubrx r{ Hx :THbrxoOnactsx. Olo npegonpeffenemonpegoB nporpaMMnpoBaHilfl3alaq ar{ann3an o6rLrx, a TaroKe cyuIecTBOBaHHeM pa3nHqHtrx rcrs o6rexroB, Hx csoficrts H onepaUnf,nag

Marr'nyn'poBa*H.f, (sMrDno#fi_';Xffi'#'"ffi;ili":fff, EaHHBTMH

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penfl[|oHHue MII, I TaIoKeM.[, ocnonaHnble na 6xnapHbrx_orgoruegnfx,ceMaHTI{qecKHx cersx, Ha nonffnril pacuspegHrrx Mgoxecrg H r.A. rcrac"iit,ronr"efi Aa]rHLrx cyuesfBeHHo pagnilqarorcff Bblpa3nTenLHocrblocpetrcrB [+zJ. npeAcraBnerrgrcseficrB H orgourernrftSJIeMeHToB rno oanruoll nomqecxofi rroAenn 3Hanuil,ypoBHeM npeAycMorpeH'blx -raKnx onepaurfi sal dagofi AarrHblx (EJD onepaunfi -H ot[Qer<mr"or""o peanuraunfi npH cyuecrByK)u'Etx cpeAcrBax oSpa6orrcl p.o"rt*. Pagnnrue M.I o6rr,mo o**"r"rd", npxrrrDrrrranBHbrM'TaK qno nrr60p rofi umr rrofi MII npH co3A:rfiuHEJI , p"-"on *orKDeTHEIX SAnru rrn,r.pr n6fr h^r,^ rMyu.ecrBa. uyqecrBoeaune paanuwux MJI fxrrreKTypbr CYE.[, coqerarouefi eEil{HcrBeHrlnrM rMCrroM BHypeHHnx u aHeurH:tx MII Dt(eHhr oEHofi MoEenn n gpyrrcli. B cnyvae CanrHofi florfiqecKofi rrroqeml gnarmf, B JIoTB HnTepnperar[tu nonrqecKof, rroAerrn [an_

30

PaccrrcrpeHua* Korflrenur{r xoporuo couracyercfl c npnpogofi cro)Krrbtx qeJroBeKo-MartrulrHblx cncreM npHHf,TlIff peueuiui H rlo3BoJlffer, Hcnorlb3yfi 3HAHHfl:

- crpouTb MoAeJrHpacno3uaBaHHfrcocrosnnft l) 3KcneproB-ynpaBJrerrreB oOrercra n cpeqbl ynpaBrrenrr.E,KlraccnQnrcaurll cocroffHr{r, rreJre[oJraraur,r.fl, gucaborrcH I

-

grg g vnnenrr qrornrx H nDI{H ---f --f ---'------'J

nerr rprrrrfi .

2) sKc[eproB-nocraHoBu-(HKoB noKirnbHbrx3agaq ynpaBneunfl,- crpor{Tb anropHTMoB, xapaKSynrcqnollilrlbHo nonurtfi KonJreKTr{BBbrqucrrHTeJrbribrx repn3yrouulii rcoHrcpenryn o6nacm FrpaBneril{ff; 3) gKcneproB - nporpaMMl{croB BbrtmcJrr{TeinrHux anropurMOB, - "HanorHHTL" nporpaMMHyrocucreMy KoHKperHbrMcogepy.(aHr{e M; 4) 3KcneproB - KoHcrpyKropoB cr{creM rrpuHflrlrfl petrleutui rpoercrr{poBarb I{ reHep}IPoBarbnporpaMMHoeobecneqerne cr{cleMbrH opraHn3oBbrBarb ee npo6neMHyroopr{eHTaunro. Pesrcvrnpya cKa3auHoe,MoxHo 3aKnroql{Tb,qro paccMorpeHHauKoHIIe[qfin norlHocTbro orBeqaer npo6nevrala qertoBeKo-MerrruHHoroynpaBneHr{.g q[o)KHbIMHTex]IoiiorFlecKHnano6lercTaMn, MeTotraMH Teopnu nocTpoeHu-fl 6ol uruux y[paBJrErouux npo rpaMMrcrx KoMrmeKro B. 3.2. npoqeAypbtnprHnrxn peurexufi B Hacroflulee BpeMff B TeopHHcucreM flpoqeccbr r{3MeHeHH.ff orleHwBaeMbIx BeJIHqIIHpa3nlflHbx o6rercToB, BKnrcqa.qH sHeprocucreMbr,nonnMarorcff KaK npoueccbr 3BonrorIHH@croflHnf, HeKoTopofia6crparcrHoftlruraMl{qecxoft cucreMbl' MareMarnrlecKaffMoAenb roropofi orpaKaer BHyrperrHuenpl,tqI{HHo-c'neAcTBeHI{bIe c9fl3H odterra Cocronuuer4 sHep?ocucTeJqu6ygerraHa3blBarb @Bol(yfiHocrb napaMerpoB, Koropbre B KiDKIFTfrpaccvrarprraeurfi MoMeHTBpeMeHHorpaxalor Han6oneecyrqecrBeHHbre, c roqKH 3peHrls ynpaBfieHnfl,,cTopoHbree noBeAeHHf,. floH.sme cocroflHt{t nrpaer rnaBnyro ponb B om{caHr{;rH3MeHexrni,npoucxoAfflrtr{x B sHeprocl{creMe Bo BpeMeuu.HsueneHue cocronqua OygervrpaccMarplfiBarbKaK HeKoroPbrfinpoqecc, Hocrulllii rexHorrornqecKlfr xaparrep. Cncrenry, cocroxnnfl Koropo,fi ugr"reHmorcflBo BpeMeHHnotr treficrBgeMB3arrMocBt3aHHbtx I{ B3aI{MHoo6ycnoangHHbrx BHyrpeHHHxH BrreuHHx np5ttrlH, 6ynertn Ha3braarb dunatuuuectcoil cucreuofi. 3HeproclrcreMa orHocr{Tcrr K Knaccy E{I{aMI{qecKHxcHcreM, Koropbre B KarKADrfttvroueHT3peMeHu t HaxoAETcf, B cItlIoM tt3 Bo3Mo)KHbrxcocroxHnfi z yr clrocnOnrr nepexolurb H3 o[Horo E Apyroe notr AeficrBHeMBHyfpeHHHxr{ BrreruHHxnpHqnH. Onpe4cnenl{e cocro sntrfr, gHeprocncreMhrno AaH}rbrMr{3Meperrni Bxo,q{brx H BbDKotrrbD(cl{rHanoB Ha3blBaercnnadnrcdenueMcocronuun [54]. Ey4erur BcflKoe @croffHl're cHcreMbl Z paccMarpnBarb KaK TorrKy B BeKTclpHoM npocrpaHcrBe. Brtgenuu n srolu npocrpaHcrBe HeKoropyn earrxnylyro o6nacTb zs, orpauHqHBalouyroBo3MoxHbrenepeMeulen]flrfl,lOrrKU Z B npoqecce QyHrIryoHnpoBulHrrflcrcreMbl. Tarurtr o6paroru, nro6as roqKa ,, uzodp:DKarcIrlax TeKyulee cocroEHue cHcreN{u, 6yger BHyrpeHHefiroqsoit odnacrn Zs,. 3l

Ilnr rnepnoctcrcMbtoGnacrrZs uurepnperHpyercflKaK oonacru AonycrHMbrx tn?procHcreMbr. Yparxernle rpaHHrrbrodnacrn z s sawilfieM B Bn,[e Pm'|ot

f(ro) = 9.

(3.1)

Cocronrne 3HeprocxcreMblB MoMeHr t e, T o6ogrrawrMrrepe3z (t) c Z , lro[true || BbD(o[HbrecHrHarrbi- coorBercrBeHHoqepegx(f) e x- v.(t\ € e v r r ^ ^ . r v ts r-. iiepexoEcHcreMbrH3 cocroffnunz (rr) n cocroflHHez (tr), t.2 ) t1, OqPCICJI'ETCf,

AH}IAMI{qCCKHMI{

CSOfiCTSATUH CHCTEMbI H

BO3MYIUAIOIIIHMH

gog,qef,crBnaW:/., Bce aoal{oxrrbre Bo3Myrqeuun, geitcrByrou-u{ i, 6ynem noApa3AenflTb Ha BHeIITHHe(napavrerpu o6r,erru " "r"TeMy, yrpaBnfrrcuorecnrHurtr) H BlryrpeHHHeBO3MyrrIrHrnr(nce ocranrHrre). " "*o*rr PaccrvrorpnM rr3MeHenfifr. cocrofiHnfi cucreprbrnoA geficrnner y r p e H",t rrepexoH H x npruI{H.-IIpn HenpepbIBHoM I{3MeHeHHr{ mcrofiHr.rfioneparop Aa o6ogxaqHMP*, npn I{3MeHeHuI{cocro.sHrci, xapaKTepn3yeMbrxorKa3aMI{ ofupyaosamtrfr., - Po. flycrl B HaqanbHrtfiuoueHT BpeMeHHf o cHcreMaHaxo[HTcff B cocrofiHgr{ z (to) e zo. flonaraeM, qro BxoAHbre'cnruanu orcyrcrByror r.rH3MeHeHHe cocro.fiHHflo6ycnorneHo BJII{.EHI{eM BHyrpeHHHxtrpurluH, TorAa om{lueM gro )apaBHeHreM Z (t)'= Prf t, to, Z(til, t ) to. (3.2) flputrrHrt, BbI3BaBIrrHe I{3MeHeHHccocroffHl{fl cucreMbl, He MeHfirorcfiAo t = t *- t'topteHTa BbIxoAaroqKr{ z € Z 3a rpaHurly obnacrn Zs.qro6u Hafirn 3ror MoMeHr'tryxHo coBMecrHoperrHrb ypaBHeunx(3.1) w (3.2). flpeglronoxnM, rrro B MoMeHTt* s increre npoucxoAr{TorKa3 ofopygoBaHr{.E, TOrtraee cocroflHHeB MOMeHT t*+ 0 onpeAenflercffyp:lBHeHr{eM

Z (t* + 0) = polt*, Z(r*) l.

(3.3)

MoueHr

(3.1)

n (3.3).

orKa3a

HurxoAl{Tcff ooBMecrHbrM periler{HeM ypanHeHuri

Kaxtroe H3MeHeHlIe cocroflHH' cncreMbl npHBoAr{TK ToMy,.HToHa BbHoAe Qopr'rnpyercr cnrHan, QurccnpFourrafi3To H3MeHeHr{e B coorBercrBqg c ypaBHCHHCM

Y(t*) =ZIf*, Z(t*)7, T. e. fupMupyercff coo6ulerure,lto KoropoMy MoxHo cocrosrmfrcucreMbr"

(3.4) ua6nmAarb H3MeHeHHe

PaccrvrorpnM H3MeHeHHecocrofrrtlrfr cxcreMbr noA AeficrBHeM B H e ru H H x npI{tMH. Ilycrr s NIoI'IeHr tt e T, KorAa cucreMa HaxoAr{rracb B cocroflHr.ru Z (t' ) , ua ee BxoA noAaercfl cHrHarI x(t' ) e X. flpH arovr cr{creMa rrepexoAa B COETOflHHE

Z (t' + 0) = p^lt , Z (t')1,

(3.s)

rge P" - oneparop nepexoAa. Ec.nn (3.1) u (3.5) HMeIor @BMecrHoepeuJeHne,ro B c1creMeua6nrcAaercx co6blTr{e BbD(oAa3a rpanurrbr ynpaBJrfleuofi o6nacrn H cncreMa Bbrtraer 32

Ha6nrctraer"ruficnrnan

Y(t') = L' It' , Z Q'), X(t')1.

(3.6)

Tarcuu o6paaor"r,noBeAeHI{ecucrbuu Mo)KHoorucarb B BHAgrroeJre4oBarenruofi cMeHbIcocroxmni noA AeftcrBr{eMBHyrpeHHHxu BHe[rHrD(npuuffx. Ha6uroAeHns3a HapFxeHr{eMcxcrervrofiorpanxuenrdr,ofipeEeJrgx}u-urx oGnacii ynpaBrreHuff,ocyulecrBrrfltorcr c floMoulbrc co6rrmfi, Koropbre orrncbnarorcfl (3.4) u (3.6). BbrpalKeHnnvrr flpn ormcanuu eHeprocucreMbrHeo6xoAnuo peuurb pflA 3a,qaq:ilepBafl onpetrenenne u orrucarlue sneMeHToB,mnfirculrD(cfi rurQoprvraruoHxofi MoAeJIbKroorexra H cpeAbl ynpaBrreHl{fl; BTopafi - onpetreJreHHeH om{caHHe onepaTopoBnepexotroB Ir BbD(oAoBcHcTeMbr;rpeTbff - opraHH3arllrflcBfl3H oOtercra c BHeIrrHt{MMHpoM, c UelrbroHanoJrHeHH.E f
rrnnoononrc9 JrrywrLwtLrLA.

l1-+rlLrL

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r4r\vru

vlDEtd

ntLrlJAUl.44Ir4u

SarlalD

BHtrbI TexHonorHrIecKHx cocrommfi o6tercra, yKa3aB coorBercrByrcus{e rpaunqnble yclroBnff H npoBepnB Bbr[orrHuMocrb grux ysrosufr no xaxgofr nepeMeHHofi cocrosrmx. flycrr, HanpuMep, ycnoBne HopMurnruofipa6orocnoco6uocrn aHeprocucreMbl no HeKoropofi repeMeHHop, fi C Z (fi - uacrora) 3agaercfl B Br{Ae HepaBeHcTBa /i"(f1

4f1r,

rAe 4u, f i" - nH)I(HeeH BepxHeeAotrycruMbre 3HaqeHr{ffqacrorbr B gHeprocl{cTeMe. Brrxou /, 3a npeAenbr Hr{repBana Vr*, f irl Qrnrcupyerc.fi KaK npo6JIeMHa.ffclr.ryal4wfr., a coorBercrByrcuee traHHofi curyaquH cocror(HHe gHeprocl{creMbr - KaK rpe6yrculee ilpuHflTHflperrreHr{fino yupauricnuro. Tarcupro6paaor"r,o6utan npo6ner"raaHarrlr3acocroflHllfl nupa6orrcH H npxHrrnfl. peureHni B cncreMe CIIPHHT gaKrlro,Iaercfi. B [ocneAoBerenbHoMpetueHItrI clretryrcIrlux 3atraq: onpetreneHurrcocroffFmx o6lercra H cpeAbr y[paBrreHHff (zadaua rua1"trcdeauacocronnua); orueceHr{fl KrDKAoro r,r3 cocrosHrd t( o[HoMy rr3 3aAaulrbtx BI{troBcocrosnnfi (sadaua rnaccufiuKln4uu cocroflnuil); nocraHoBK[ 3a4aq noncKa perueHrri B coorBercrBnu c rreJrflNru,Aocrnxl,IMocrb Koropblx ueoGxo&rpro o6ecnetuTb B KIDKAoMH3 KrraccoB cocrorHrui (eaoouafiopuupoaaHun crpareeuil qertu noucKa peruenuil); nrr6opa obnacm noncKa peurenuft (zadava uodenuuott rcttaccuSurcaquu); ^.?ancKa peureurui ArIfi l(axtroro H3 IslaccoB coctonntdt (zadaua noucKa perueuuil); onpeAeneHuffAocrLI)KHMocrI{qenefi ynpaBrreHns,npr peann3arluu ynpaBnffrou[|x peruenufi (zadaua onpedeaeHun eosMoJtcHbrxucxodoe); oueHKH KaqecrBa peuewwit, oilpetrenfleMbrx [ocrHxr{MbrMH pe3ynbraraMHIIpH Hx peum33

3rltttll Hr oEDeKTeynpaBreHH.fl(tadaua oflocnoeaHu,npewenuil); cyxeHgff xrbxecrBr ynppl-fl rorqru( peKoMeHE utnir (tadaua rur riro p ewen'uil) ;' rn r*.rflf, 3t nonrrof, "11atrrp'111b1x" paccyxAeHr.flinpn noHcKe peueH*tit- (ladaua tpctTtpeKu pewexufi); oprarlsarrnn qenoBeKo-Mrrrrgl{Horo nrau*rogefrtt'Erd ttPn PeuteHHii3?n2Tf Ha cHcreMe (zaoavauufiopuaquoHHo?o duanote:a) . Paccuorpru nogpo6tee ?TH3a.qaqH H oflpegennrurHa6op npouetryD. DearrH=y-rorw-rHx E cncremeCIIPI,|HT. llycrt 1 _ HHriropMarluonuaff ;fr.;r:;;;;xarcuiur crrcTofrH:/,fr o6rexra lI cpeAbr ynporr.rm"; s _ ,"ry.q"r, rpe6yroU{efr npHHnrHfrpeureHnfi,onpeAeJleHHaffHa srleMeurax / . B coorpeTcTBult c ntnoregofi MoAeJrbHocrH npoueccoBo nepamBHo-IHcnerqepcKoro ynpaBrl eHrff [55] ' qenoBeK{leparop Hcfionb3yer cBorc MbIcJreHHyro rvroAerrbperueH6rr M2 'qJI' noHffTHf,BDKHbIXH oIIeHoqHbIx acneKToBcHTyaIrHn.Hnur*rn crloBaMr{, oH paSoraeTc noMoultto M2 KaK A'Iff UCCneAOB 'IItUfrCHTyaTIHH .S, rarc H Nrfr, ron)^IeHHfr cBff3aHHblxoueHoK H peueHtri o Aeficraus;; ilg|"re Heo6xoglrMo npegnp2rHflTba garnrofi clrryawn S. npn eroM JroruqecKa-E nocJreAoBaTe'rbHocrb3TarIoBpa6orrl qeJIoBeKaMoxHo oro6pa:nrr a*rron, uso6paxeHuofi na pnc' 2'2' IlpnrquruarlbHblM KoM[oHeHToM MoAenHnp'HffTr{ff peuewtfr M2 fiBnfierc.fi ry?.q.rypa no'cKa H np,HffTr{ff pe,,,eHnfi rar ,,poqecc g BHAa 'burya4un - qenb - uodeno - peueHue npednovreL,:TPT:Ip:S rr,ic . .rra crpyKrypa o6ecneqnBaerpearru3atu{rc om{careJlbHbrxcsoftcrs curYawm,s, uenefi 4 u oqeHoqrrbrx craHAaproB o, a""ro"ri* a s, pa3rr',rHbrx itrlbrepHaruB rro'cKa peruexni, KOTOpbre Aonycrr{Mbr grn ^s il Nrfr ee K'HTponff' B cocras G sxoMT npeAcraDJre*He HnH r*rogenr M, cnryaqHu s; ' otuee B paMrcaxi4, arr6opa ".prr"rir B COOTBCTCTBHI{ C UEJIfiMH lFfDlf!

Jlnu

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PEUJCHHT-T;

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Mzl npocTpilHcTBo npefinoqTeHHfi Bbr,rnrfi s cHcreMe ,S u cocrogrnft MoAe;TBOnoHcrcan M2 pa3nHqHbrx perueHHr-r,

nPetrno'rre*H.E (r).M9n entM, nrnoffi; fftrffiIl,;";i:T.i#I

rI}rrr n npeAcKa:r:IHr{.s s n reprvrHr{il( arpn6yros ,s H Hx Bo3Moii*r* cssgefr. Ilacm onucaxnfi cBfi3ana c rnaccnsurcrrun* cocrorHni ,S Ha HeKoropoe rIHcIro pS3rIHtIHoIxKareropuft, nueHyeMblx B A:ulbHefiureu KnaccaMn crryatlacrr Apymx oruca'nl isnga'a ryfi &' c'orpegefleHr{eM npocrpa'crBa reurerrfi {url w, *ogoro H3 Knacronb3yeTcs,NrE Oru{CaHHfl, CTpyr(Typr{_ rruennriR un" KiDKAoror{3 3neMeHToB I K[acce crryaqlfi r(ri. ublMu o6terranau c Hcnorlb3oBalrueM cHcreM A:lHHono KIIacca 6ygerrl paccMarpuBarb KaK rrenoBeKo-rralrlgHgyro AefiTetrbHocrb no onpeAerleHHKtcocromnrfi o6rercra ynpaBneHr{rr, Tpe6Foufix npuHffTr{s pemelrni, noHcrq/ n nrrbopy peruenrui qar., uejrcHanpaBJreHHOIO cDFIaCOBaHUg aodeteil ynpasnsnulei derrcrtbHacru, sanoxeru{ofr B

-t;.-r.';;;;;;;;$.*

34

craBrleHue onpeAenflercfr, HaKorrneHHbrMr{ 3HaHHffMHo6 o6nacrH yflpaBn en4fl' uen.EMI{ ynpaBireHHff, orpaHr{qeHHffMH, npuCyuHMH KaK Ootercry, TaK H OpraHy ynpaP.neHtrfr, MHoxecrBopr o6rerrr{BHbrx w :yltercfl,rBHbrx [pe4norrTem rii n^ nrr6^-" r-r-?rtt ilu jtbluoP.y

*'---; llyreH

noHcKa

PerdeHrui

E oIIeHKH CTe[eHH I{X IIpHMeHUMOCTH.

HHrepaxmBHocrb B3al{MoAeficrsHs rrenoBeKa c cncreMofi opraxn3yercn rryTeMBBeAeHHffnoHffTH.EqeJroBeKo-tvrnrrrlurHofr cr{Tyaur{H,Tpc6yrcutefi npn_ HflTTIfr'pelueHufi Sy ^ onpeAenflIolqero 3To l;oHflTl{eMHoxecTBaarpu6yron. Xaparrep 3Tofi AefiTeJIbHocrI,I, c oAHofi cropoHbr, 3a,qaeTcflrrerroBeKoM11yTeM ynpaB.rleHHflnpoueccaMHnocraHoBKH 3aAaqn clrexeHHff 3a xotroM ee peureHH-E. C gpyrofi cropoHbr, cucreMa yroqHfler KoppeKTHocrbnocraBneHHbIx 3a'qaq,upe4[araeT anbTepHaTIiBHbIe nyT]I HX pelueHn.fl,I{Cnofib3yff"3HaHHfr.tr oIrbIT" rroncKa pe[reHl{Ii, orpor(eHrrbrfiB cBoefi MoAenr.r.Taxurtao6pa3oM' rlenoBeK n cI{cTeMaB3aHMoAeficrryror KaK napTHepbr,conracyrcil$e cBcH Merofipt pelueHlifl 3aAaqynpaB.rreHH.fi c ueJrbrononyqeHtrfl yAoBnerBopr{TeJIbHoro Nrn qeJIoBeKape3yJlbTaTa.CHMdHoe Syger onTHMaJrbHbrM Jrgtub TorAa, KorAa paOora cncreMbl oprarin3yercff B pe)KHMe"HHTenleKTyaJrbHoro" coBerql{Ka qeJIoBeKa,ocyrqecrBn.flg pyrr{HHbre Synrum aBToMarl,[qecKoro pacno3HaBaKufl,cnryarytfi, rpe6yrougrx npntfrTtrfl. peureHr{ft, noncKa peineir-nfi Ha ocHoBe mr$oprr,ralqllil4, non)'qenuofi rarc or naprnepa, TaK H c HCIIONb3OEAHHCM CI{CTCMHbIX 3HAHHII. B BHtre IFyx Br{AoB crpyr(rypnpoBiu [40] H reopemKo-MHoxecrBeHHbrx[c utrx (nozttKo-urzedpauvecxux t8l tr J AeneftoueHKHcnryary{n H rroHCKspettrr AeneH Ha curyauufij<. Wff Koropbrx Mo)Ker 6rrm Harigen aflropr,rrM,cB.fl3btsarcUlnfi I{cKoMbIe napaMerpbl c 3aEaHHbrMH, I{ nepe6op Bapr.rauToB He oqeHb BenuK.'Bropofi BHA MoAeJIeftcnyxnr rJtfl.rroncKa perueHnri,n culrHoft creneHI{ 3aBl{cfiIr&x or curyaqufi lr rtre nepe6op qpe3BbrtrariHo Bennr(. Moxno crca3aTb, IITO BbFMCTII{TgrIbHbIe H Teoperr{Ko-MHoxecrBeHHbre Morenn rrBnffrorcff aHarloraMt{ pacqerHblx onepaqlfi rtpn noLIcKe peuremafi, a trHarroroBbre H SKcneprHbre- auatofaun MerotroBnoxcKa perueurul. HcxoAs H3 cKa3aHHoro, KolilIenqrlfl cncreM Turra CilPI4HT BKrrroqaer n ce6s rcarc co6crBeHi:o cucreMy npnHnr:lrr perrreHr&i,TaK r{ JIIIP co cBorrMr{ BO3MOXHOCT.SMH nO pacno3HaBaHHrc H OrIeHKeCnryaUyir, a TaKXe noficKy perueHrd. Bogr"roxHocrn raxlofi hrs B3aHMoreftcrryroqux cropoH onpeAeJlflrcTcfi nonHorofi rvroAenefiyflpaBnnloqefi genrerrbHocrr{,flpoqe[ypaMr{ npgHflTHflpeUrermftH MoAerrbnuvr6agncoMnpoueAyp upHHffrHf peruenmi. lIpH arot"r npoueccbl npI{HflTHx perueHrui H Mbrrrrneuafl paccMarpr,rBarorc.fl KaK ceMHorlrqecKl{e(rHarcorrre). Zcnonbsyewafl. npn eroM nocJregoBarerrbHocrb IIIarcB (cursarn$x npHtMHHo-cJIeAcrBeHHbrMH, BpeMegHbrrlu, npocrpalrcrBeHrrbrMr{ n, trpwutfin orHorueHurun) HD(oxr{eHu..r yflpaBnfironMx perueHl{I-lHa Kaxqlyro npo6neM}ryrc Dnrya:4czrto paccMarpuBaercfr KaK noeuKa noucKa peueuuit. Gre.qosarerlbHo,Ha Kax,qoM uare B3iuMoAeitcrnwn rreloBeKa n CIIPHHI' oEHofi nr cropox$opM$pyercfi 3ar{poeB BHfferrpodneltnofi eyrryar\}rflw (wrn) l<

noAMHoxecrBa alreOPaFIecKHx oneparlr{ri MoAerIu B @orBercrBur{ c Jromxofi IIoHcKa peureurni. 3a,qaqaCnP cocronT B orbrcKi[rnr{ Hr{Tepnperarlgrd sTHx Onepaqufi n repMullax csoefi MoAenr{, Hx BbrnorHeHnr{H B orBerHoM dopur.rpoBarilH 3arrpoea (cgecl ucrcouufi pe3i,rrbrarrpaKryerc.fi KaK .an#c). MoEenl ynpaBrlfl loulefi AeareJrbHocrr{npn o neparr{BHoMnpHHflTHr{peuenrui saEaeTcfi Bbip:DKeHIieM

Mr -- ,

(3.7)

rre T Y n - < L r y A , A K SO, )

(3.8)

- reopr{.g ynpaBnffrorqefiAesrenbnocrn (rraogenr sHaHltri cncrertor) npn onepaTHBHO-IplcneTqepcKoM yIIpaBneHHHpe)KHruaMHpa6orrr sueprocncreMbr; Il4! = ( x',

b', f',

p' >

(3.e)

- nHQop rurargloHHaaMoAeJrb AaHHbrx, o rrHcbIBaroulafi aHepro cHcr eMy ;

IfT =( HTr, IIlf2 )

13.10)

TeMbI' 3a'qanulaff sKcnepTHO cooTBeTCTBHenpaBHna ycTaHoBIIeHI{.ff cooTBeT. crBH.fi Mexry cHHTaKcT{qecrofi crpyKTypofi snepreHToB fi3brK? L ru n H r4X cMbIcJIoM B oEnacru ynpaBneHl{fl pe)KHMaMr{ pa6orrr sHeprocnci6#u (ce. MaIITHKa noJlb3oBarenr) ; I'IT2 M:lurur{Hafl HHTepnpeTarlur orreMeHToB, 3a,qarcuraff sKcnepTHo arrropHTM yCTaHOBneP.ilf,,@orBercrBH.E MexEy ceMaHrnqecrofi crpyKTypoft eneuenroB fl3brKa Lrvn14 uxncrnnnocrbrc s rcnrr1gbrfi rercyugft MoMeHr rol{cKa peruemfi (npiirtirnxa o6nacrn ynpauennx). Teopur ynparnxroulefi tretrelrbHocru B 3aBr{cr{Mocrg or orpo*ar#i, HaIsIa[bIBaeMbD( Ha npaBI{JIa BbBoAa yrBep)Kgeunfi @, Moxer 6lrru om{caHa cpetrcTBaMu rrorHKH npeAr{r(aToB lrepBoro nopffAKa, npo[yKrtr{oHtrbrx r{ anropurMnqecKr{x cHcreM lSZl. AefrcrsnreJrbHo, B noruKe [peMKaroB Her orpaHH'IeHltri Ha IIpHMeHeHHe [paBun BbrBoAa. K nroSouy yxe BbrBegegHorvry yrBepxgeHl{Io noAxoA}rr nrc6oe npaBnno BbIBoAa, ecJru AaHHoe yrBepxAeHge AorlycKaer ero Hcnonb3oBaHlre. B nponyrcUl{oHHbD( cucreMax, dasrpyrorrrgxcff s CIPHHT rarcxe Ha rIorI{Ke npe,q{KaroB, uMerorc.fi AononHgTeJrbHbre yglloBHff Ha npHMeHHMocrb roro lInH l{Horo npaBfina BbrBoAa. 3ru ycnoBr{fl MoryT MeH'flTbcff B [poqecce QyHrcI+roHHpoBaHHrI nFntryKr$onHofr clrcrerurr B 3aBr{.

I I I

npoqeAyp, 3aEaBaeMblx KoprexaMH: HOCTIT

npouedypacuryaraenoilrcnaccufiuKauuu gt = ( S, '1, Kp, Ks),

( 3 . r1)

lteKoropblM orHotueHneMHa MHoxecrBe 3nertre ,S - c1Tyaqufi, 3aAaBaeMafi MeHToB I; i - MHoxecTBooKcnepTHbtxnpefnoqTenru?no srt6opy npaBHn roaccnQnKaIIHH,3a,qarHoeHa unoxicrne { S x Kt} ; Kp MHoxecrBo npa' KnaccoB MHoxecrBo ,Kr peuarcu$x npoUefyp; BI{n rcrfuccu$nKaUl{H peuteHrfr; nollcKa Mofeltn cyuIecTByIoT KoTopblx cnryulltir, Wfr npo4edypa ModenbHoil rcnaccufiuKaquu no3Bonffer onpeAengrl ro MHoxecrBo r"roAeneftflpuH.ffTufiperuennfi, opraHu3yff Bbltlncflenvrfl,Ha Koropblx Mo)KHoHaftrn rpe6yert,tlle peluenufl : 9z = ( S, Ks, AI, Mr) ,

(3.r2)

rtre A, - MHoxecrBo iurbrepHarr{nnuGopa Mogenefrnoucrca peruenufi, necoBbre rcoeSSruweHTbrKoropbrx 3zrBucsror S u Kr, ttoxer 3alaBarbcff qepexqMe pa6ornt c cucreMofi; Mr - MHoXecTBo JIoBeKoMB HHTepaK[tBHoM r"roAenefrrIoHcKaperuemlfr; nporyedypa fiopuupoeaHufl crpareeuil qenu noucKa perueuuil [o3BoJr.ffer onpeAenr{TbMHox(ecrBoJroKanbHbrxn(wm) uo6annurx uerefi yr1paBnennfl,, Koropbre HeodxotruMoAocruqb c noMoulblo perueHufi,uaffAeumlx B AaHHoM KJraccecnryarylfi:

9t = ( ,S,Ks, IL KP, C> ,

(3.13)

rne II - MHoxecrBo reKyulux uelefi, croRrqlD( nepeg yflpaBnflrculeE cucrernrofi; yP - MHoxecTBo KpI{TepI{eBAocTnxrenufl,Uenefi (n qenn, v Kprrepnu qerroBeKoMH MeHffTbCflC TeqeHHeM BpeMeHH,HaIIpHMOryt Bapbl{poBaTbcfl, Mep trpu ynpaBneHr{r{oHeprocncre*rofi qenu H KpHTepI{HMeHrllorcff B 3aBH' cHMocTHoT BpeMeHI{roAa, cyloK, rloro4Hblx ycnornfi H AP., tITo cBfl3auo c ero AocTaBKH K Mecry onrnnausaquefipacxoAa ToIIII{Ba H ruIaHHpoBaHHeM Hcnolrb3ouaHux); C - MnoxecrBo crparerrui qenu noncKa peurernn? (nanpr{Mep, npn uenu cra6urngarllrn napaMerpoB gHeprocncreMbl,B cJrflae ux oTK[oHeHun, Sopunpyercn crparernff noHcKa raKoro peuleHufr, peanll3aun.tr pexuu pa6orr'r); Korclporo npl{Bena6u rneprocncreMy B 3aIIaHIIblfi :t7

npoqcdypa noucKo %enesux ynpagftnrcu4b: peueHuil no3BorrfleT opraHH3oBbrBarb rroHcK peuleHHfi trIfl KiDt(AOfi Ug npOdner"ilrnrx curyargfi B COOTBeTCTBHIIC UerrrrMr.rH r(prrTepr{.flMHy[paBneHHrr: 9q = i,S, C, Mr, Ro ),

(3.14)

rAe Rq MlroxecrBo rreireBbrxynpaBngrous{x peueHr{r?,Koropbre Moryr 6rtrt HafrgeHtt B MoAenHnoucKa peureurfr (6aee aHanld) M1, nactpoeHHofr Ha reKyIIyIo cHryaqHlo si € S npn Hcnonb3oBaHur{ crparerr{r{ ci € C. .[anHax npoueA-/pa BbIrIoJIHflerIFe $yuxultl - [naHupoBr{Hria BbFucrruTetrbHofr nocJleAoBarenbHocrnnoucKa pcurenufi H peuarenr. llepaar Qynrculs 3arorrcqaercq u Qopr',rupoBaHHHpetuarcu1efino cnetroBare.J'r bHocffi npo rpaM M, Bro paffB OpraHH3aUHHBbtrIOJrHeHHfl 3THX [pOrpaMM V nonrterrHfl yfipaBnflrcr4{x peKo Merlquga.irB KoHKperuoft Bbrt{HcJrHTennHofi cpege; npo4edyoa onp eoeneHu.rI o3woJtcHbt x ucxodoe p emusa4uu p ew eruzr7 nossoJrEer 3aAarb AocfixHMocrb JroKarrbHbrxu (ruru) rnoozuiuHbtxueJrefi ynpaBIIeHHg rlpll peall{3aqHH Tex wl]'tl H}IbI)r-WpaBnEIouS{x peueHUfi. 3rO strnonHflerct rryTeM opraHu3auxn srlrncflerrfr Ha MoAenH AonycrnMoft o6nacrn fipHH.frfr{ffynpaBJrsrculHxF,eueHn}"r- Mnor, onpeAeneHHHsrofi o6nacTHOOrp B coorBercrBHH c UeJIflMH Ii u rcfiiipuflvrtr - R?,xapaKrepHbrrunE/rfl AaHHoroypoBHfl rrpHHffmflperueHlfr.I[aHnan npoueAypa3adaercff

gs = ( ,S,R,,, 4, *p,*"oy

Onrr, Rur )..

(3.1s)

rAe Rqr MHOXeCTBO TeX yllpaBnfrcUlnx peUrenUfi,KOTOpbreffBJrffroTcff yAoBnerBopHTenbIIbrMH HcxoEaMfi,T. e. HcxoAaMH,npn pJanH3ar${nKoTopbrx MoryT 6trrr Aocruruyrbr rroKanbHbre u(unn) rno6anrHbreueJruyflpaBneuuff; npoaedypa oflocuolaHun. peweuuil no3Bonfler ouelprrb KaqecrBo perueHni (nx onrnuanruocrr) ryrreM opraur{3auuu Bbrqr{creHnfiHa MotreJrr.r onpegeneHHfl onrr{pranruofr o6nacru rpnrrffruff }'npirBnflrournxpeueHnft (Ivtoor) wn sntbopa o6nacru onrr{MarrbHbrxyrpaBnf,rcuslr- peurerrrui (Ooy) B coorBerCTBHHC rIenffMH r.r KpHTepH^fiMr{. Sner"reur KopTexa Rq1 fiBflffeTcflMHoxecTBoM Tex ynpaBnffrorqr;x peurermii, Koropbre y.EoBn3TBopflrorOoyp r{ MoryT 6rtrr B nepByrc oqepe4bpeKoMclrAoBar{br 4rtff pearru3aunnHa SHeprocucreMe. [annan npouep,ypa

g e = ( , S ,R u r , I { K o , M o o r , O o y r , R , ^ z )i

(3.16)

npo4edypa cuHTe3operuenuil rro3BoJrreryMeHbur{TbKorrHrrecrBoogrroBpeMeHHo pel(oMelflyeMbrx cncrevofi IIIP ynpaBnffrcr.qnxperueHni BHe 3aBHcHMocrH or roro, cKoJrhKocr.r'ryar1u]-i oAHoBpeMeHuo6mno Ha Bxoge cl{cre.IenoBeKy ynpaBrrflroMbI. Kpor"re roro, npoqeAypa piu{xnpyer Bbr[,ilBaeMbre une perrreuwfr.KaK no nuQopvarruu, noJry.reHHofr or npoUeAyp gs , e5, T?K ll nonb3yficb MHoxecrBoM flpeEroqTeaufiuo "cyxeHuro" MHoxecrna Ro. 3nr llpetrnoqreHn-ffMoryr 3aAaBarbcff3KcneprHo.Ilpoqegypa 3aAaercffB BHne gt = ( S, Ruz, On"r, Oo"o, R ). (3.17) 38

HHQoprtaau{flDrfl JIIIP nocre padorrr erofi npoue[ypbl Bbrrqaercf,B BHAe =l ({S} O Oo"r} . UtnoBeKMoxer cBfl3arbreK}rrryrc ctryatn, o"r, peuJeHI,IffMH c fleroM Hx trpnHaEJtexHocru* OE", u{rc c seo6xorurMblMl{ wm Oo"p , 3?E&BiLa Ruz I npo4edypa ewSopa pewenuil flo3Bonfier opra]Iu3oBarh npoqecc qeroBeKoMaururrHoro B3ar{Mogeitcrsflfr. c ueJrbro npwnnrns, o4uoro perueHnfi, rIoEIexerrlero pearrn3aru{u.flpu sToM nnP Moxer au6parr oAHo H3 peKoMeHAyeMbrx cncrevrofi peurenfi wnv npwnfl,TbcBoe, orJrnqHoe or peKoMeHAyeMbD(, Ro, o rreMoH AorriKeHcoo6turrr olcreMe. Ecnn Ru fl B = 0, To 3To peuenl{e MHoMoxer 6uru pea[H3oBaHo.3Eecr .R =Ro fl Ror f] Rur - 3anpeu{eHHoe xecrBo peueHnfi. oopuurHo 3ra npo[eAypa

(3.18)

9a=(S,R,R,Ro);

npo4edypa oqeHKu p$ynbraros peanu3a4uu pewexutt Ha 3HeprocricreMe no3Bonf,er oueHrrBarr aQQeKTHBHocrbnpl{HfiTbrx r'r pearrn3oBaH}rbrxpeuewtit c uenbro KoppeKryru (r pe>rurvreo6yueHrar,wrrl ca;vroo6yrenun) MoAenH gHaani cucreMbr 14 nepeBoAa rlacru vrnQoprvraryrsBHAa { ( cnrya' \

lrylE/

-

-

-

/

\

^ ' .

L

IJerueHue I I

- - -

- l - . ^ -

- - -

n3 c(PePbr urlultrMbl

-

- l

n uqJUPy JruKaJrbtrun

a|'r'oMa-

TrrKH.3ra npouegypa

(3.1e) Q c = ( . S ,R U R u , M r , p t r ) , rAe 9r g - npoUeAypa ooyterIl,In (car"roo6yreHua) cHcreMbl I{ KoppeKUr{Hee Motrenn zuawfi M 1; 3a npo4edypa rpaccupolKu peweuuil rro3Borff€r opraHn3oBarb cJle)KeHlre rtoeurcoil tvtauuHHbrx paccyxdenuil npu rIoHcKe pelueHwi vr ucnorlbsyeMoM npn 3roM rnQopr"rars{o}rHoM6asuce.3ra flpoueAypa Bo3Bpauaer IIIIP csoficrso Ha6nrcEaeMocrn,T. 0. Bo3MoxHocrbycrancBfleHut lrcGrx orHoureunfi Ha uJreMeHraxnpoqetryp rrpwrflrur,,peruenrfi. tlpoUeaypa rpaccnpoBKn cTpo' p1 uTcrr ila ocHoBe rrac4lQnrcauHr{yflopf,AoqeHHofinocneEoBaTeIIbHosTI{ B Ka)KTIo rpoUeAypy ge-npoqeAyp.tvloprQHrcar+ra3aKnloqaercstso DBetreHHI{ yTBepxAeHr{f,o npaBr.r,rrbHocrH [oJrrleHHfi c ee noMoulblo pe3yJItTaToB. \ Oopruur:Io ora npor{egypa 9ro = | lh :9r,

ltz1 92,

Itg 1 9s, CO>,

(3.20)

fflg u1 , F2, . . ., lJg - ycrroBHff Bbr[oIrHe[ufl (yrnepxpBHr.I-q o npaBHrrbHocru) pe CooTBercTBeHHo, 3aIrHcaHHbIe nPoueAyp grr Qz B BHAeh: 9t. C noMOUIbIOSJIeMeHTOB3TOrO KOpTCXa qelOBeK I,IMeeTBO3MO)KHOCTb IIyTeIU B3aUnlogeficrsnfl c cyrcret'rofr ncnxoJrornqecKn rroBepuTb B npaBnnb;rocrb HafiAegHbrx peu ewfi,. Y rs epxge Hfifr., rrp:'rna,4nex(aun e CO, o npe4errff rc T co rn acoBaHHocrb norl{Kn CIIPHHT n JIIIP, r. e. oHrr no3BoJr.flror cr{creMe coo6urart JIIIP o roM, r{To oqepeA}Iofi uHKn noucKa r{ [pr,rHffTr{s oetueurui 3ageplueH; np o 4edy p a u u S o p ua r4uo HHo?o d u an o za opr anvt3oBbrBaer qeno B e Ko -Marrrr{HHoe B3lr{Mo4eficrnne JIIIP c cucreMofi c uenrrc ronyqeHnq Heo6rotrHprofi er',ry 39

craBneHuni

9t=9r

9z- 9r

Pu c . 3 . 2 .

rAe gr

9a -

MHoxecrBo

gJreMeHToB ypoBnfl

MoAenH 3HaHHfi tr

3.3. IlornKa noncKapeuexnf,

un$opuarun. 9ra nporlegypa = ( 9r, 92, 9g, 4cl ,

EA

raHrrbrx; npo 4edypa aero r4arusuposaHHozo npoeKrupoeaHun CTIPHHT, wrn, HHaqe, EpliuoroBa.ff o{creMa aBroMaru3npoBn}rHoro npoeKrr{poBanur ([I{CA). nns JIIIP u cncreMnblx aHanurHKoB-npoeKrnpoBrr$KoBCIPHHT oro nporleAypa q t q = ( ^ SL, ^ o , L g . o . . , M ? (3.24) "*), rAe ,S lrpoeKTuafi cnryaqrfl, H3 r(nacca curyu]fift qenoseKo-MarrruHHoro npoeKmpoBaHHfl, orpDKarouaff npeAMerHo.opHeHDrpoBalrHyro nocTaHoBKy sa,qaqu nocrpoeHn.fi mQoprraawoHlro.MoEeJrbHoro6aguca. (HME) i L , .,^, L roo - flsblKoBblecpeAcrBa orrucanilfr.3rreMeHToB MogeJrbnoro6agucd'g-Hirrlfi ilgaffirrl; M1rBM - Marrrur{Hoe HME. npeAcraBrreHr{e B @orBercrBlrn c BbrIueHUIoxeHlrbIM,JlornqecKag nocJleroBarerlbHocrb npoUeAyp qeJIoBeKo-MaIIruI{HoroynpaBlleHl{fi eHeprocHcrer'lofi B CIIPHHT npefcraBJleHacxeMofi, uso6paxeuHofi Ha puc. 3,2, tge AnP - aBroMamqecgnuori PP - peaJrn3aqfifi rclni noncK peuellufrtl II - qerroBeKo-Maurr{Hnbrft peueuni; OUCY odlercr H cpega yrpaBrreHr{fi; UE - unQopr*raWorntrfi 6asuc; ME - MogerrbHbrfi 6aexc.

Sxcneprur

?tr

E,

(3.21)

yxe paccMorpeHHble [poqetrypbl, B KoTopblx [poH3BeAeHbI

crleAylounenoEcraHoBKH: sl@A, MtlMa, clcry, UlUz, Rlao; @n - MHox(ecrBo 3anpocoB,rrocrynarorrlnxor JIITP; MA C Mr - MHoxecrBoMoAenefi noHcKa orBera no o6lacrnM onpeAerleHnfl3anpocoBi C n - MHo)KecrBocrparernfi uerlu rIoHcKa peulelrnfr, papKr{poBaH}rr,rxuo r'ti6xecrsy M,ai 4n MHO)KeCTBO TeKyUIHXqenefr; @o - MHoxecrBo orBeroB, BbrAaBaeMbrx IIIP IIpH peaKrsrHcHcTeMbrHa 3a[poc; npo4edypa onpedeneHun unSopua4uoHHo?o flaeuca dna npunarun peueuuil ocyulecrBnffer cBfl3b c cncreMofr renec6opa uHSopM:uIr{Hc ueJrbroopraHI{3aIIHH o6pa6orrcn profi nHQopr"raunu 14 sarmcrr ee B nrQopr"raquoHHyro Molenb (6asy gannrx) cr{creM.Oopr"ranrHoera npoueAypa: 9rz = (S, 9r, gz, g?, gc, Mt, M,A), Q.22) .|t Mn HHQopr',raquoHHtlflMoAerIb, xpauflrrla.ff TeKyulee cocToflIil{e oobeKTa; npo4edypa adanra4uufodyuenun ro3Bonffer opraHn3oBarb aBToMarH3HpoBaHlryrouacrpofrrcycIIPHHT Ha o6nacrb yrpaBJreHr{ff.3ra npouetrypa prt = ( L^, 4, Eo|, (3.23) f!9 L ^ - MexalM3M KoppeKryu r'ro4enefi 6as aHaHtdrvr traHHbrx(cpeUcrsa flo3 n floIl,), no3BonffrournfrcBr3brBarr nHQopr"raru{rcB ee MerrrgrrHoM npetr40

Ilomra nol{cKa peuenr.rft (IF) flBnfiercff ytro6Hofi *reraQopofi, noasonxronlefi noKa3arb, {To xapaKTep B3iuMogeficrzus, JIIIP c cucrer"roft orrpegerlfl,eTcE,nocJIeAoBaTeIIbHocTbIo uraroB, HlrTepaKTI{BHo cBff3aHHbrxc nporleAypaMI{ MHoxecrBa Csrgr Mexgy . orr.rMu ruaraMr{ BcerEa HMeeTcMbrc[, tg} noAl(perutensrtfi norurcofr paccy)KAeuvir,r. e. HeKoroprrvr HabopoM yrBep)KgeHrui, HcrrIHHocrb KoropbD( Moxer 6urr ycraHoBneHa nocJretroBareJrbHo. Hau6onee HauIntrIIo JIP s CIIPI4HT rporBnflercr B npoueAype rpacclrpoBKn peueHutr, KorAa rronb3oBarenbMoxer QoprvrynnpoBarbB Auilrrore yuroBnfi, AocTHXeHHeKoropbD( Aorr)KHao6ecnewrrb eMy cncreMa B npoqecce nor{cKa yflpzlBrlsrcrrlnxperueunfi.9rn ycnoBurr rronb3oBareJrb Qopvrynupyer g;tfl KDKAofi ng npouetryp MHo)r(ecrBa { g }. I,IHuun crroBaMu,JIP nossoilfrer co3Aarb B cncreMe cpegcrBa, c noMoulblo Koropbrx csoficrsa pa3peuuMocru wrr Hepa3pellruMocrr,rMnoxecrBa basuce a nHSopvriulnoHHo-MoAenbHoNa tg) orHocr{rerrbHo cnryaqnfi, rpe6yrourirx npuHflTrrfr.perueuuri, Moryr 6urr QopMarIbHoAoKa3aHbIKaK Arrfl ortrerrbHbrxvrogenefi,TaK r{ EJr.snrc6oilt ux npo6nevrHofi KoM[o3ur.u{fi.MynrmMotreJrbHocrr o6nacrn rroncKa pelreH}rfi norpe6osana rrpetrcraBnenufl,Bcex Bo3Mo)Gbrx (nrrrerougx cMbrcJrB AanHofi o6nacru) yrBepxgeHrui JIP Ha ADyx ypoBHflx: ypoBHe yrBepx[entfrt Wn KIDKH ypoBHe yrBep)Kgenrd urn Aoro Hs Bo3Mo)IGbrx THrroB naogelefr trff, MexAylvfotrenbHoroB3anMotreficrswn- JIPE' 127, 371. IJ4tn Soprvranu3atrJ4r Aanrueft urnx paccyx,qemd la4{M psg o npegel eHrui. OnpegeneHue 3.1. Ilom.Iecrcafi Teopl{.fi npoqeAyp rIeroBeKo-M4III}It{Horo ynpaBrleHuflHil3bIBaercfl, pasperauMoil, ecrm,cyulecrByer xorfi 6nr o,tgraaQ$erc4l

THBHa.f, KoMrrc3'uuf, Wg

3r'x

npoue'yp

(. {r, ), no3BoJrffrcrqaff y3Harb i, = l nrcfuro )trBePx
Cpew )'raepxgernrfi IIP Bbrgerrr{MroAMHox(ecrBa U, , } { + }, *otopute t HilnBeM 'rrBep)Kqenns,Mtro pearrn3yeMocrr{rpoueAyp MHo)KecrBa g, n { } nPaBHtlbHocril nonyrernrrrx peureHrci p, Ku(Aofi ua uogeneii unn trIrfi ) t np6ofi Hx coBoKyltrIocru.flpu arorvrpi 6iger paccMarpuBarbKaK ycrroBur, onpeAenfrKrune[puMenr{MocrbnpoqeAyp K Bbrrr'cleHH.fiMB MoAen.Ex\Mil , : qr o3r A ar y r M Bb rp :D r(e l rn e Mn(n a a : g rl Mr). h Onpenenerne 3.2. Bueodou B reopnu JIP HasoseM rrocJreAoBarenbHocrb Itr, liz Fn, B roropoft nrc6oe p, ecrr nir6o aKciioMajIP, nn6o cJreA,crBr{e KaKHx-ro npeAbt4ru[lx yrBepxAeHrui no otrHofi H3 pa3peuruMbD(KoMno3r{_ rufi npouegyp MHoxecrBr

ft

(vr) . torr*acrBnflroulue BrrurcnnrerrbHbre npoqrrrtor= pearr'3arprrc seeexrunrfbrx KoMnognryrfrnpoueAyp s cnPHHT, 6ygenr 3aEaBarborobpaxeHHeMBHAa n K

('n.\' AXtr Yr, -->,, t " ' ' - - " t ' , * '

3Aecn A cG - MHoxecrBo rrBepxgeHni, om{cbrBaroqlx csoficrBa cpTyarrufi npHHflTHffpeuremni; E =E" U Eo - MHoxecrBo sJreMeHrosHME. .[,arnroeoro6paxeHue Koprexcy ( A* Ei, lri ) scerAa craBur B coorBercrrue p, yrBepxAeHHe npaBruIbHocTllnon)rqeHHblx pe3yllbraroa-peueuld. flonsrue npaBrmbHocrunoffcHuM onpeAerrennffMu [6, Z7l. Onpegenelare 3.3. flycrr A cG - HeKoropoe yrBepxAeHne,om{cbrBiuoulee npeFlonaraeMble csoficrBa 3neMeHToBcrryarlr{H npn}tffTr{.fi peruenrui ^S, ; lr i - yrBepxtreHue o peanH3yeMocTH npoqecca BbIBoAa (noucrca peruermfi) n - yrBepxtrerne, orrncbrBarculeero, rrro Mbr rro npeA- t .{.= l (9r' ) no HME;' p,

f

n

nonoxeHHlo troJIxlIbI non1nn415 B pe3ynbrare BbrnonHenunnpoqecca (r, ) . ,5, Eygevr cq'rarb, ,rro npoqecc, 3aAaBaertui ft (g,' ), wrcrltqHo npaeuneH i=l (no ornoueHuro rc ( Ar , Fi, ero 4 ) ), ecJru rrpn KDKAoM BbrnoJrHeHHr{ c 3JreMeHrauu S, , yAoBnerBopflIolr$Mn At , cyulecrByer peaJrn3arlur gToro npoqecca, Koroptu yAoBnerBopfier pf tr Mfl rcoropofi cnpaBeMHBo yrBepxycrroBuu, rrro npouecc .ft - (r,' ) saxornnrrcx. l'=l

onpenenenxe 3.4. flpouecc (no oruoluerrurcrc(A* 42

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PaccvrarpwBaf,.npouecc

rcarc rporpaMMy, pearr'3ye}ryro Ha ,tr{rr) 9BM, MOXHOcrMTaTb'IITO eCnn nporpaMMa yAoBIIeIBOpfleT yCJIOBHffM, 3a- 1 f A'aHHbIM t p, p ), ro lrpn Aocrtl>I(eHHIr nrcboft H3 ToqeK nporpaMMbr, c KoroPrIMH cBt3tlnblonpe[ereHlrble {pr, 1t-;}, moraererBJnou$. tp, , pr! 6yAyr cnpaBeAIII{BbI' Cne4ona-reJlbHo,ecrlu Aocrnruyra KoHeqHaf, ToqKa nporpaMMbI' ro cnpaBe[IlrBo yrBepxAellHe o npaBIlIIbHocTH (Rocrnramocu), cBff3ilHHoec grofi ro,rKofi, T. e. nocrpoeruraff nporpaMMa 6y1er qacrgwlo npatrrnr rraj.. TT*rDrurDnrrltrr /4t^ AuKa3areJlbc.Il'aTIOJIHOH npaBHnbHocTI{nocrpoeHuofr [poIpilMMbI BHaqa[e Heo6xoErMo Aol(il3arb ee qacnilfiyro npaBrrrrbnocrb, a 3areM JDI(OAoKa3arb, qro rpe6yer"trfi pe3yJrbrar 6yner nonfreH. HHrepuperarplfl nporleryp MHoxecrB" gi t ) s o6nacrn Hx trporpa.nnrofi peurtsal4lrtrno3BotrteT olrHcblBarbHx Bsal{MocBfi3bc I4ME H aBToMaru3rrpoBarbnpoqecc nocrpo eHfifi npo rpaMM, o cylrrecrBnflrorr[D( noncK ueo 6xoArlubD( yfipaBnfirorrs{x peuremn?. Hueruro era B3auMocBfl3b H omrcbrrlaercs, frBep)Kgelrg.srufi JIP.

la ^E\ \J.LJ )

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3.4. Moaenunurfi6asnc nprrnTnf, peurernf, Bnrdop MoAenbHoro 1asuca H MeroAoB noucKa peureHni ocHoBbrBaercff Ha norpebHocu npaKil{qecKoro IIpHrIoxeHHfr.c frercrM Ha3HaqeHnffcHcreMbr r{ MHoxecrBa llpoqetryp npwlf.frTllfr.peureHrul.MHoxecrso MoAeJrefin CIIPHHT crpollTcr Ha ocHoBe MeTotros smMcflnrenrnofi MareMarHKH,JIorEKr{ r{ TeopHH MHoxecrB [5, 12, 40, a9]. trencrBnre[buo, Bce 3a,qaqn,peruaeMbreB Hacroflulee BpeMfi Ha 3BM, npetrcraBnxrcr codofi MHo)KecrBo[porpaMM c pa^enurofi nomrcofi rIoHcKa peualoqero nyru or trcxogrofi mr$opMar4{r{ K uenesofi. Ilelesoe o6leArureHHesrHx [por?aMM B paMKax MHoxecrBa rlpog, IIeAyp rlo3Borlfier c rrcnonb3oBaHueMyrBepxAenrui JIP aBroMarr{3u{ } poBarb npoqOccrt troncKa peIueHIai B MoAeilbnonr 6aguce, .[arurrrfi 6asuc s CIPHHT coAep)Kl{rqerblpe rfina uogurefi: BbrrucrruTerrbHbre (IIPTI), nonarcoanre6par'rvecKue I{ Jlorl{Ko-m{}rrBucrr{qecKr{e (IIPT2 ) , Teoperr{Ko-MHoxesrBeHHbIe(IIPT3) I{ E{arlororue (IIPTa) rrrogenu.B xaqecrne nparprr BbrBoAa Mrn gwrx uogelefi npnMeH.ffrcTMHoxecrBo anropurMoB (nporpar"trrr) rmanupoBaHu.flBbIrMcJIeHnfr ua gTHx MoAerrflx,oflpeAerleHlrbrxB nporreAypp( Mxoxecraa {9; } . KaxuDtfi ug alropllrMoB ImaHr{poBaur{.fi, ocHoBbrB:lflcbHa yrBepxgeHuxx JIP, nuler orBerbl Ha Bonpocbl: Karcne [poqeccbr pai]pe[rnMbr Ha MoAerrH (nonHocrblo npaBl{nrHu) ? CyurecrByer nr{ norcanrsaa (w^ omroro rl{na rtaogenefi) KoMno3rarlr{r npoueAyp

crpoffrrlafl Mn nrc6oro ;r@), pa3pelrmMoro npoqecca Ha MoAenu alropuTM (nporpavnry) ero BbrnorrHemrn? Cyuecrayer nu rno6alnHu (ws pa3rrbrxTHnoB rvrogenefi) KoMro3HrIHt 43

m (ro) , crpof,Ilrafi Ann nrcGoro pa3PeIuHMoK)npouecca Ha MHo' _[. c=l xocrBe uoAeneft altrcpnrM (nporpaVr'ry) ero BblnonHeuu.n?Cyruecrnyer JIH enFoptrrM, no3BorrfirouuniAnn npboro npouecca Ha MoAeJIuI{nH nx coBoKy[? Eocril yK&taTb,6yqer IIH oH IIoIIHocTbrcnpaBHnbHbIM(paapeunrr*rnrnr) CoorgercrBerno Ntfr Kaxgoro rrma uoAenefi B cl{creMe HMeercfi MHo. xecrao (orrprrro e Wf, nonoJrHeHfir) r"rerogoB IrIIarIHpoBaHI{fisrnucreHuft: Mo4enefi - r"reiog Tpalrsr{Tr{Bnoro3aMbIKaI{nr rpa$a WIfr BbrntcnnTerrbHbD( Mcro4bt nprlrofi u o6parnofi nonsrt [a0] ; Mfl tlorHKo'arre6panuec' [39I, KHx H ,Ion{Ko-JlrfiIrBncrl{qecKru( naogenefi,oIIHca}rHbIxfigbIKoM norHKI{ rtpeAHKaroB nepBoro nopffAKa - Merog pmorrrcrryfi, ocnonaunrtfi Ha BbIfiBleHI{I{ non{FlecKoro crregoBaul{.nHeKoroporo yrBepxEenl{.a Hs MoEeJrH F7l; g,irx E{uronoBbD( Mogerreft- Merog noncKa B cerffx llerpn 1321, [Ipn opruursaIgrH nnarrpoBarrnfi B vrynbruMotrenruofi o6nacrn noHcKa Hcnorlb3yeTcfi npullr[dn pe3onrolr{fiu yraepxgeHru JIP 125, 26, 271, Pesutrnpys cKasanHoe,floruKa noucKa peruenl{fi a CIPHHT Artfi Bcero MogeJrbnoro 6agnca orrpeAerrxercn BbrpDKeHHeM npoue$p

JIPE= (A, E, tt,y,' q =trl ' '(p-)), u

- IPiu n

J I P \ = ( A , E' , l \' , Ft i , . I . ( r'r ) ) . f = 1 3Aecr

n (p, ) c @i .{. f =1 '

rpaKrylorcn KaK npaBlrnaBbtBoAa

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P

(3.28)

3gecr 7 - uuoxecrBo repMur{aflbHbrxcrrMBorroB;H - MHoxecrBo cI{HTaKcnqecKllx npaBEI, npu noMouru KoTopbrx H3 gneMeHToB T crponrcfi BblpaxeHll"fi V; V MHoxecrBo [paBHrlbHbrx rrrpaxeHlfr, B rlnclto Koropblx 44

i

t__

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P u c. 3.3.

(3.27)

B MynbrnMoAenbHofi cpege H B Kax(trofi ng rnnoBblx MoAe[eft cHcreMbl. OprauHsaqufl ?rnx rrornK B CIPHHT nplrBeg,eHa Ha pl{c. 3.3. flpu sror"t sKcneprbr CIIPHHT r"roryr Brrn.flrb KaK Ha onpeAenenne yrBepx4euufr MHog) , ,}, raK H Ha oneMeHrbr MotrenbHoro u nn$opvrarrnoHnoro 6axecrB { t 3HCa, [yTeM BeAeHr{-fl Ar{anora c cncrer"rofi qepe3 cneuuaurHrlfi Bxotr. on

= ( T, H, \Y, O) .

I I I I I

(3.2d1

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m c @, {. (e") v a=I

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Au=(o,x,E).

(3,2e)

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floAcncrelura yIIpaBrreHHs 6asaMfi AaHHbrx

crHTaeTcfl rryreM Hc[on63oBaHl{.fi AefyKTrrBrrbrx MexaH}r3MoB [or{cKa B dasax snaurdi H AaurIbD(. , fI o n cnc r eMa o6yrIeHHs. flo[cncreMa frBrrfi.ercs,gJreMeHToMcr{cTeMbl' no3Boflfircu#M qpraHu3oBblBaTb ppI{eHTaII}Ito sceft cucTeMbr Ha ry nry ,trrJry oOnacrr ynpaBneHuff nyteM nono'nneHus. 6asfi guarrni u Aarnrux. .Uas oroft qerlH uMeercfl nd6op qerroBeKo-Merr[.rHr{brx npouetryp ofuJ reru.fi, no-

P n c. 3.4. Oynxr[roHarlblraf, Hrnepnp€rarys apxfireKrypbr. AHUTH3 OygKrry1fr , peann3yeMbD( cl{creMaMn TI{na CIPHHT, no3Bonnrl HuTepnpernpoBarb apxr{TeKrypy cHcreMbl B sfitre HePapxErtecKofiKoMno3l{t-u{u crren/rou$x noAcncreM ( pnc . 3. 4) : fI o g c H c r e M a c p e A c r B K o M M y HHKaTIHT{. llogcncreua ffBrrfiercfi BeroruIefi noAcHcreMpfi s cMbrcneopraHrcaqE{ o6pa6orru mr+op. MaIrI{H' nocrynarolqefi or o6leKTa n cperDl ynpaanennff, IirP, oKcrreproB. Jln-1 sroro HIDtctI ycJlym noAcncreu: o6urenufl, - B rlerrx pacno3gaBagr{a H "nolilrMaH}r.fi" BxoEroto sanpoca or JIlIp, gKcnepra u aAMuHI{CTparopa; ynpaBneHr{.8 H nprlHfirir{fl pefteHrtri - B uenfix nocrpoeHHfi rurrfoprvraruorurofi MoEenH no reKylqeMy cocroffHHlo o6tercra ynpaBrleHl{.f,,opraurr3arlrdt{ Bbrpa6orrcu npnnsrrn H peaJrrrsar[fi ynpaBrlfirorrryD(petueHlni, fon ,oo"rrerBope_ mu ntQopMaI$oHIrbD( 3anpocoB-qelroBeKa; oGyreuur (agarrtais;1 r ireJI^EX opHeHTaIU{Hcl{creMbl Ha o6nacrr npnMeJreurrff; npoeKTnpoBagr{f, B IIenD( qoloB eKO'MaUIUHHO nO KOHCTpyHpO Barrur ynpaBnffrcIrlero nporpa,MMHoro KoMnnercca; cpeAcrB nporpaMMHofi nor.qepxKlr _ B rlensrc nurGonee nonHoro yAoBrlerBopeunff nontgogarenefi qeloBeKo-Marrrr{HxbrMn Bo3MoxHocrtMH cHcreMbU ynpaBrleHnfi 6asaMuananrni r{ AaHrrbD(- prirfi,opragn3arg1f, xp aHeHufi lntQo prvrar[IoHHo-MotrenbHoro 6aguca cHsf eMbr. AC^

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eroro B CflPHHT cyulecrByer cucreMa craxgaproB Ha o4opr"urerure npo. rpaMM H Hx npeAcraBrlem{.n B BHEeHcxoggbrx,o6rercmbrx H 3arpy3orrHbrxMorynefi n 6u6nnoreKo( nPorpaMM M3 cncreprtrr,B KaqecrBe cr"r.gapro3 Bbr6punr npeAcraBrreHr{ffuog5rneft B onepau{oHsofi cncreMe OC EC. Tpo*"p]4outylq cHcrerwycrpoET Ha OCHOBe CpeAcrBnperpaHcJr n$u n nauxe nporpaMMr{poBarrr{.8 nn/l, a ncnoJrb3oBirHHecraHtraproB Ha MoA}DrH H CpeAcrBa peAaKmpoBaH[fl csngefi B Morynflx [o3BoJrffer crpouTb nro6rre rlporpaMMrrbrenporleccopbr. Paccuorpl{M KparKo pexqMu pa6oru rpaucrrnp}norqefi cr{creMbr CIIPHHT H IIpHHIPIIIbIee opraHI{3aIII{H.flonrsosareJrfiM cr{creMbrfipetrocr:rBneH Ha6op fi3blKoBblx cpeACTB,onpeAeneilufr H MallruryJlnpoBanutrnnsoprrraquefi, lretoAI{Ka npoeKTHpoBalInfr.cl{creM npwnfrT:aff peurenr.rfr.Ooprvrynnpya 3atrag}re Ha [poeKTHpoBaHI{ecHcreMu (ee aganrarqlo)wru ngueueHre M3 u lanH51x), qeJIoBeKCTaBHT 3agaqy u c noMorr(hlocpeAcTBAHarroraAoBoAHTee coAepxaIrHe Ao TC. tlperpaHcrlffTop, ilon)ryafl. Ha BxoA nocJregoBareJrbHocrb orreparopoB' oru{cblBarcu$x' HanpHMep' 3a,qaHHeHa rIpoeKTHpoBaHHe MoAeJrHnpeAnaerHoft o6nacrn, Hcnorlb3yfi ceMiulTntrecxuri pena*rop Mo.qerrqgnarnnl c6creMbI' CTPOHTIOrrqeCKyIo. CXeMy CBfl3r4sIIeMeHTOBMOAenH,OKglrqarenrHUfi Bapnarrr roropofi noMeulaercff B o6rerrrryro 6n6nuorery M3. Orulcanus npolleAypHblx cocraBnfirou$x o6lexnrofr vrotrenn guaunfi nocryfiarcT Ha BXSA rpaHcrlfiropa IIII/1, a 3areM (r cnyrae npaBnrrbHofi rpancn ^*i) n 6m6nuorcry o6rercrr{BHblx rvrogynefiIII/I. O4Haxo He Bce rpoue4ypHbre cocraBJrsrou[Ie ormcblBalorcf, ff3bIKoM nn/I. Ecrr cocraBnfircu.0{e,Koropbre om{car{br cpeAcrBaMn fi3brKoB oOprpau, Accerrr6nep H orurcanufl Ar{aflora. B sToM cJIWae rur0oprvrarg{x o @cTaBnffrorr[lx qepe3 npeTpancrrffTop c ,rgl4srlbro ceMaHTr{qecKoropeAaKTopa M3 trotratraer B JloruqecKyro cxeMy cBfrsH gre53

MeIrroB Mogentr, a caMH@craBrrflroul{erpaHcrrnpyrorcfi or[erlbHo. I4x o6texrHble r't,nflH 3slloctrcE B @orBeTcl3ylou$e 6n6nnoTeKH, xot'Oplte cB.ff3brBalorcfi c o6rercrrofi 6u6truorexoft M3 pegarcropoM cssgefi H )Dl<eo6teguRefiHbtc3amtcbllarorcf, B 3arprcouryro 6n6nuoreKy Mogerrn gHarrai cncTeMbr CNPHFIT. Henpouelypnble mcraBrl.filouge o brerrnofi M 3 (yra epxgeHnfi, BbrcKiltbrBgrrrrf,.r r. n.) BbrEBJI.ErcTcfi [perpiHcrrETopoMr H AIIfi HHx crporrrcff norHqecKrrecxeMbl cBfrsunonsrnfi flpegMerHofi o6lacrn. MHoxecrBo raKru( JrorgsecKltx cxeM cBfrgt,nonxmfr, om{cbrBarous{xcnoco6u peruenu,roupegeneH}IbD( KlracooB 3a,qaqynpaBrleHnn, obpaayror KJracc sKcneprHbrx Mogerreft.flooteAHne frBnfrxlrcfi notrcxeMaMuM3 cucreMbr. Mrrnrrccc-rnn

rrlYtlrArrttrlfrt-rv r'fv+vA\,

qrf,alraur^D 4Iwlvlvlllvp

aFwavwai.t VvDvA lnvn

ttfl ltllrt

Afrr^LrDa' r'E'v Ltffnl|'DfltO.I\rl-L+tt

cuocobrl peureHuff onpeAeJlexHbrx KnaccoB 3aAaq ynpaBrrenrr.fi,o6pasyror IJlaccbr BbFMctrHTeJIbHbIx Mo,qerlefi,Koropbre TaKx(e mrrffrcTcfi noAcxeMaMrr M3 cncrepru. O6teArurenHe Bcex noAcxeM o6rerruofi rrogenn gnaHuficpeAcrBaMn petraKropa cnxsefr OC EC IrosBorrffernon)rvHrr'6n6nuoreKy 3arpy3oqHofi protretIH sHaHuft, Ha Koropofi trroxno crirBnTb 3a,4aru pacno3HaBxnr4g.cnryarryrfi H rror{cKayfipaBnrroulnx petueHlni.

[-naea qerBepraH nPoEKTI4POBAHHEMOAEnEft npEAcTABnEHHF hHOOPMAqht4 B CHCTEMAX npHHHTl,tR pElI EHnn

OArulr"r H3 HarlpaBnennfr noBbrueHufl eQQercnmHocrn o neparuBHo-Al{crrerrlepcKoro ynpaBrleHxff pe)KnMavu paborbr 3HeprocncreM nBrlffeTcflco3Azurne nporpirMMHo-zurnaparHbrx cHcreM rrpl,i^'l'frT1,1^fr. peruexn?, aBToMarH3upyrculrx [poqeccbl pacno3HaBaHnflcnryarylft H noxcKa yflpaBrrffrouptx peruernal, B rcaqecrBe o6nacrH noHcKa peureHroiB TaKHxcncreM:x Hcnonb3yercx M3, HHTerpHpylouafl' B ce6e sce ac[eKTbt, xapaKrepn3yrouge pa6ory gHeprocucreM, MeToAbI' npI{eMbI H aIIropuTMbI ynpaBJIeHH.E sHeprocucTeMiur{. flocrpoeune rarcofi obnacru IIoHcKa rpe6yer paapa6orKn cpetrcra QoprranpoBaHr,rfl coorBercrB).toulHx MoAenefi cpeA,blu o6rercra yflpaBneHnfl,pac[o3HaBaHn.fl H rc[accnQnxaqn'ir cHryar+rfi, rroucKa u nrrpa6orKn perueunfi-u trpyroro, r. e. scefi nn0o prtrarprn, n pncyrqefi o 6n acrn yrrpaBneHHr 3Hepro cHcreMaMH. Bprecre c reM o6nacrr noncKa tronx(Ha6rrrr KoHcrpyKTr{BHa,T. e. rlogBoIrf,lu- aBToMarH3HpoBarb npoqeccbr rleJroBeKo-MnrrrHHHoro npnHflnre peureHnft c fIeToM y[paBneHnff 3Heprocncreuofi B pearrbHoM pracrura6e BpeMeHH. PaccruarpnBaeMaffo6nacrl nplrMeHeHrrsCIIPHHT xaparcrepn3yercffHarrutIHeM e Heff 6onluroro KoJluqecrBaarIroplITMoB, uerleBoeo6re4ruenge KoropbIX B BbItIHCJIHTeJTbHbIe H AHirnoroBbreMoAenH no3BoJr.EerH:D(oAIfrbynpallJIffIourHepeureHrrr. Bnaecre c reM [nn arofr o6nacru xapaKrepnbrH onucaHx-s 54

[poqeccoB noHcKa penremlfr,npellcraeJreHqbre B BHAgHer(oropbrxMHoxecrB yrneprqAelil{fi (excneprxble H Teoperul(o-MHoxecrBeHHbre rurogenu).Bcr rur$oprtlaqrx (rtlogenr y[paBnflrcu1efr gexreJrbHocrn np,a oneparr{BHoM 1,pHHE-

Tlftrf rrsr

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DAnu66 ^^ r-^r^r itePr-rvv cu iiPcAcra3iieii-rig,

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Oa3HpygTcfr. Ha noHffTr{H riloprtrarrr-

uofi cucreMbl' 9To no3BoJlfiernocrpouTb eAHHoerpe4crzrBrreHge Ipasuornmrofi mifupvrarryH, eOf,JIaCOBalrHoe B paMKax etrHHOrO QOpr,,,rarrHarnra. Ytmumax ro, r{To rurfopr"ra4rfl, xapaKTaprryrul as,olnacrb yrrpaBn enLtfl., MOXeT Oopa6aruBarbc.flqerbrpbMff TlrrraMu rro4enefi, onpeAexg, no*pur*, oroft o6aacrH KDKtrbIMTHnoMlrogerefi. Botvucrturenblbteuodenu rroKpbrBaror o6nacm 3atraq oneparr{BHo-AncnerqepcKoroynpaBrleHHfl.,orr4cbrBaeMyro MeTOtraMH

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o6nacrl 3aAarlnrrpa6orrcu H rrpnHnrlfl yfipaBnflroullx peruenrui .,Iuanoeoeute uodenu noKpblB:uor o6nacrb 3a,qaqqenoBeKo-MilumHHoro B3:lr{M o\eitcrrjun npH yrlpaBneHnn, o6yrenrul H npoeKTHpoBaHrM.Teoperurco-*rHoilcecrseH^ue uodenu tloKpblBilK]r o6nacrb oIIHcaHHflsJreMeHToB xapaKTepu3yro,q,uulHblx, ugrx o6lacrb y[paBJreHr{fi. AHa[Hs npnMeHe]rnffpa3Horo rlrrra uogelefr noKa3arr,rrro HX coBMecrHoe rpocro Bo3Moxr{o, Ho s Heo6xou}rMo. CnelonarerrbHo, :tXglT3tl_-"r s r-rrryiitr Aonxeii 6ltru MexarII{3M,tlo3Bolr.srculurirlpeAcragrlrrrb MHoxecrBo proAenefi B HeKoropoli cnnramrori KoMno3r{rrrrHH irMerb MexaHH3MAocryna K Mogerrflu n nrcdlrM Hx sJIeMeHTaM. costraHHe MexalIH3ManpeAcrilBJrerruflMrroxecrDa MoAenefr n nar"rarn3BM HMeer notr coooil peanrrrylooctloBy, IroroMy uro cgcreMa clry)KHT Qopr"rarrbHilfl 4lfi CO3AAHHfl, CpeAcrBHllTcrpanbHoro om{caHH.8H [peAcraBJreHH.E nroopr"raIs{Ho Bcex rr{nax uoAelefr cr{creMbr. Enr*'rrfr Mexan'sM Aocryna paccMarp'Baercrr B nByx acleKTax - Aocryna c uerlblo aBTOMarH3HpOBallHoro HJILIaBToMar[qecKoro rroHGKaH rrpv:H'{r]frfl. peureuld r{ Aocryna c ue''bro orrpegeJre'HrrMoAeJrbHoro 6asuca. 4.1. cerr l'lerpr,rKaK cpencrBonpeAcra'ne'n' unsopnaaqrn B noc'letrHue roAbl cern flerpH [4], 42] 3anoeBarruurupoKoe rpgsgs]r1ae KaK YAoornrfr w Harna4rntti HHcrpyMelrTorulcalrnq roAen -ornuque efi,w flpoueccoB npeo6pa:oBaHr{fi rurtboprvraruaH. B or rpalHur{oHHbrx aBToMaroB, cern flerpH no3BoJlflIorolutcbtlarb r\.nroxecrBopa3Horr.rrrHbrx vrogerefr H npoHCXOA.EIIS'Ie B HHX npoueccbl IIyreM ycrarroBn gHHfrrroKarrbHbrx orHoru entdt MEXIY

KOMNOIICHTAMH H OTCIIC)K]I'f,AHHfl.JIOK{I]IbHbIX H3MEH ENNfi COCTOflTUNI

scefi cllcreMbr MoAenefr. Onpegenexue 4.1. Cerr llerpn - 3ro Ha6op ^A/= ( p, T, I.-, H, Mo) ,. rtre P - rcoHeqHoeHenycroe MHoxecrBo cHMuoJroB,HNreuyeMbrx MecraMH; T KoHeqHo e Herrycroe MHo)Kecrrlocrrrvrtsonoa, r{MerryeMbrXnep exotraMH;

F:p x?.*{0,l}l .- Qyl{Ku}rtu'tru{l{Aellrllocr,; H :T x p * {0, + l

Mo:P

+

{0,t,2,3,

}

-Haqarbrra.rrpa3MerKa.

H1

r u c. 1.t,

Cerr flerpH npeg,craBnflIor pa3MeqeHco HbIM opHeHTlIpoBaHHbIM rpa$or"r U T. BepuII{HbI P Beptulnr MHoxecrBoM Mecra uso6paxarorcx Kpy)KI(aMH' Bep' nlHrlbl-nepexoAbl - 6apnepaMu. Hs nep' [uHHbI-Mee'rAp B Bep[Iul{y-nepexog, I ne' Eer [yra, ecII]I H TonbKo ecJII{F (t, p): : 1. Hs BepuHlIbI nepexoAa t B BeP' rrrHIry-MeCTOp BeAer ura' ecJIH H TOrIb' Ko ecJIH H(t, p) = l' BePurI{HbI-Mecra noMeqalorcfl uerIbIMH HeOTpHUaTeIIbHbl' MH tlucnaMu (pa:r'rerrca Mecra' MapKu' rPa$ruecrcor"t B ponrca), KoroPble

nso6paxemur cern pa3MeularcrcffBHyrpH Mecra-KplDKKaHnn Hso6paxalor' cfi @orBercrBylounM qHcrIoMToqeK (Quurerc) B Mecre'KPYxrce. Ha puc. 4.f noxa3aHacre4nouo ittu flerpu: P = {Pt, Pz, Ptl , f

lMerKHM s pelynrTare nocrreAoBarerrbHocrrr cyulecTByeT[ocJreAoBamrrb[ocTl p:BMeToK M' , gnec:or _ croBo H3 MHoxecrtsaI* scex Ws.-lt. tlepesR ( ) dygerrroSogHaqarr oK. fo My 6yaeruH&rbrBarr B coorBerL

= to, b,c, dl, Ms= '|"r" o6'.

npniirMaror niiiub EEa sHaqeint.n:0 n 1, Tax rarc QyHxruru HHrg{EeHTHoerr{ Hx MolxHo npeAcTasnrb KaK MHoXecrBo nap (p, t) wtv (t, p) TaKHx' tlro Spxtttlfi F (p, t) = I HJrHcoorBercrBerffioH (t, p) =1. Taroe rpeAcraBJIeHHe Heo6xoFlMo E-rff Toro, tlTootl [pHMeHffTbK HHM TeoperHKo' r{HrI{AeHTHocTr{ MHoxecrBerluble oneparyH. Kpor',reroro, qepe3F (p) 6ygeN!o6oguaqaTbMHo' wmr N, ecJrHB R (/\) p:urMerKa p)rer cpa6orarb npu IW'.tFqecrByer ) K e c r B o t r e T l F ( p , t ) = l ) ; H q e p e 3H ( p ) - M H o x e c t n o { t e T l H ( t , nepexoA A9STHx.HM - I nepexotr.Eor pa3MerKH K pa3MerKe. ) . Cerr llerpu QynxryoHupyer, ntoOof,pa3MerKHns R (il). cerbHaqnHaer Ce6 flerpH _ K a x g a s p a 3 M e r K a - -t t o Q y H r c r u s M : P - + { 0 , t , 2 , 3 , . . . } ; pa3MeroK npoucxoI4s. Cuesa paavretxe HaqarnHofi npn SynrcruoHnpoBarb EI{T B pe3yrlbrare cpa6artlBaHl{.ffoqloro H3 nepexo4oB: ceTn flerp* Nr u .r1/zarcs,,'-iiir.r"i'"::",t::."t Mecra olp:r'urreHbr. M, ecrlu V p€ P, M(p) flepexog / taoxet cpa6orau r{pn pa3Me-trce rlvce'r n""pn N1 n N2;;ru"iH" "uiJ*f"'"*l;^',rr*rooo*," Ha6o_ F (p, t) >)?0. 3ro ycJIoBHeo3HaqaeT,rIIo Bce BxoAHbIe MeCTanepexOga/ to"ot ctrltraeM' 'roo n"ron *;;friTronR 31-ffi. - pannn,ecrrr{R(i/r) _ = oAsoft 6rt no xoTfi ""on f) co4epxar p 1], F(p, wfo raKue, Mecra t. Bc€ [r.

o*#ff ;,;"'{:ff:#';1i"ffiTff"#;":#sro,r, woM(p') (K sA,r nro'on

-;Ifr.""Jffi *ll#T:frffi r":r#ffi ";;; f :#r;:fiTr

Qnurxe. nepexoga / upu pa3MerKeMnocneAH-s.flcMeB peaynnrare cpa6arbrBaHrr..fi Y p e P, lt tp> = Hrrercfl pa3MerKoi M' no clrerorrculeMy npaBl{ny: - FQ), t) + H(t, p).ApymMr.r crroBaMl{,repexoA f H3bIMaerIIo M :M(p) otrsofi Qnuxe r{3 K3lK,qoro cBoero Bxosroro Mecra H Ao6asn.Eerrlo olFtofr M@To, T. e. B KtDKAoeMeCTop' TaKoe qTo Qruurce B KaXAoe cBoe BbIXoA,Hoe H (t, p) = 1. EygeM cr{HTarb,rrro pa3MerKa M' cnegyet 3a pa:r"rerrofi M, 'Iuf . AM, npe$xecrByer M' u o6ogHallarbaror Qarcr: M llepexogpr cpa6arbn:lror rrocrreAoBareJrbHo,Ho HeAerepMHHHpoBilHl{o: Anrrrr

r{Fnr..^rrrr.r..1

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cnl6arr,rnal'r,-

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Th"

BbrnucbrBarr'eM cHMBoJIoB

nepexo'oB HaqrHiuou.u{xc.E B xaqaruHof,seputnteMs,

;t;*j*reror, .'c M, raK """""d"u*1#"H:?r;Lrg1ffi t#I"ffir""#:ffiTf.", #in*r*i, Oyd.*;;po Ba'u'.Mo*"J

nB nnercs I rlHrrn'en)"'"*T::1j3' "Ha,ran'*rf, ;6p"rrrxr". ";;;;{;HjFff"Th Hro.i^i_i"ifi

or_.ar' rl'' rr_

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L_o" srorc pz; rvmxeJ#r,L*#,xr'"x}'"#t 3:lMecro #;*tff-ruru;r;",ry, nsMs, io =,,i; rs-ru{x,"-rin""r"s x<wBbr..,H "rr*H noeroMy cerb

nro6ofi r{3 rulx. Cerb ocraHaBnnBaercfi,ecJlr{ lrpu HeKoropofi pa3MerKe HH ffi:Tffit"Tx'Mbl otrHHH3 nepexoAoBHe Moxer cpa6orarn (ryrurconax pa:r'lerxa). 56

s7

';pIff Ortremlu HeKoropne ocHoBHbIe nocnetryrcrr1efo l{3rloxeuu.r Qar
I I I I I I I

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IpaSonoe npeAcraBtrerlue cerefi llerpu no3Borrfier Harn.Elgro H3o6pp1arb HX CTPYKTYPIIbIE OCO6CHHOCT}I H &IHAMHKY SYTTrcuHOHHPOBAHHff. Hb Wfr

I I I

P n c. 4.2.

a rrl<)|(e

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4.2. Il pencr0gne'xe Bbrqrrcn,rrenbHbrxMoAenefi ArF onhGaHHn anropHTMoB OneparHBHOroynpaBneHrF pexuManrrn pa60rur eHeproc]tcTeMbl

58

xtc2 - H3MeHeHI{e di trT - It3MeHeIMe Ui ac4 - pacqer ycraHoBrlBruerocs pexrMa; pasrer nepexopfloro rpoqecc€,i ffio - nponepra yn; *l - npoBepKa L - I'1i 1e I npoBepKa T-YI. neynpouieruroro pacqera ycrofiruruocrr{ crporrrct conoKymrocrr .ftr ropof, paccqul:t'rBarorct [ouoJrHl{Terrbrrbre cBeAeHr{r Nrfr wcflsFrcpa.

rc5 re -

Mo4enefi, n Ko-

HccnegoraHr{fi MHomx aBTopoB [], 4, 8, lz, u, s7l noK:ubrBax)T,rrro BCe 3a'qatMAl{CnerqepcKoro ynpaBneHHfinpeAcrilBHMbrB BHAe MOgenefi, Ha KoTopbD( MoxHo opraHH3oBblBarb pellrenr{ff (rrrwrcnennfr) . Tarcue MoAerrn, qpeuoxeHrrbre 3. X. Trryry, Ha3brBarcr euquarurenbHbrleur [3g, 4oJ Onpegenenue 4.2. IIpo crofi BbrrucJrnTenbHofiMogenbxlI 6yger"r Ha3brBara napy ( r, A) , rge.r - Hafup nepeMeHrrbrx;A - KoHeqHoeMHo)r(ecrBoorHoIIIeHuIi' cBfisblBaloulrD(slrr ilepeMeHllble. OrrrorueHnff coAepxaT cBeAeHHff o B3aHMHofi 3aBI{cI{MocrI{ [epeMeHrrbrx H ucqoJrb3yrorcfl. Wrf,,BbFrncrreHrrt 3HaqeHltri rloclretrrrux. flou.srne "on{ourenufl.i' KouKper}rgnpyercfi TaKrrM ID/TeM' lIrc OnpeAeIIflrcTCflqaCTI{gIIbIeOTHOIII€HHfi, 3elr-.aBaeMble HafupOM 11e. peMeHIIbD(Ir MHOXeCTBOM OneparopoB, BxoAaMn n BbDoAaMI{ KOTOpbD(flBilflroTcfl.nepeMeHHbre n3 eToro Ha6opa. 59

slqs

ir i I

MOAeIIH IpaS, BeprrrHHaMH KOTOPOTOmrrffrcTcfi nepeMeHIIbIe H OTHOIIIeHH-fi nepeMeHHblMll' coeE{rrflrcT oTHorrreHH.ff c HX CBff3AHIIbIMU n pe6pa roloporo

rarofi crPyK' cxeuoil uodenu. MoAennflr'nfrercfr' Oyirril Hagtnarn nozuqtecKoil HeonpeAefleHllble I{ gIIeMeHTbI I{MeTb Moryr roropofi rlrpof nHQOprvrqlul,

3HAqeHU.fi. SbItlUC' t4s OnepasPOB, IlopoxEaeMblx OTHoIIIeHH'MH MOEenI{' Co3EtlrcTcfr' 3aBeplueHnfr' Kaxtroro nocJle cocToflHue ee rT\Tenb\ile npo\eccbl, MeHfiIoIIU{e - UP.J3Nodutu Ha3oBeM napy (14, W), t*e ry oneparop^, tonorHueJil ll cocTonHuf; xa6op oIIeMeHrloB M9AgIIH, Ha3blBaeurrfi cxeuoil BbIqHcII{TeIIb' "orri"uoi 3Haqegue Ha$opa W. nW o11peAeIIeIIH.EMHoxeCTBa AoIrycTuMbIx npocTo Hblx nPorleccoB Ha MOEeIIU 3aAa,W{M CTqATe?UK' ynpasneHufl wlll ynpaBIIeHI{e, .EBnfiK)I{eeCfi CoBOKym{OCTbIonpaBl{n. YnparneHne MoXeT 3aAaMOAeBaTbcfi: npeAHKaTaMH Ha MHOXeCTBeBCex BblqHcJIHTeIIbHbIxnpoqeccoB ofleparoponeparopoB' }I3 JDr, rpaMMar?rKaMI{ HaA an$asuraMl{' cocrofiIUHMH sofr cxeuofi nporpaMMbl. ButuucnurettbHile uodenu c ynpa1neHueM paccMaTpgBaloTc.ffKaK CpeAcTBo npegcTaBneHHtr npOUeCCOBnoHCKa perUeHlfr. B ornutrue oT aIIropHrMoB BrlT[{CfiHTETbHbiE MOE,EJIHC YIIPABNEHHEM 'TBJIfiIOTC.EHEACTCPMHHI{POBAHTIbIMH orrucilug.ffMg llpo4eccoB (n o6ufer"r cnflae nPoqecc He onpeAeJleH Ha Mo[eJII{ nu6opoM ynpaBlleHlrfi o4Ho3HarrHo I{cxoIHbIMH traHHbIMH) . Ho noAxopulnr"r MOx(Ho OrpaHHtIHTb MHo)KecTBOAOITyCTI{MbIXBbIqHC[I{TenbHbIx npoUeCCOBTaK' rrTo MoAenb BMecTe c ynpaBnetMeM npeAcTaBilfleT npoueccbl TaK xe oAHo' 3Haquo, KaK HeKoroprrit alropl{TM , uodanu 6y4er'r Ha3blBarb rpofiry , 3ada,aeilHa lbrquarurenuttoil - na6oprr nepeMeHHblx Motreri (U, I/ - nxoA I{ BbIxoA r"rogenu); Ue U i V - cxeMa sagaw. BHu - aHaqeruaeHa6opa u (ucxoAnue AaHHbre); (u, n cocroffHnff HaqanbHoro H3 MoAerIb rrHcruTerrnnui upouecc, nepesoMullli

(Wo, !)-"

q*rto,

3aAaqy'ecnuWo=Uo, V cWr3ua' (Wo,fro)-,peluurcr

qeHHe V CWu BbrxoAa 3atraqu 6yneru Ha3bIBaTb oTeeTotvt. yIIpaBIIeHI{H' 3aAaqa .sBJlfleTcfl pa3pewu6oil na uodenu IIpH HeKoTopoM ee petuaeT' rcoropaff npoqedyp, KoMnosurlufl ecJrH cyqecrBer oSfiercTueHaa MOAeJIb no3BgnffeT B TepMHHaX nepeMeHHbIX H KaXgan BbrrIHC;114TeJIbHa.ff yflpaBrleHH-ff' HX eHa.reHHfi OnpeAenflTb 3aAaql{ oneparHBHo-A,HcrlerqepcKoro I43 cocroffulHe sKBHBiIileHTHocrH' Bce srH 3aAar{H Mo)KHo paa6nrn Ha Krraccbl 3atraq KJIacca TaKoro K1pKAoro V). (U, nls 3agaq c otrHHaKoaofi cxeruofr gagaql{ AaHHoro Hulyr aIIropHTM co BxoAo1y- U H BbIxoAoM V, peuatou-Uli peura ro oH r.ni.... Ec.nu raxofr alropgTM cyulecrByer Ha MoAeIru' -3agaqy U' Sanawt K HSXOA,HbIM AaHHbIM TorAa I{ TOIIbK9 TOrAa, Korga oH npHMeHI{M Ha MOAeIIH peIIIaIOTCflB EFa gTana: ImaHHpoBarMe peiletFtnfl' T' e' @cTaBIIerMe llonrleHHe anropHTMa, peuiiuolliero 3atraqy; HHTepnpeTauHfl aJIf,opHTMa u pe3ynbTaTa. yflpaBneHl{t MHOxecTBO pa3HomnHblx 3aAaq o[epaTgBHo-AncneTr{epcKoro pa3Pe' 3agaru 3rH KoTopblx ua 6ynerra npeAcTaBJIsTb MHoXecTBoM MoAeJIefi, nrau-rttoyrn' MOAeIIefi ]I IIIuMbI. oAHarcO MHOTHe H3 3aAarl, a cneAoBaTeIIbHO' B lIX BbInOnHeHItrr' 3aHbI, T. e. CyuIecTByeT cI{HxpoHHocTb n acHHXpOHHOCTb 60

MoAeJrbH B nrodyrc [;ls omtcarus raKoro crr)nlaffBBetreruB Bbrrtncsrr{Tetrbrryrc MoEenefi noHnme ynpaeneHun Ha uodenu c. coBoKynHocrb BbFIHcrrHTeJrblrbIx IIpn oroM BbrttrrcJrurenbrr)loMogenb sam{rueM B BHAeP (G, Q, tpre G = = (4 .d) onpeAenrer ee nn$opMars{onnyro crpyKrypy; C - yrpaBrrffrculaff cTpyKrypa fiInr Bce Bo3MoxHbrerlenoqKH oneparopoB, KoTopbreMoryT @cTaBI{TI BbFmctruTenrrrfr npoqecc pe[renr{ff 3aAaqr{. nln npeAcraBnenv.fr,g 6ygeN{ r{cnoJrb3oBarbnpocrbre Bbrql{ctrnTeJrbrbre MoAerrH,tr;tfl npegcraBJreHufi C-enrnllerpu. Brnmcnnrorblryro MoAerrb paccMarpl{BaeMB Br{Ae fyAonbHoro rpaQa, cocroflrrlero H3 nepeMeHlrbrxr{ cBfl3brBarcrrs{xI{x oneparopoB. [Ipu nocrpoeHHii MyfrbTHMotreirbirorEiiPeAcTaBiieHi{.EFjlfi, 3atrari onepafiiBilo-E{cneTqePcKoro ynpaBneril{fl BHaqiue crponM HHQopMarryoruryrocrpyKrypy raxgofi H3 MoAe[efi, a sareM TonbKoynpannflrouyro crpyKTypy, Ilonyurvr yrpaBnfirou)no crpyKTypy B BHre cem llerpn. nln sroro B coorBercrsur{ c 132, 41,481 BBeEeMprg onpegeJrerufi. Onpeqenexue4.3,,S-cerrrc Ha3oBeMcerr flerpn, B rcoropofi Kaxgoe oo6rtme Moxer no.EBnffTbcff TorIbKoorEH pa3 H 3anycK nepexoAaHe BrrerreT3a cobofi yMeHbrueHnfiMapKHpoBKHB ero BxoElrbrx no3r{r.u{ffx, Onpegenenue 4.4, Ynpannnrculefi crpyxrypofr C Nrfr, Bbrrrr{cJruTenrnofi MOAeIIUffinneTgfl,,s-Cetr, KOTOpaflflOrytaeTcfl H3 MOItenHnpH OtrHOgnarUrOfi - no3r,${flM}rr 3aMeHeBCOXO[eparopoB nepexoflaMr{r{ nepeMeHHbrx .U[.s uonHoro onpeAeneHltfiMoAe[r{ Heo6xo4ruo arr6parb Haqanbu}noMapKHpoBKJ/,T. e. sa[arb HaqarrbuoecocrorrHne ynpaBnffrcqefi crpyKType. nnn sTOrO HeKOTOpbIMnO3HIS{flMIIpI{CBar{BanTTOqKtr,T. e. noMerrlarcTl,rx Bo Bcex nq3lrl4{.fix, @orBercrBylou-u{x BxoAxbrM nepeMerrnbrMMotrefln, 3aAAqa MOXeT per[aTbcn Ha MoAeJrHTorAa, KorAa Bce no3r{I[fl{, @oTBeTcTByKru[4e Bblxo4rbrM nepeMeHlrbrM 3aEarm,6ygyr npoMapKr{poBarrbr. BseAeNr onpegenemfifl,, xapaKrepusyrcrrlne yrpaBnffrcuryro crpyKTypy MoAenefi. Onpegenenne4.5. Cxeproft cocroxrnni ,S-ceu llerpu 6ygervrHa3brBarbrytronrHrfr rpaQ G(Q, O), rge BeprrfiHaurr qi e Q 6yWr @crofir{r{s,S-cem n trWaMH gi € O - oo1r;twrz (oneparopu).'CocrofiHr{e ^S-cern 6y4err.roArro3HaqHO OnpeAeflflTbJIOIHqeCKI{M

BeKTOpoM MapK}IpOBKyIV

=t (Vr,Vz,

..,, rn),

r4en-quclronoslugft;

v'. = l

mI. l' ecnm L o, ecnumI.

(4.1)

mi - KoJrr.IrrecTBo MapKepoBB [o3r{rlH}r pi . nyra pi € O HcxoAHr Hs @crofrHfifl ql e Q n npnxoAnr B cocroflrue Q1 e Q, ecrln co6rrrne gr. Moxer noflBJrffTbcflB cocrof,rrnn 1'rtr,cJrercrBue qero cHcTeManepexoMT B qt Cperpr cocromrru? HMerorcffHaqanbHoe- eo e Q, o$ro3naqHo onpeAeir.fleMoe Haqarrnofi Mapra{poBrcofi,n KoHeqHoe - Q, e Q, npn r(oTopoM Bce no 3r,[r$Hn po Hyrvrepod affi r, 6t

4.3. l'lpencraBneHre3KcneprHbtxMo4enefi4na onncaHHF ynpaBrnloulef, Aenrenbnocrl,tAxcnerqepanpr ynpaBneHnr pexuMaMtr SHeprocncTeMbt

----\ \ c r l, /

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AHanHs npoqeccoB snrpaGorrcn ynpaBnffioupil( peiiieinn? FicnerqepoM noKa3an, qro Bce paccyxfeHlrff crpoflTct Ha ocHoBe enanml, HarcoEIeHr{bD( B .r'rbrcnermofi MoAeIIH. 9rll 3H:lHHt oKit:rilJlocb Bo3MoxtrbrM npeAcraBnTb MnoxecrBoM npHWHHo-cneAcrBeHrIbIxontotuernlft, Koropbre Moxno oIrHcarb B nonffTlrffx ri ornorrreHnRl( rurQopr"rarg{oH}ro-MogeJrbHono6aguca. IIeu onurllee qeJroBeK,reM 6oratle y Hero na6op ornoruemn? H TeM rrmpe vr tloJrnee mr$opr"ra4loHHo-MoAenrHrrfi 6asmc. Crpyrrypnsarr:rn ornoruenni n

a

i

r

P t t

3

\ - < P n c . 4 .4.

Onpegelenne 4.6. BpnucnurenblrbrM npoqeccoM Ha MoAeJrHc ynpaBrreHr{eM 6yger*t Ha3blBarb rrymiHa cxeMe cocromnni, HarmHarorr1luicrcocroffIrnew eo H Kolrqarculdrcn q r. Kaxqa.s yrpannfirorrlaff srpyKrypa C nopoxAaer HeKoropoe MuoxecrBo BbFMcImreJIbIrbD(npoqeccoB, oIEro3HaE{oo[pegerrffeMbrx cxeuoft coc.rofllni. PaccuarplrBaff MHoxecrBo Bbrrucnrlrellblrbrx uogelefi 3a,qaq oneparnBHoEr{cnerqepcKoro yflpaBnexnff, yrrpmnffrorrlaff crpyKrypa raxgpft H3 Koropbrx npeAcraBneHa cerbrc llerpu, Mbr 3aMeqanu, qro ornr rpe6pT wrfi. cBoero [peAcraBJreHr{ffBo3MO)KHOCilr O6UeHOArurQOpUaqnefi,T. e. Tpe6yror opraHH3aIIHUaCI{rD(pO IrHOro BbrqHcIIIfT eJIbHOrO npo qecca. Brtqennu noclretroBarenrnrrfi Bbrruc[HTenrxrlfi [pouecc, npn KoropoM HeKoropafi IIeilorIKa olleparopoB (nepexogon) na cem llerpr{ Bbrnonnfiercff ToJIbKo noqlreAoBarerlbHo. .[;lr opranu3argu acnlD(poHllbrx npoqeccoB pfrr. AenI{M Bce no3l{Is.tn cereft llerpu Ha IIBa MuoxecrBa: nosrn[an cnuxporru3ar[,m, toJrfirorq]recff oEusar"ruEIfi HecKorrbKrD(naogenefi,qpr{ noMotrgl KoroPbD( CruD(poHr{3HpyercflB3aHMotreficrsHenpoqeccoB Ha MotreJrD(; no3r{ql{u ripyrperumx cocrofiHr{fi rrrogeneft,nueroupre no otrFIofisxo4roii u o4rofi srIxornr6fi tryre. Kaxqafi TaKatr no3urs{.ff npuHalue)Klrr roJIbKo oArIoMy npoqeccy, olpra Hg noerlrsrfi cocromnni Koroporo npoMapKapoBarla, BbrpoKaff TeM CaMbrMTeKyrrlee cocTofiIlHenpouecca. Ecnn npeo6pasoBarb rerrepb KaxAjrlo ug cerefi llerpu ror, q1s6br H3 IIognutfi BlryTpeHHrtx cocromuri HcxoAIdrIHTonbKo o4loHanpaBrleuubre ryrfi, a wJ noerflfffi currxpoHn3arsru - IpyxHanpaBneHHbte, To MolKHo nonfil{rb KoMno3r{rsrrc uogenefi, Ha Koropbrx pa:rpeilii{Mbi acfi}D(poHrlbienPoqeccbr. Ha puc. 4.4 Wrs. rroffcHeHur cKa3zruHoro npe[craBrleHo rpx acHID(poHHbtx npoqecca P1, Pr, P3, KDK[lrfi pealusyercn csoefi cerbrollerpn.- 62

4lrRrtnlrltr|arrr

nr v^

rrarreii r{w^v.r

rr .r

'lotttrrr r../1sa

itrr^oo-orrrrd JtLywJLwLLrn

trnDDnndar rrannbaurr rr\r.rD\rJlttwL'aqrl'\r.DfrI\J

.arr-ft l,grrrlllD

npo6nerrry nepe6opa npn noncre peuund Meto[aMu rclaccnsm
treHaua pmc,4,5. onpegorenne4.7. Jlomro-anre6paruecranMoAerrbonpetrerrffercffBbrpaxeHueM L A M = ( T r , H r , , V L , @ L ,p ( g t , @ r ) ) , (4.2) H€rHr{s fltrrr Ar{clerqepcKoro nepcoHaJra o fion]rKe nor{cKa r{ npnusrns peueaufi peAcrBa Sopvanueauun eKCnepTHrrX rr,rOAenefi Srcnepruas

MoAenb

3HaHns, gaJtoxeuHbre B AorDKnocrHbre r{ 3KCIIJIyATauHoHHbre HHCTPYTUIiU

3uanug o6 o6texre, cncreMe lr ueflsx ynpaBnenuc, H BApHaUr.fr{ eTr{x ueaef,

Cucretarbre

aHaJrI{THKr{

P r c. 4.5.

63

-rne ^-

r-L

- npaBHna llocrpoeHHt npaBI{rIbHbD( BbIpa)Ke - renMrlt - - { - ' - - - MotreJrHi ' f/rL

gaxomt o6' t*rfrrv-LAM (cmrrarccncLAI\[); *t - aKcfioMbr,om{cbtBalou.u{e nacrn ynpasneHnx (ncrrurHo rrnTepnperr{pyeMblenpaBl{nbHo nocrpoeHHble o6nacrr HHrepnpaBnna BbIBoAa; p(*t,@2,) BbIpDKeHnn); @L nperarprn. IIpn gagaHnofi uaqanrHofi mrrepnperaql{H B BIr[e aKcHoM npanma @, no3BonffIoTBbIBecTHBce HcmHHbIes LAM BbIpDKeHI{.fl(Vf n @t onpeAe' 3ru Mogenr{, B ornilqne or QopMarIbHbD(cHcTeM, rrffror ceMaHTHKyLAn. Hl{TepnpeTallr{rc,T. e-. AOITCKarcTH3MeHeHI{eCeAO[yCKarOTAOTOBOp[ryrc MaHTSKHLAM. Dln groro ucnonb3yroTcrr EDe Bo3Mo)KHocrlI: I{3MeHeHHe -p(V) n nerueHelluenpaBrtl BbIBoAa-p(@r,). cncreMbraKcHoM Hcnnnrocrb HeKoropbrx Bbrpaxennfi \ tr LAM ycraHaBrll{Baercff ADyMff HuiAexo B pe3yJlbrare JlomqecKoro BbIBoAa s LAM cnoco6annu: nn6o \ r{3 HMeprueficg cucreMbr aKc[oM no npaBnnaM BbrBoAa,ru6o l{crnHHocrb \ ' nonfraercff nyreM ee fiHrepnperallxr{. Axcnoprarr{qecKafi cocraBrrffrorrlaffMoAesm LAM nu6o nrc6oe noA,MuoxecrBo ee gJreMeHToB, onpereJrfleMoenyreM pae6neunr V, ua Klraccbl eKBI{BaJreHrHocrl{, @orBergrByer noH.ffTr{rc"sxcneprnaff Mogenb lrpuHffTl{n peurenrui n traHHoM Knacce npo6nerrmrx crrryau{fi". Hrrrnau cJroBaMH,oKcnepTHbre Mogerrn frBrrnrcTcffMHoxecrBaMn yrBepxgernfi o cnoco6o( H npI{eMD( noncKa ynpaBnffroulux perueruai n HeKoropoM Knacce curyarynl u omrcblBarorcff ff3brKoM JromKH npelu{KaroB nepBoFo nopfiAxa. Bu6op raKoro fi3brKa omrcaHltfi He cJr)nraeH,a onpeAeneH Harrr,rueM o6urefi npoqerypbl nol{cKa peruemul, HMerryeMofinpnrnunoM pe3onrotgrft 19, 471, JIln npnrrrepapaccMorpnMnpocrefiuryrceKcneprr{}loMogenbcta6unueaqruHanpfi-

I I

xeHrir B oHepnlcucreMe. B srofi MoAenr{ Hcnonl3yr,Tcf; crregylou-ue oruolrleHnff' oTox,qecrBnexrrbre c npeErKaTfibrMncrrMBonaMfi: VBII - 6strr yBeflEqenlrbru; CIIH 6rrrt coeErHeHHbIM;OIIEP - 6urt onepawefi; PE3 - rMerb peepB; PEAKTOP onpeJlerltrb @crro.f,HneperynJtropa rnna "PeaKrDp". Tepuanm ffBnfiIorcfi cocraBuble rloH.lrrrr.f,, TaKHe, KaK: YBII H (x) - yBeIIrrtMTb Hafiptxetmte H B nyHKTe .r; CtrH (x, y, Ro) coeprHeHbl IIln{KTbr x il y Ha gneKtpnqecKoM pas{yce Ro; OIEP(OTKI. PEAKTOP (/)) - orepauu.t no orKnloqelrup peaKropa B nynKre /; PE3 (z) - p€epB ynpasnfrrouefi oneparlr{il no peryrmpoBaunlo HeKoropblM runoM peryn-EropoB; PEll (z) TaBToJrorrrqecxnfirepM, onpeAenrourafi cnoco6 omrcaHnt 3anposr c qerrBronoryqerffff orBera; PEAICTOP (y, BKII) - peryntrop ntna "Pe aKrop", paslrer[err6rfi B tryHKTe/, BKnroqeH. Bupaxerux excuepruoh Mogenrr, onncafiHbre .ErbIKoM lorrrKl{ rrpe4irKaroB nep' Boro nopfiAr(q 6yAyr uMerr BHg:

(x,/, Ro) '+ vBrI ln <*ll) t (vr) 1y"1(onrn [orrn. PEAIOoP(y) ] & G.IIH (Vz)(PEH(z) & PE3(z) + oIIEP(z)) ;

(V/) (PEAICToPI y, BKII ] '+ PE3[ orrcn. PEAKToP(y) ] ) .

(4.3)

Kanqoe u3 BbrpDKerurfi necer nnQopr"raullo, non]ryellHyro or ggcnerqepa: nepBoe, orKlrrotturr perynffTop rfina "PeaKTop", eolu B rryl{KTe / cFuecrByer Bo3MoxxocrB a caM nyHKT / coeAHHeH c nynKToM r Ha HeKoropoM aleKTpnqecKoM paccrormlu R9, TO, pearrn3yfr, sry onepaqr{Kr, MoxHo noE$-f,Tb Hanpg)KeHHe B nyHKTe x; BTOpOe, perueHHe 64

PEAKTOP[v. BKJII lnrnn - J Vpnq '-

pFAr.Tnpr.,r v^ \/r I

t.

\1.'r,

rAe z - nepeMeHHaf,' IIpI{HHM:lK)uliIf, 3HaqeHHfl H3 MHoxecTBa o[eparUrfi ynpasflegfifi. B cootsersrgnH c npuHuunoil p$onn4uu roruqecKoe cJreAoBanr{e (4.5) u3 eKc[epr! xofi uofenl{, Hacrpoennofi- Ha crTyuryrc, onpellefl fl,erc1 nporgBopeq1eM Mexgy orpilrlatoreu (4'5) H MoAenbK) (4,4) , orprnrarnre 1+.s), npHBeAeHHoe x eoprue npegnoxennfi, HMCETBHA

FEril[zJ, iffi ln <e | .

G.6)

Ecnu s npouecce BbrBoAa ycriuloBneHo, .rro npn HeKoropbrx gHaqeHuffx neperreHuof, z BbIpDKeHHe (4.6) nporr{BopeqnT MoEerrH, Hacrpoerurofi Ha d{Tyaufiro, To oro 3HarMT, trro npH Tex xe 3HaqelrHFx z BhrpDKeHr{e (4.6) rorzqecKu crreAyer r{3 MOEerrn. Eyger"r piri|nl'rqarb ABa BuEa Hacrpofixu MoAeJrH Ha curyaqHro: npeADapHTenhrryKr, KOTOpaff npeAlrrecr8yer BLrnoAy pelueHrrr, H aKTyanbHylo, KOTOpaff BbrnoJrHreTcff B npouecce caMoro BbIBOAa H KOTOpaff noMoraeT coKparr{a1b HcxoAHoe MHoxecTBo SIIF MeHToB sKcneprHofi uogenn, 'ryacl3ynus{x B BbrBoAe Nrn KoHKperrtofi cnryqnr. BuBoA noKa3aH Ha puc. 4.6, 3alrentu, tfro HcrnHnocrHoe 3HaqeHHe Oopr"ryn neperreHnofi qacru MoAen[, 3aBHcsluee or crrryqll4Hr Bblqrrc4r{TeJrhr{blMrr MoAerrffMU r Soplqpyelcq axryutrHa-a Hacrpofixa- nttMepoM r'.roxer cfl}oKnrt BbFMcJrHTeJrbHaffMoAenE c HMeHeM TepMa-noHFrrlg C.IIH (x, y, Ro); rvronerll Huler MHoxecrBo nyHKToB { yl, c KoroprrMn coeElHeH nyI{KT x B TeKyuIeM cocrofiHr{H gHeprocHcreMbl. Tonrxo Ha' e-Ha.reffiffx-3mx NEPEMEHHbIX HCTHHEHIIPEEIKAT C,[H (X, !, RO). IIPEPAPHTEIIrH:UI HACTPOfiTAMOEENH ocyluecrBtra.ercg, o6relMuenneM noAMHO)KeCTra neper"rernr-fi q,lcru MOEerrH c MHOxecrBoM npHq{HHo-crleEcrBeHHbtx caf,3efi, BbIBoEoM tcex ro3Merctblx pesonbeeHr (noruqecKfix c:ieAcmufi) ' BICIIKIIIeHH€MsTHx cfleAcrsHfi B HcxoAlroe MHoxecrgo npeg.noxerurfi H nor.rcKoM B HeM HoBbrx pe3orlbBeHr, Ora npoqeAypa Nwlrcfr.qo rex nop,-PEAKTOP(/) noKa troclreAHtt pc3onhBeHra He Aacr nil (nycro) noorre noEc-r*fiteBKn repMa OTKI.' BMecro neperrerHofi z. 65

lIIann

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-

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Tononomrc sneKTpnqecKofi ceTH, xapaKTepu3ylousre cocrof,Hnff 9neKTpo' nnr141i3neKTponepegaqH T. f. Bce orHorueH[fl B c11c' cTaHULill,noAcTa1il.U{fi, TeMe 3a,q:iiorcfi Tabniiqno i{ onpeAen flJorcff,I{MeHeMorHolueuHs H crMcKoM arpn6yroB (nonueuoB:trrHbrxrapaMerpoB), Ha Koropblx oHH onpeEeJIeHbI. Hanpurraep, Erfl, nonrrnff JISII cyulecrByer orHorueHue c HMeHeM JIgn, 3a[,iluHoe Ha Hortlep II3II, nMr Haqana JI3fI, HM.E KoHIla JI3II, HanptxeHfie n3n, cocToffarpn6yrax: neperoK no JI3II H T. A. Taxne oTnoureHnt cyulecrByrcr s 6a3e ruri n3n, AonycturtrH gHeproq{cteMaMu' EAHHbrx g.;nr Bcex nourrnfi, xapaKTepn3yrcru1x o6nacm ynpaBneHnt xapaKTep, T. e. He Menf,xlrcf omlcareflbHo Ha nportxeHHu H HocfiT ycIloBHo-nocficffnnfr prrgTen6goro nepnoga BpeMeHH. B mo xe BpeMfl Bo3HHK:lIor H Hcqe3alor orTIoIIreHH.f,' peruerurfi. xapaKTepu3yrlu-u{e npoueccbr pacno3HzrBarrfls c'Hr1falrylfi, noncKa H npnntux Hanpnrrrep, B [pouecce noncKa peruenrrq Bo3HHKaeT norpe6Hoctr y3narb no rononon{H c KoHKpeTHbIM oneKrprqecrcofi cem, KaKoe MHoxecrBo nyHKToB { Y } coen*reuo ""Tn gi4ar,furs (clrryanreErHaMrtecrol nyHKToM B. Taxa-s norpe6Hocrr pearru3yercr nyreM B. flossnexue lpffiaMl{qecortrotueHur (coeprHerurs) C.IIH tfi, Ho) nomlnf;roulentcs He ronbKo KHx orrroureprfi cBssaHo c Hamtquer"r s CTIPHHT npegc'TitBneuufl rulQopuaulu Ha ypoBxe EaHHux, Ho H Ha ypogue gHarurfi [tZ].-Ur"remro Ha ypoBHe sHaru{fi B rrpouecce nogcKa peurerrfi Bo3rtr{K:lror EoIaMHqecKHe oruolrleHHl., Nr;l, Koropblx Heo6xo4lr'ro ycranoBHTb Hx reKyulyp HcrnHHocrb nl'1eM Hrrrepnperdlru{ Hx Ha 6age trarn$tx.

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I27, 45, 671. 72

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OrHourerm-spa3Aenfirorcfr,Ha ycnoBHbre u 6eaycrroBHbre.flepame BcerAa HocfiT KoHKperHrrfi xaparrep, cnpaBegnnartfr TonbKo pgirs.trarrmofrofinacrn npxMeHeHr.rfl(Hanpuuep, Ycrosux BKJrroqenr{fln3n (1, 2): BKnrcqHTb JI9n G, 2) s PafionoHepro). KourperHocrb 3a,qaerc.f,ycrroBueM rrpgMeHeHIfff SToro orHoluennn, Eesyc.noaHbreoffioLuennfl.HocflT xapaKTep 3aKoHoB, Bcertra cnpaBeEII{BbIx B sneKrposHeprerr{Ke (nanprM€p, 3aKorrbr KHp*ro Qa), Apyrn&ar cJroBaMH, HMeroro 6uresHa,lrurrfrxapaKrep. Bce orHotrleHnfl H ycnoBn.fi npHMeHeHHA(rarcxe paccMarpnBarorcff KaK orHorrreHr{.ffco cnoefr o6nacnrc HHTepnperauu) MoryT -(x, 6nrrr 3rreMeHTaprrbrMu (nanplruep, ornorrrenue coe,qglrenrwHa cerr CAFI y, Ro), cocr:lBrrbrrw (uanpHMW, PEAnH3OBATb [OTKJI. PEAKTOP (/) ] & C,[H (x, y, Ro) -+ -+yBJIlH(x)J) n ueonpeAeneHl{brnau. IIpn 3roM ycrroarrfr.rrpnMeHerrr{.ff Moryr HMerb roJIbKo rlornKocrarrrecrcHli IIIIH JrornKo-Al{HilMlrqecrcufirrm. ,[pyrue orHolueHl{fl MoryT l{Merb errle H BbrrmcJrnTennnrrfirnfl. PasHfiua Mex[y sTr,tMH THnaMH (ncrcnroua.aHeAoonpegeneumrfi) aarcnrouaerc.E B ToM, rrro BbrrMcrrHrenrHrfr THII Aaer noclle Hl{Tepnperarlr{HToJrbKormcJroBbre3HaqeH6rrnapaMerpoB. lpyrre THITbIAalor nomqecKue 3HaqeHHrHcrr&rHocrrr,HnH rro)KHocTH wHTepnpeTaIIHHB coBoKymrocTH c qHcnOBbiMH3iraqeyr4frMr4, napaMeTpoB, gTa l{crntrHocrb HJIHJloxHocn. C orHotxeHntrM}IHeHa Koropblx ycraHoBJIeHa AoollpeAeneHHororuna CIIPHHT nocrynaer KaK H c noHflTr{ffMr{,r. e. rpedyer mr6o lD( Aoonpetrenefiitn (sararnfl o6nacrn Hlrrepnperarprrr), nn6o ncrclroqeHl{f.

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3uuorft (npnnun ,FplarposafiH.fi rarcofi MoAerrH H3noxeH B cnegyorqefi rnrae). Tr,nru o6paron, nocrponB 6a:y sHaxfiii s Br{AeMHoxecrB r'logenefi tr trtf,llbtx H onpeAelrrn .flo3 rar cpegcrBo om{caunff, paccMorprrM cpeA. ctEt norcxa peruemi HaMoAen.D(,

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iTBTOMATH.

qecKH pelllaTb 3al,ally flnaHr{poBaHylg, T. e. cTpo}rTb no 3atraHHbIMHaqanbHblM AalrHbrM u rIeJrH pacrrera qenorrKn npeo6pasosamill mQopt"tuullt, HHTepnperaI-U{fl KOTOpbD( no3BorrffeT nOIrrMTb HCKOMbIe pacqeTHble AaH}IbIe. Hua,Ie saKaK 3a,qarla [o]rcKa rryryr B flpocrpaHcrBe Aaqa nnaHHpoBaHnE Qopuylmpyercff cocrormul MoAenH 3HeprocucreMbl. c [9, 10, 34, 35J nnaHupyloutyto cucreMy E,rtfl Bbrtucnn' B coorsercrBnu TerrbHbD( uogelefi c ynpaBneHueM onpeAeJruM KaK KoMno3Hlu{rc QyHxttttfi 76

C, (J, V) , wn Koropblx cyqecrBFor 3agaqr (U, U, V) , parlpeunr' Mbre Ha vrotrenw M, npr{ 3atranHoM yflpaBneutnt C. llnamrponaxue noerregoBarenbrrbrx Bblttrrcm{Tenbnrlx nBoqeeeon Ha oiFinowroft BbrrtncrrnTernnofi MoAeJrH.flpegluerHa-s oOnacrb MoAenI{ @crouT H3 fleperrns Berrr{ruHU n V, Ha6opa npm6parcsarffit P, nuQopMalu{oHxoro rpa' Q; G H MHoxecrBa orpaHruewdr Z e IJUV u asapufiHrrxco6uuft K e UUV. U H pe3yrlbraraMu lcr npm6pa3oBaCoorsercrBne Mexgy apr1nr,tenTavrtr r. e. fYAoIIbIIbIM rpaQou c rpaSorra, V nnQopr'aargoHrbtM 3a,qaEHM trrdt ( Ma,

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9i , eonoeraBnsrcrr\tlrloHeKoToPbIMqeTBeprca*t( M ^, C, U, 14 oneparOp B (pl)[Mn,Y C, U, Vl co BxoAoM Uu stxopov. V, rqe Mt -Bblqucnn.R' = 1 f u tt v - Ha6oprr nepeMex}IbD( renbHal MOAenb; c - ynpawrem{e ua Mr; Ha MoAeJInMn n C, U, Vl onpeAengMo wrfl' rex qerBepoK K (V,)IM,, 3xaqerue u '

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