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Constraint solving in uncertain and dynamic environments - a survey

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(1)Constraint solving in uncertain and dynamic environments - a survey Gérard Verfaillie, Narendra Jussien. To cite this version: Gérard Verfaillie, Narendra Jussien. Constraint solving in uncertain and dynamic environments - a survey. Constraints, Springer Verlag, 2005, 10 (3), pp.253-281. �10.1007/s10601-005-2239-9�. �hal00293900�. HAL Id: hal-00293900 https://hal.archives-ouvertes.fr/hal-00293900 Submitted on 7 Jul 2008. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

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(14) T. Real world. Control system. User. Physical environment. Other entities. Physical system. Supervisor. Executive. Reasoning control. Solution execution. Time. reactive deliberative. Offline problem modelling and solving. Online problem modelling. Problem pre−processing. Problem definition. Online problem solving Search control. Online solution maintenance. Time. Problem solution. Search algorithms off line online. ‰ h™ÃCxudiN®*‘¯ƒ¡W¹W´z¶Ü¸Ÿ¹¸¢z¡Ÿ$¼C»"¸´zŸ´–¶ˆ¾f´‡é’ºˆŸw¿fŸwº ¹¼fÀ?¸j¡¼fº4·H¤‡·H¸ŸwÏ ¼C» £͖´?¤‡·j¶Û¹£Cº ·H¤z·H¸ŸÏ›Õ @9‹Ig‹=O>KM"B ŽGI*OqM!>K`=*zQ@6Wn[XJL=  ° If] Ž">A=  M±L~kO =cI?JK@!GGI@I?@!J1@>eI IfO=I*OAŽ">G=cM!F O = fI ] uWJL=3s!=uJpI*M ‹6O>KM9Jq`"qO=aW²M!F=uIfO =?>à@9‹E@9ŽOqM ‹GM=WdM ŽQÔ@>KO=?FÌ@'I*O MÌ>KM6Y:M'O P @!ILe> Ib>C@ F O P G@O=uJKJKIfO= P =3OKI  ^M!>0@›JK@>K]!=*q`"qO=aW M7[Q>KM"B ŽGI*OGIfM ‹ P BXIKKO>AI@Y ŽOGIfM ‹ P O>A@F u iI P 3= OKI  ^  D

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(26) Ig‹ ] Ò L =‡‹‹Q=?=uBQ=uh B O =1BQ3= i3‹QfI OGfI M k‹ M!F O X= [XK> M6YXJLa= W<MH?^ OqMàK M9fJ s!= P @!@ÔFHŽ G‹ I*OGfI M ‹ M!2 F O =ÙIg‹Q F M!%> W.@ OGfI M ‰‹ I*M=WIgG‹ ] F’K> M=WÕO =Ù>G=u@!QJ LXM!>AJK‰B s"IKd@ O =AGŽ [3=?K> s"IKq M!> U O l = $'&G>f/ &:?¿8:+;$=<*>?3AÖ(*$>f½a/0&ˆdWnM

(27) B6ŽQJL=IKÉIgd‹ I @K> ]!E= M!FÁq M9fJ s"Ig‹ ]kO j= [QK> M6Yu Ò JLa= WMHb^ÙBQ3= i6‹"=uÏ B Y`×O ‰= [Q>G3= s"fI M ŽQd WdM"B ŽQJL= P L =‡‹"3= s!=?t> O = AGŽ [3=?K> s"IKq M!> U >A= Ø

(28) ŽQIL>A=u*fI O OqMcY3=Ù'@ YXJLh= OqMyW =?3= OoO =Ø>G= Ø

(29) ŽXIL>Ga= W =‡=‹ OG» M!2F O =ُAGŽ [3=?K> s"IKq M!> P fI ONIKy  I*M=Wc[:M9=uÙ B M!FÙÙ @ (?K-'+;"*‹Ë"%$'&1),+;$>CGŽ YWdM"B ŽQJL‡= L @I I I*M =‹ OK> M9JKNIg‹ OAŽQ>C‹ @ 3= OEM!w F [X@>C6@ W 3= O=?>AIK=uB<BQ=uB GŽ I*OGfI M ‹ @9‹XBE=u@e> I @!fJ ]'M!>AfI O W. U O y = $'&G>f/ &:?l(*$>fŒ),/0$6&€At-6/ &1)·?&-'&"˜?nWnM

(30) B ŽXJL=›IKÔIg‰‹ I @K> ]!l= M!2F O 9= W@!Ig ‹ u Ò O=‡‹X@9G ‹ Ibh= M!pF O =Øq M9JgGŽ OGfI M ‹ƒMHbN^ [Qe> M

(31) B 1Ž Ib=u‰B Y=`‡O h= [Q>A3= s

(32) fI M ŽQj WdM"B ŽQJL= U O Ú = ?K ?K"Œ),/0½Ã?_I?@9\ ‹ Y3=)=?=‡‹ @!¶ O =)Ig=‹ O=?>GFH'@ IbÏ = Y33= O­L=?=‡\ ‹ O  = I*M =‹ OK> M9J Ò P K `

(33) q Oa= W @9‹XË B O x = [ `"G@I I?@!mJ M ‹"= IgÚ ‹ I @K> ]!r = M!lF O =*= z

(34) = IuŽ OGfI M Ú ‹ M!lF O = K M9Jg Ž OGfI M ‹ƒMHb»^ [QK> M"B GŽ Ib=uB @9‹Q¶B Wa= WdM!>AIK=u‰B Y`‡O k= [Q>G3= s"fI M ŽQ! WnM

(35) B ŽXJL=u U i3‹Q@!JKfJ ` P O x = $;ÊË/ &R?98:+;$=<*>?3AÛAd$Š=?3> >f/0&ˆ-6&Šx(*$'>ޱ/ &ˆ_WdM"B ŽQJLy= I?@9_ ‹ Y3= Ò G=?=‡‹<@!à@0F M!%> WÕM!ºF [XK> M6YXJLa= W²[X>G= [QK> MIb=uGGIg‹ ] P L @I I Wa@ ` GI Wn[XJKIL0F ` @9‹QB =‡‹ @9G‹ Ibk= M ‹QJKIg‹Qh= [QK> M6YXJLa= W K M9fJ s

(36) Ig‹ ]  ¾ ‹"n = M!EF O =NBXfI ÜcIuŽQfJ OGIL=ul M!EF [QK> M6Y JLa= WÝWnM

(37) BQ=uJKJKIgG‹ ]<@9‹QBöq M9fJ s

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(49) =I*OGIfM ‹ É P L=›JKIKqOXO =#W@!Ig‹ >A=Ø

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(54) B 1Ž I?Ig‹ ] K> Mu Y ŽXq OM!p > ùX*= zQ@I YXJL=1K M9JgŽ OGfI M ‹Q  Ð 9‹ D

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