战术导弹对单个目标射击效能的马氏链决策分析模型

200777:100026788(2007)07201662051,2,1(1.,710025;2.,100085):,.,,;,;,.:;;;:TJ762:AAMarkovChainDecisionModelforTacticalMissileCombatEffectivenessinAttackingSingleTargetWANGMin2le1,WANGDe2wu2,LIUGang1(1.TheSecondArtilleryEngineeringInstitute,Xian710025,China;2.EquipmentAcademyoftheSecondArtillery,Beijing100085,China)Abstract:Aimingatthecomplexproblemofevaluatingtacticalmissilecombateffectivenessinattackingsingletarget,themarkovchaindecisionmodelsfortacticalmissilecombateffectivenessinthewayofshootingindependentlyisputforwardonthebasisofmarkovtheory,anddifferentshootingconditionsareconsidered,thecorrespondingmarkovchainmodelsareestablished.Thetacticalmissilecombateffectivenessanalysismethodpresentedinthispaperisconciseandconvenientinuse,andcanoffersupportforquantitativeshootingdecision.Keywords:tacticalmissile;combateffectiveness;markovchain;decision:2005211207:(10377014);:(1964-),,,,,,,50,16;2;6.1,(:),,,,,[14].,.2,,m,.K+1K,,:T,:T={0,1,2,}m1,2,,m,E={1,2,,m}.X(n)n(n),{X(n),n=0,1,2,}.,:1,;.1)n,m,,,P1=P2==Pn=P,Pi(i=1,2,,n)i.Xk(i)K(K)i,Xk+l(j)K+lj,K+l,PK+l:Pk+l=[00100]miPk+1Pk+2Pk+l=[000100]PlPK+llK,P(Xk+l(j)|Xk(i))PK+lj,P(Xk+l(j)|Xk(i))K,:.2),P1=P2=Pn=P,.3,1,,,.1,,m,1.1P:P=P11P12P1mP22P23P2mP33P34P3mw0wwPmmP,P,.,ji,ij,,Pji=0,.,m,().,m,m,,Pmm=1..nP(n),n,7617n,.:P(0)=[P(0)1,P(0)2,,P(0)m],(1)P(0)i=P(x(0)=i)nP(n):P(n)=Pn=[Pij(n)]mm,(2)n:P(n)=[P(n)1,P(n)2,,P(n)m]=P(o)P(n)=P(o)Pn,(3)P(n)i=P(x(0)=i):P(0)=[1,0,,0],.1[5]limnPij(n)=pj,i,jEi,.,:pj0(j=1,2,,m),mj=1pj=1,{pj,j=1,2,,m}.2.iE,m,Pim(n)imn,n,,:limnPim(n)=1,,:limnPij(n)=0,jEjm.1:,():PLim=(0,0,,1)m3,.[5]n:{P(n)j,j=1,2,,m},:limnP(n)j=limnmi=1P(0)iPij(n)=mi=1P(0)ilimnPij(n)=mi=1P(0)iPj=Pj:limnP(n)j=Pj,j=1,2,,m.3:,,.,,K(K),K,86120077[6].,K,.f(k)ijiKj,[7]:f(k)ij=bEbjPibf(k-1)bj.,f(1)iji1j,:f(1)ij=P{X(t+1)=j|X(t)=i}=Pij,t.,f(k)ij(i,jE;ji;k).,Kj.j,Fijij,:Fij=P(k=1Ak)=k=1P(Ak)=k=1f(k)ij,(4)AkiKj.Fij:Fij=f(1)ij+k=2f(k)ij=Pij+k=2bEbjPibf(k-1)bj=Pij+bEbjPibk=2f(k-1)bj,:Fij=Pij+bEbjPibFbj,:ij,Pij,ijbbj.44.1,1,,,,.4.2,,..,.,,q(k)ijKij,KQK:Qk=q(k)11q(k)21q(k)220wq(k)m1q(k)m2q(k)mm9617KPk,KHk:Hk=PkQkTnHT(n):HT(n)=T+nk=T+1Hk=T+nk=T+1PkQk.(5),.5,,,.,,,,.:[1]Fleming.G.H.Adecisiontheoreticapproachtorecommendingactionintheair2to2groundaircraftofthefuture[R].ADA248158.[2]EdmundG.Boy.Aninvestigationofoptimalaimpointformultiplenuclearweaponsagainstinstallationinatargetcomplex[R].ADA141034.[3].A..[M]..:,1982..A.Matwachoke.HandbookofOperationsResearch[M].Beijing:NewEraPress,1982.[4],.[M].:,1993.ZhangZuiliang,etal.MilitaryOperationsResearch[M].Beijing:MilitarySciencePress,1993.[5].[M].:,1988.WangRongxin.RandomProcess[M].Xian:XianJiaotongUniversityPress,1988.[6]ClarkeAB,DisneyRL.ProbabilityandRandomProcess[M].JohnWileySons,1985.[7],.[M].:,1995.FengYuncheng,etal.FundamentalsofSystemsEngineering[M].Beijing:BeijingUniversityofAeronauticsandAstronauticsPress,1995.07120077