变论域自适应模糊控制器-(完整高清版)

*李洪兴(,100875)基于模糊控制的插值形式提出以变论域为手段的自适应模糊控制器.首先定义了控制规则的单调性,证明了作为模糊控制的插值函数的单调性等价于控制规则的单调性,从而保障了在论域变化之下控制规则的无矛盾性.然后讨论了变论域伸缩因子的构造.最后给出3种变论域自适应模糊控制方法,即潜遗传自适应模糊控制方法显遗传自适应模糊控制方法以及逐步显遗传自适应模糊控制方法.[1~7]:,,,.,[1]:.[2]MamdaniMizumotoSugenoTakagi.,;,,,,,.,[3];,().,,,.,.,.,,;,,.,,[1~3].1,,X,Y,Z;F0(X),F0(Y),F0(Z).F0(X),F0(Y),F0(Z)1998-04-27,1998-07-24*(:69674014)中国科学(E)291SCIENCEINCHINA(SeriesE)19992/M0,(F0(X),M),(F0(Y),M),(F0(Z),M).F0(X),F0(Y),F0(Z)AF0(X),BF0(Y),CF0(Z).[2],RR:A@ByC,(A,B)|yR(A,B)C,(1)R.1R(A,B)A(),R(A,B)A(),PAc,AdIA,AcMAd]R(Ac,B)MR(Ad,B)(R(Ad,B)\R(Ac,B)),R(A,B)B().R(A,B)AB(),R(A,B)();R(A,B)A()B(),R(A,B).1,R,R;1..UI{X,Y,Z},PAIF0(U),A,,/0;()./M0:(PA1,A2IF0(U))(A1MA2Zx1[x2),(2)x1,x2A1,A2.[-a,a]NB,NM,NS,ZO,PS,PM,PBNBMNMMNSMZOMPSMPMMPB.RifxisAiandyisBjthenzisCij,(3)i=1,2,,,p,j=1,2,,,q,[3],F(x,y)=Epi=1Eqj=1Ai(x)Bj(y)zij.(4)f:X@YyZ,(x,y)|yz=f(x,y),F(x,y)f(x,y),:(PE0)(vN)(n\N]sup(x,y)IX@YF(x,y)-f(x,y)[E).(5)(5),F(x,y)f(x,y).,f(x,y),(5).,R(A,B)(A,B)f(x,y)(x,y)().1,(3),AB([1]),R(A,B)AB(),R(A,B)(),R(A,B)F(x,y).,.1:33.R(A,B)A,B.F(x,y)x.,P(xc,y0),(xd,y0),xcxd,AB,vi1,i2I{1,2,,,p}vj0I{1,2,,,q},F(xc,y0)=Ai1(xc)Bj0(y0)zi1,j0+Ai1(xc)Bj0+1(y0)zi1,j0+1+Ai1+1(xc)Bj0(y0)zi1+1,j0+Ai1+1(xc)Bj0+1(y0)zi1+1,j0+1,F(xd,y0)=Ai2(xd)Bj0(y0)zi2,j0+Ai2(xd)Bj0+1(y0)zi2,j0+1+Ai2+1(xd)Bj0(y0)zi2+1,j0+Ai2+1(xd)Bj0+1(y0)zi2+1,j0+1,1=Ai1(xc)+Ai1+1(xc)=Ai2(xd)+Ai2+1(xc)=Bj0(y0)+Bj0+1(y0).R(A,B):(Pi)(zi1\zi2\,\ziq)(Pj)(z1j[z2j[,[zpj).x1x2,i1[i2.i1=i2,F(xc,y0)-F(xd,y0)=(Ai1(xc)-Ai1(xd))(Bj0(y0)zi1,j0+Bj0+1(y0)zi1,j0+1)+(Ai1+1(xc)-Ai1+1(xd))(Bj0(y0)zi1+1,j0+Bj0+1(y0)zi1+1,j0+1)[(Ai1(xc)-Ai1(xd))(Bj0(y0)+Bj0+1(y0))zi1j0+(Ai1+1(xc)-Ai1+1(xd))(Bj0(y0)+Bj0+1(y0))zi1+1,j0=(Ai1(xc)-Ai1(xd))zi1,j0+(Ai1+1(xc)-Ai1+1(xd))zi1+1,j0[(Ai1(xc)-Ai1(xd)+Ai1+1(xc)-Ai1+1(xd))zi1+1,j0=0,F(xc,y0)[F(xd,y0).i1i2i1+1[i2,F(xc,y0)[(Ai1(xc)+Ai1+1(xc))(Bj0(y0)zi1+1,j0+Bj0+1(y0)zi1+1,j0+1)=Bj0(y0)zi1+1,j0+Bj0+1(y0)zi1+1,j0+1,F(xd,y0)\Bj0(y0)zi2,j0+Bj0+1(y0)zi2,j0+1,F(xc,y0)-F(xd,y0)[Bj0(y0)(zi1+1,j0-zi2,j0)+Bj0+1(y0)(zi1+1,j0+1-zi2,j0+1)[0,F(xc,y0)[F(xd,y0).F(x,y)x.F(x,y)y..F(x,y)x,y.Ai,Bjxi,yjF(x,y)F(xi,yj)=zij,A,B,C,R(A,B),F(xi,yj)=zijR(A,B)A,B...2211,X=[-E,E],Y=[-U,U],EU;XY.34(E)292A:Xy[0,1],x|yA(x)X,(1):(PxIX)(A(x)=A(-x));(2):A(0)=0;(3):A[0,E];(4):(PxIX)(|x|[A(x)E).xIX,X(x)A(x)X[-A(x)E,A(x)E]{A(x)xc|xcIX},X(x)X.YB:Yy[0,1],y|yB(y)YY(y)B(y)Y.1.1(5):(5):A(?E)=1,B(?U)=1.10S1,A(x)=|x|ES,(6)A(x)1.B(y).212X=[-E,E],Y=[-D,D],Z=[-U,U].XY,A(x)B(y)ZC(z).,YX;X,Y,D=EC,Y=[-EC,EC],BX@Y,B=B(x,y).,:B(x,y)=|x|ES1|y|ECS2,B(x,y)=12|x|ES1+|y|ECS2,(7)0S1,S21.2,yx,BB(y),B(x,y).3,2.,,x(t),y(t),z(t),,X(x(t)),Y(y(t)),Z(z(t));,,/0Ai,Bj,Cij/0,Ai(x(t),t),Bj(y(t),t),Cij(z(t),t).(3)R(t):1:352ifx(t)isAi(t)andy(t)isBj(t)thenz(t)isCij(t).(8)t=0,(8)(3),(3).,F(x(t),y(t),t),F(x(t),y(t),t)=Epi=1Eqj=1Ai(x(t),t)Bj(y(t),t)zij(t),(9),R=R(0)R(t)(t0);,,F(x(t),y(t),t).1,3F(x(t),t).3(a)t=0,(b)t=t10,(c)t=t2t1,3:/0/0(t=t1,t=t2,,).(3).()./0.3,,.(),.36(E)294411R(0)=R:ifxisAithenyisBi,i=1,2,,,n,{Ai}(1[i[n){Bi}1[i[nX=[-E,E]Y=[-U,U],{xi}(1[i[n){yi}(1[i[n)-E=x1x2,xn=E,-U=y1y2,yn=U.k=0,1,2,,,xi(0)=xi,yi(0)=yi;Ai(x(k),k)(i=2,3,,,n-1):A1(x(k),k)=[x(k)-x2(k)]/[x1(k)-x2(k)],x1(k)[x(k)[x2(k);0,x2(k)[x(k)[xn(k);(10)Ai(x(k),k)=[x(k)-xi-1(k)]/[xi(k)-xi-1(k)],xi-1(k)[x(k)[xi(k);[x(k)-xi+1(k)]/[xi(k)-xi+1(k)],xi(k)x(k)[xi+1(k);0,;(11)An(x(k),k)=0,x1(k)[x(k)xn-1(k);[x(k)-xn-1(k)]/[xn(k)-xn-1(k)],xn-1(k)[x(k)[xn(k).(12).:0:x(0)IX,y(1):y(1)=F(x(0),0)=Eni=1Ai(x(0),0)yi(0);1:y(1),x(1),xi(1)=A(x(1))xi(0),yi(1)=B(y(1))yi(0),y(2)=F(x(1),1)=Eni=1Ai(x(1),1)yi(1);2:y(2),x(2),xi(2)=A(x(2))xi(0),yi(2)=B(y(2))yi(0),y(3)=F(x(2),2)=Eni=1Ai(x(2),2)yi(2);,k:y(k),x(k),xi(k)=A(x(k))xi(0),yi(k)=B(y(k))yi(0),(13)y(k+1)=F(x(k),k)=Eni=1Ai(x(k),k)yi(k);(14),A(x),A(x,0A(x).1:372:y(k+1)=B(y(k))F(x(k)/A(x(k)))=B(y(k))Eni=1Ai(x(k)/A(x(k)))yi(0),(15)F(x,0)F(x),(Pk)(x(k)X0).A(x(k))B(y(k)),limky+]x(k)=0]limky+]A(x(k-1))A(x(k))=1,limky+]B(y(k))B(y(k-1))=1,y(k+1)x(k)y0,a=limky+]y(k+1).,x(k)A(x(k)),a=0.(13)(14),(15).y(k+1).y(k+1)-y(k)=F(x(k),k)-F(x(k-1),k-1)=F(x(k),k)-F(x(k),k-1)+F(x(k),k-1)-F(x(k-1),k-1)[F(x(k),k)-F(x(k),k-1)+F(x(k),k-1)-F(x(k-1),k-1),F(x,k-1),PE0,vD0,|x(k)-x(k-1)|D,|F(x(k),k-1)-F(x(k-1),k-1)|E3;x(k)y0,vK1,kK1,|x(k)-x(k-1)|D.F(x(k),k)=B(y(k))B(y(k-1))Fx(k)A(x(k-1))A(x(k)),k-1,M|F(x,k-1)|,F(x(k),k)-F(x(k),k-1)=B(y(k))B(y(k-1))Fx(k)A(x(k-1))A(x(k)),k-1-F(x(k),k-1)[B(y(k))B(y(k-1))Fx(k)A(x(k-1))A(x(k)),k-1-Fx(k)A(x(k-1))A(x(k)),k-1+Fx(k)A(x(k-1))A(x(k)),k-1-F(x(k),k-1)[MB(y(k))B(y(k-1))-1+Fx(k)A(x(k-1))A(x(k)),k-1-F(x(k),k-1),B(y(k))/B(y(k-1))y1,A(x(k-1))/A(x(k))y1,vK2,kK2|A(x(k-1))/A(x(k))-1|D;x(k)y0,vK3,kK3|x(k)|D.,kmax{K2,K3},x(k)A(x(k-1))A(x(k))-x(k)=x(k)A(x(k-1))A(x(k))-1DD=D,Fx(k)A(x(k-1))A(x(k)),k-1-F(x(k),k-1)E/3.vK4,kK4B(y(k))/B(y(k-1))-1E/3M,K=max{K1,K2,K3,K4},kK|y(k+1)-y(k)|E/3+E/3+E/3=E,y(k+1)ya.38(E)29,x(k)A(x(k)),x(k)/A(x(k))y0(x(k)y0),(15)a=0..4A(x),x(k)/A(x(k))y0(x(k)y0).,A(x)=(|x|/E)S(0S1),,x(k)y0,x(k)/A(x(k))=x(k)ES/x(k)S=x(k)1-SESy0.5/0yi(k)((13))F(x(k-1),k-1),B(y)y(k)=F(x(k-1),k-1).4120:x(0)I