1、M 1 a e *李洪兴( =Sv “,100875)K1 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a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.1oM M % y0 1 a e1 e Ri“B AE 1 7 : a Y e, e5, erT X,G L.d e.s yi 4,Y L D 1X: e .D 2B “ - e M a
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3、3 .1 ?5 ef B, I n e , X, Y, Z;t ? “ 8sY:F0(X), F0( Y), F0(Z).F0(X), F0( Y), F0(Z)?1998-04-27 l, 1998-07-24 l*SE1 S “( |: 69674014)a =Sv t W Sh #SE t W !9 “中 国 科 学 ( E ) 29 1 SCIENCE IN CHINA ( Series E) 1999 M2 1“/ M0, “(F0(X), M), (F0( Y), M), (F0(Z), M).F0(X),F0( Y),F0(Z)sY |0“A C, (1)R e ?5?5 o.l
4、1 ?5R(A,B)1A9(h), TR(A,B)1A (Q ),PAc,AdI A,Ac MAd R(Ac,B) M R(Ad,B) (R(Ad,B) R(Ac,B),“ V?R(A,B)1B9(h).R(A,B)1AB (9(h)H,R(A,B) 9(h);R( A, B)1A9(h)71Bh(9) H,R(A,B).1 f,RB_ f ,g 4?R; s (1 p l1 V./ (L L uW. !U I X, Y,Z, PA I F0( U), AB,5V Z T | V, |/ 0;“V( B)?.C 8?B1“/ M0:( PA 1, A 2 I F0( U)(A 1 MA 2 Z
5、x 1 x 2), (2)x 1, x 2sYA 1,A 2?. B uW- a,a NB, NM, NS, ZO, PS, PM, PBL V NB MNM MNS MZO MPS MPM MPB.B e e?5RYif x is Ai and y is Bj then z is Cij, (3)i= 1,2, ,p, j = 1, 2, ,q, D3 , e B=s fF(x,y) = Epi= 1 Eqj= 1Ai(x)Bj(y)zij. (4)T e“d ef :f :X Y yZ, (x,y)|yz = f(x,y), * F(x,y)f(x,y)/, / T:( PE 0)( vN
6、)( n N sup(x,y) I X Y F(x,y) - f(x,y) E). (5)(5) Til/, F(x,y)f (x,y) jB8. ,f(x,y)Y dLf,(5) T e dL/ ?. ) eT, V_v?5R(A,B)1(A,B) ? ef f(x,y)1(x,y)(%V ). 1 B e“d, e?5( 3) T, AB (=MF(nD1),5R(A,B)1AB9(h),R(A,B) 9(h),R(A,B) sA1Hq F(x,y) M. f , f .1 :M 1 a e 33 A1. !R(A,B)1A9,71Bh.5F(x,y)1x9.Y L , P(xc,y0),
7、 (xd,y0), xc A(x)X - A(x)E, A(x)E A(x)xc| xcI X,X(x)X M. V?Y % y0B: Y y0,1, y| yB(y)#Y M Y(y) B(y) Y.% y0M 4ilnm1.l1x 4w % y0 /Hq(5):(5)?: A( ? E)= 1, B( ? U)= 1.m1 n!0 0);i“ % V,?5W 3 ,V7 ef F(x(t),y(t), t)r. f M f Xm1,m3V U M ef F(x(t), t)M .m3 ef HWM(a) t= 0, (b) t= t1 0, (c) t= t2 t1,m3 P 3“BXE:
8、 S ef 1+ “ HWwM$/L.0/0 ef ( t= t1, t= t2, ,). S ef ( 3) T S e?5.7 S e?5 5E( C T )9.yNL./ 0B j5.3 L. “ - .L. E, y TV,4 3.kv f / eYV9 ( ) LC,#/ I n HW“d.36 S S ( E )29 4 1 a e 411 .L.1 a eZE S e?5R( 0)= R: if x is Ai then y is Bi, i= 1,2, ,n, Ai( 1 i n)Bi1 i nsY S X = - E, EY= - U, U LF, sYxi( 1 i n)y
9、i( 1 i n) - E= x1 A(x).1 :M 1 a e 37 2 .L.1 a e E / 9 T: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),i OL !( Pk)(x(k) X 0). TA(x(k)B(y(k) ,limk y+ x(k) = 0 limky+ A(x(k- 1)A(x(k) = 1, limky+ B(y(k)B(y(k- 1) = 1 ,5y(k+ 1)A x(k) y 07 l ,:a= limky+ y(k+ 1).+Y, x(k)
10、 A(x( k) kl,5a= 0. V(13)a(14) T, 4(15) T.y(k+ 1) l . I ny(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) ,yF ( x, k - 1) f ,#PE 0, vD 0,| x ( k) - x ( k - 1) | K 1,L| x(k)- x(k- 1)| K 2| A(x
11、(k- 1)/ A(x(k) - 1| K 3| x(k) | maxK 2,K 3,x(k) A(x(k- 1)A(x(k) - x(k) = x(k) A(x(k- 1)A(x(k) - 1 K 4B(y(k)/ B(y(k- 1) - 1 K| y( k+ 1) - y(k) | E, E( k) A(x(k)E (k= 1,2, ,), X(k) - E(k), E(k) (k= 0,1,2, ,); M(k) sup F(x,0) x I X(k) , k= 0, 1,2, ,.yF(x,0) O( 0,E |s|- E,0) |,#F(0,0)= 0. x(k) y 0 H,M(k
12、) y0.ixi(k) I X(k), V| F(xi(k),0)| M(k),yN,y(k+ 1) = 6ni= 1Ai(x(k),k)yi(k) maxi yi(k) =m axi F(xi(k),0) M(k) y 0 (k y ),yNy(k+ 1) y0 (k y ).8.1 :M 1 a e 39 413 AL.1 a eZE0: n(16) T;1: n(17) T( 18) T;2: y(2) 3“d , I 1 e x(2), |xi(2) = A(x( 2)x 0(0),9 yi( 2) =F(xi(2),1) = Ens= 1As(xi(2),1)ys( 1), x(2)
13、 I X(1);F(xi(2),0) = Ens= 1As(xi(2),0)ys( 0),5;(22)y( 3) = F(x( 2),2) = Eni= 1Ai(x(2), 2)yi(2); (23),k: y(k) 3“d , I 1 e xi(k) = A(x(k)xi(0),9 yi(k) =F(xi(k),k- 1) = Ens= 1As(xi(k),k- 1)ys(k- 1), x(k) I X(k- 1); ( 24)F(xi(k),0) = Ens= 1As(xi(k), 0)ys(0), 5; ( 25)y(k+ 1) = F(x(k),k) = Eni= 1Ai(x(k),k
14、)yi(k). (26),6 E - EI,L LC;yi(k)s T,#L (15) T( 21) T *“dBVr T. l / . 4 limky+ x(k)= 0 limky+ y(k+ 1)= 0. :J k1,k2,k3, ,= k| x(k) I X( k- 1),Jc kc1,kc2,kc3 , , = 1, 2, 3, , J, I n/+ f .f 1 JcK“, HvK,k K,yi(k)(24) T9 , N(k) sup| F(x,k- 1) | x I X(k- 1)F(x,k)/ V,k K, N(k)/, Ox(k- 1) y0 H,| X( k- 1) | y
15、 0, | X(k- 1)| uWX(k- 1),yNN(k) y 0. | y(k+ 1) |= | F(x(k),k) | N(k) y 0 (k y ).f 2 JK“, HvK,k Kyi(k)(25) T9 . 3 V,x(k)y0 H, y(k+ 1) y0.f 3 JcJ (K“.| x(k)s 0 x(kcj )x( kj),x(k) y 0 H, x(kcj ) y0 Ox( kj) y 0, PE 0, vJ1 0,j J1, y(kcj+ 1) J2, | y(kj+ 1)| K,| y(k+ 1) | maxy(kJ1),y(kJ2) $,Z . s.:0, 199142 S S ( E )29
