%用隸屬函數型神經網與模糊控制融合的解耦程序（FLch7FNNeg3.m）
1) 開發的程序

p1=0.5;
q1=0.5;
p2=0.5;
q2=0.5;

p3=0.5;
q3=0.5;
p4=0.95;
q4=0.5;

p5=0.95;
q5=0.5;
p6=0.95;
q6=0.5;

p7=0.5;
q7=0.5;
p8=0.95;
q8=0.5;

p9=0.5;
q9=0.5;
p10=0.95;
q10=0.5;

p11=0.95;
q11=0.5;
p12=0.95;
q12=0.5;

p13=0.65;
q13=0.05;
%隸屬函數型神經網的中心值、尺度因子和權向量初始化部分
a10=[-2 0 2];
a11=[-2 0 2];
a20=[-2 0 2];
a21=[-2 0 2];
b10=[1.5 1.5 1.5];
b11=[1.5 1.5 1.5];
b20=[1.5 1.5 1.5];
b21=[1.5 1.5 1.5];
v0=[-1 -0.5 -0.5;-0.5 0 0.5;0.5 0.5 1];
v1=[-1 -0.5 -0.5;-0.5 0 0.5;0.5 0.5 1];
%系統部分的初值
yp0=0;
yp1=0;
ep0=0;
ep1=0;
up0=1.05;
up1=1.39;
x1=0.12;
x2=0.24;
y0=0;
y1=0;
u1=0;
e0=0;
e1=0;
sp=10;
k=1;
se=0.02;
sd=0.02;
su=0.0522;
%開始
kp=0.284;
ki=0.03;
kd=0.626;

%the second channel reference
p12=0.5;
q12=0.5;
p22=0.5;
q22=0.5;

p32=0.5;
q32=0.5;
p42=0.95;
q42=0.5;

p52=0.95;
q52=0.5;
p62=0.95;
q62=0.5;

p72=0.5;
q72=0.5;
p82=0.95;
q82=0.5;

p92=0.5;
q92=0.5;
p102=0.95;
q102=0.5;

p112=0.95;
q112=0.5;
p122=0.95;
q122=0.5;

p132=0.65;
q132=0.05;
%系統部分的初值
yp02=0;
yp12=0;
ep02=0;
ep12=0;
up02=1.05;
up12=1.39;
x12=0.12;
x22=0.24;
y02=0;
y12=0;
u12=0;
e02=0;
e12=0;
sp2=5;
k=1;
se2=0.02;
sd2=0.02;
su2=0.0522;

kp2=0.284;
ki2=0.03;
kd2=0.626;
%+++++++++++++++++++++++++++++++++++++++%子系統1(SUB1)的J循環開始  
for J=1:50
   ep1=10-yp1;
   pid=kp*(ep1-ep0)+ki*ep1;
   up2=up1+pid;
   yp2=0.5*yp1+2.5*up2+2.5*up1;
   %yp2=0.8333*yp1-0.1667*yp0+1.6667*up2+1.6667*up1;   
   yp(:,J)=yp2;
   up0=up1;
   up1=up2;
   ep0=ep1; 
   yp0=yp1;
   yp1=yp2;
end  
time=[1:1:50];
n=0.28*rand(size(time)); %產生的SUB1隨機噪聲
n1=0.3*rand(size(time));%產生的SUB2隨機噪聲
while(k<=50)
   %function deal with
 for(T=1:20)
   X1=x1*se;
   X2=x2*sd;
   
  if(X1<=-2)
     X1=-2;
  elseif(X1>=2)
     X1=2;
  end
  if(X2<=-2)
     X2=-2;
  elseif(X2>=2)
     X2=2;
  end

%the hiddening layer output of FNN  
for i=1:3
   for j=1:3
         A=[(X1-a11(:,i))/b11(:,i)].^2;
         B=[(X2-a21(:,j))/b21(:,j)].^2;
         h(i,j)=exp(-(A+B)/2);
   end
end   
%the output
sum=0;
for i=1:3
   for j=1:3
      sum=sum+h(i,j)*v1(i,j);
   end
end
ot=sum;
cu=su*ot;
u2=u1+cu;
disp(u2);
if(u2<0)
u2=0;
elseif(u2>=1)
 u2=1;
end
 y2=0.5*y1+2.5*u2+2.5*u1+n1(:,k)+0.01*y12;  %+n1(:,k)+0.01*y12表示隨機噪聲和子系統間的相互耦合
disp(['the output y number is' int2str(T)]);
disp(y2);
Y(:,k)=y2;
E=0.5*(sp-y2).^2;
e2=sp-y2;

Es(:,k)=e2;
x1=e2;
x2=e2-e1;
e0=e1;
e1=e2;

 delot=(sp-y2)*2.5*su;

for i=1:3
   for j=1:3
      dv=v1(i,j)-v0(i,j);
      v2=v1(i,j)+p13*delot+q13*dv;
      v3(i,j)=v2;
   end
end

%refreshing the center and width
%a11
  s1=0;
  for j=1:3
   s1=s1+v1(1,j)*h(1,j);
  end
  pa11=s1;
  a110=a10(:,1);
  a111=a11(:,1);    
  dela11=pa11*(X1-a111)/b11(:,1).^2;
  da11=a111-a110;
  a112=a111+p1*dela11+q1*da11;
  a10(:,1)=a111;
  a11(:,1)=a112;
%a12
   s2=0;
   for j=1:3
   s2=s2+v1(2,j)*h(2,j);
   end
   pa12=s2;
   a120=a10(:,2);
   a121=a11(:,2);    
   dela12=pa12*(X1-a121)/b11(:,2).^2;
   da12=a121-a120;
   a122=a121+p2*dela12+q2*da12;
   a10(:,2)=a121;
   a11(:,2)=a122;
  %a13
   s3=0;
   for j=1:3
   s3=s3+v1(3,j)*h(3,j);
   end
   pa13=s3;
   a130=a10(:,3);
   a131=a11(:,3);    
   dela13=pa13*(X1-a131)/b11(:,3).^2;
   da13=a131-a130;
   a132=a131+p3*dela13+q3*da13;
   a10(:,3)=a131;
   a11(:,3)=a132;
% b11
   pb11=pa11;
   b110=b10(:,1);
   b111=b11(:,1);    
   delb11=pb11*[(X1-a111)].^2/b111.^3;
   db11=b111-b110;
   b112=b111+p4*delb11+q4*db11;
   b10(:,1)=b111;
   b11(:,1)=b112;
%b12
   pb12=pa12;
   b120=b10(:,2);
   b121=b11(:,2);    
   delb12=pb12*[(X1-a121)].^2/b121.^3;
   db12=b121-b120;
   b122=b121+p5*delb12+q5*db12;
   b10(:,2)=b121;
   b11(:,2)=b122;
%b13
   pb13=pa13;
   b130=b10(:,3);
   b131=b11(:,3);    
   delb13=pb13*[(X1-a131)].^2/b131.^3;
   db13=b131-b130;
   b132=b131+p6*delb13+q6*db13;
   b10(:,3)=b131;
   b11(:,3)=b132;
%a21
    s4=0;
for i=1:3
    s4=s4+v1(i,1)*h(i,1);
end
    pa21=s4;
    a210=a20(:,1);
    a211=a21(:,1);    
    dela21=pa21*(X2-a211)/b21(:,1).^2;
    da21=a211-a210;
    a212=a211+p7*dela21+q7*da21;
    a20(:,1)=a211;
    a21(:,1)=a212;
%a22
    s5=0;
for i=1:3
    s5=s5+v1(i,2)*h(i,2);
end
    pa22=s5;
    a220=a20(:,2);
    a221=a21(:,2);    
    dela22=pa22*(X2-a221)/b21(:,2).^2;
    da22=a221-a220;
    a222=a221+p8*dela22+q8*da22;
    a20(:,2)=a221;
    a21(:,2)=a222;
%a23  
     s6=0;
 for i=1:3
     s6=s6+v1(i,3)*h(i,3);
 end
    pa23=s6;
    a230=a20(:,3);
    a231=a21(:,3);    
    dela23=pa23*(X2-a231)/b21(:,3).^2;
    da23=a231-a230;
    a232=a231+p9*dela23+q3*da23;
    a20(:,3)=a231;
    a21(:,3)=a232;
%b21
   pb21=pa21;
   b210=b20(:,1);
   b211=b21(:,1);    
   delb21=pb21*[(X2-a211)].^2/b211.^3;
   db21=b211-b210;
   b212=b211+p10*delb21+q10*db21;
   b20(:,1)=b211;
   b21(:,1)=b212;
%b22
   pb22=pa22;
   b220=b20(:,2);
   b221=b21(:,2);    
   delb22=pb22*[(X2-a221)].^2/b221.^3;
   db22=b221-b220;
   b222=b221+p11*delb22+q11*db22;
   b20(:,2)=b221;
   b21(:,2)=b222;
%b23
   pb23=pa23;
   b230=b20(:,3);
   b231=b21(:,3);    
   delb23=pb23*[(X2-a231)].^2/b231.^3;
   db23=b231-b230;
   b232=b231+p12*delb23+q12*db23;
   b20(:,3)=b231;
   b21(:,3)=b232;
   v0=v1;
   v1=v3;
   if(abs(e1)<0.00015)
      break;
   end
  
end  
a11
a21
b11
b21
v3

   
   y0=y1;
   y1=y2
   u0=u1;
   u1=u2;

%adding the second channel

%權向量初始化部分
a102=[-2 0 2];
a112=[-2 0 2];
a202=[-2 0 2];
a212=[-2 0 2];
b102=[1.5 1.5 1.5];
b112=[1.5 1.5 1.5];
b202=[1.5 1.5 1.5];
b212=[1.5 1.5 1.5];
v02=[-1 -0.5 -0.5;-0.5 0 0.5;0.5 0.5 1];
v12=[-1 -0.5 -0.5;-0.5 0 0.5;0.5 0.5 1];
%+++++++++++++++++++++++++++++++++++++%子系統2(SUB2)的J循環開始 
for J=1:100
   ep2=5-yp12;
   pid2=kp2*(ep12-ep02)+ki2*ep12;
   up22=up12+pid2;
   yp22=0.5*yp12+1.25*up22+1.25*up12;
   %yp2=0.8333*yp1-0.1667*yp0+1.6667*up2+1.6667*up1;   
   yp2(:,J)=yp22;
   up02=up12;
   up12=up22;
   ep02=ep12; 
   yp02=yp12;
   yp12=yp22;
end   
%while(k<=250)
   %function deal width
for(T=1:20)
   X12=x12*se2;
   X22=x22*sd2;
   
   
  if(X12<=-2)
     X12=-2;
  elseif(X12>=2)
     X12=2;
  end
  if(X22<=-2)
     X22=-2;
  elseif(X22>=2)
     X22=2;
  end

%the hiddening layer output of FNN,  
for i=1:3
   for j=1:3
         A=[(X12-a112(:,i))/b112(:,i)].^2;
         B=[(X22-a212(:,j))/b212(:,j)].^2;
         h(i,j)=exp(-(A+B)/2);
   end
end   
%the output
sum2=0;
for i=1:3
   for j=1:3
      sum2=sum2+h(i,j)*v12(i,j);
   end
end
ot=sum2;
cu=su2*ot;
u22=u12+cu;
disp(u22);
if(u22<0)
u22=0;
elseif(u22>=1)
 u22=1;
end

 y22=0.5*y12+1.25*u22+1.25*u12+n(:,k)+0.01*y1; %+n(:,k)+0.01*y1表示隨機噪聲和子系統間的相互耦合

disp(['the output y2 number is' int2str(T)]);
disp(y22);
Y2(:,k)=y22;
E2=0.5*(sp2-y22).^2;
e22=sp2-y22;

E22(:,k)=e22;
x12=e22;
x22=e22-e12;
e02=e12;
e12=e22;

delot=(sp2-y22)*1.25*su2;

for i=1:3
   for j=1:3
      dv=v12(i,j)-v02(i,j);
      v22=v12(i,j)+p132*delot+q132*dv;
      v32(i,j)=v22;
   end
end

%refreshing the center and width
%a11
  s12=0;
  for j=1:3
   s12=s12+v12(1,j)*h(1,j);
  end
  pa112=s12;
  a1102=a102(:,1);
  a1112=a112(:,1);    
  dela112=pa112*(X12-a1112)/b112(:,1).^2;
  da112=a1112-a1102;
  a1122=a1112+p12*dela112+q12*da112;
  a102(:,1)=a1112;
  a112(:,1)=a1122;
%a12
   s22=0;
   for j=1:3
   s22=s22+v12(2,j)*h(2,j);
   end
   pa122=s22;
   a1202=a102(:,2);
   a1212=a112(:,2);    
   dela122=pa122*(X12-a121)/b112(:,2).^2;
   da122=a1212-a1202;
   a1222=a1212+p22*dela122+q22*da122;
   a102(:,2)=a1212;
   a112(:,2)=a1222;
  %a13
   s32=0;
   for j=1:3
   s32=s32+v12(3,j)*h(3,j);
   end
   pa132=s32;
   a1302=a102(:,3);
   a1312=a112(:,3);    
   dela132=pa132*(X12-a1312)/b112(:,3).^2;
   da132=a1312-a1302;
   a1322=a1312+p32*dela132+q32*da132;
   a102(:,3)=a1312;
   a112(:,3)=a1322;
% b11
   pb112=pa112;
   b1102=b102(:,1);
   b1112=b112(:,1);    
   delb112=pb112*[(X12-a111)].^2/b1112.^3;
   db112=b1112-b1102;
   b1122=b1112+p42*delb112+q42*db112;
   b102(:,1)=b1112;
   b112(:,1)=b1122;
%b12
   pb122=pa122;
   b1202=b102(:,2);
   b1212=b112(:,2);    
   delb122=pb122*[(X12-a1212)].^2/b1212.^3;
   db122=b1212-b1202;
   b1222=b1212+p52*delb122+q52*db122;
   b102(:,2)=b1212;
   b112(:,2)=b1222;
%b13
   pb132=pa132;
   b1302=b102(:,3);
   b1312=b112(:,3);    
   delb132=pb132*[(X12-a1312)].^2/b1312.^3;
   db132=b1312-b1302;
   b1322=b1312+p62*delb132+q62*db132;
   b102(:,3)=b1312;
   b112(:,3)=b1322;
%a21
    s42=0;
for i=1:3
    s42=s42+v12(i,1)*h(i,1);
end
    pa212=s42;
    a2102=a202(:,1);
    a2112=a212(:,1);    
    dela212=pa212*(X22-a2112)/b212(:,1).^2;
    da212=a2112-a2102;
    a2122=a2112+p72*dela212+q72*da212;
    a202(:,1)=a2112;
    a212(:,1)=a2122;
%a22
    s52=0;
for i=1:3
    s52=s52+v12(i,2)*h(i,2);
end
    pa222=s52;
    a2202=a202(:,2);
    a2212=a212(:,2);    
    dela222=pa222*(X22-a2212)/b212(:,2).^2;
    da222=a2212-a2202;
    a2222=a2212+p82*dela222+q82*da222;
    a202(:,2)=a2212;
    a212(:,2)=a2222;
%a23  
     s62=0;
 for i=1:3
     s62=s62+v1(i,3)*h(i,3);
 end
    pa232=s62;
    a2302=a202(:,3);
    a2312=a212(:,3);    
    dela232=pa232*(X22-a2312)/b212(:,3).^2;
    da232=a2312-a2302;
    a2322=a2312+p92*dela232+q32*da232;
    a202(:,3)=a2312;
    a212(:,3)=a2322;
%b21
   pb212=pa212;
   b2102=b202(:,1);
   b2112=b212(:,1);    
   delb212=pb212*[(X22-a2112)].^2/b2112.^3;
   db212=b2112-b2102;
   b2122=b2112+p102*delb212+q102*db212;
   b202(:,1)=b2112;
   b212(:,1)=b2122;
%b22
   pb222=pa222;
   b2202=b202(:,2);
   b2212=b212(:,2);    
   delb222=pb222*[(X22-a2212)].^2/b2212.^3;
   db222=b2212-b2202;
   b2222=b2212+p112*delb222+q112*db222;
   b202(:,2)=b2212;
   b212(:,2)=b2222;
%b23
   pb232=pa232;
   b2302=b202(:,3);
   b2312=b212(:,3);    
   delb232=pb232*[(X22-a2312)].^2/b2312.^3;
   db232=b2312-b2302;
   b2322=b2312+p122*delb232+q122*db232;
   b202(:,3)=b2312;
   b212(:,3)=b2322;
   v02=v12;
   v12=v32;
   if(abs(e12)<0.00015)
      break;
   end
end   
   
if(abs(e1)<=eps & abs(e)<=eps)
      break;
else
      k=k+1;
end
   y02=y12;
   y12=y22;
   u02=u12;
   u12=u22;
end
L=k-1; n2=n;
%L=k;
m=1:L;
R=ones(size(m));
sp=R*10;
sp2=R*5;
a112
a212
b112
b212
v12
%plot(m,sp,'r',m,y,'g',m,y,'go',m,y,'g.',m,yp,'b');
subplot(2,1,1);
plot(m,sp,'k', m,Y,'rx',m,sp2,'k', m,Y2,'bx',m,Es,'r',m,E22,'b');
legend('sp is SUB1-input','Y is SUB1-decoupling','sp2 is SUB2-input','Y2 is SUB2-decoupling','Es is error1','E22 is error2' ); %圖標炷 
title('The decoupling by FNN algorithm'),
xlabel('k'),
ylabel('yp,y and sp2,y2')
subplot(2,1,2);
plot(m,n1,'k',m,n2,'r');
legend('n1 is SUB1-noise','n2 is SUB2-noise' ); %圖標炷    
xlabel('k'),ylabel('random noise')