1.軟件版本
MATLAB2010b
2.模糊神經(jīng)網(wǎng)絡(luò)理論概述
? ? ? ? 由于模糊控制是建立在專家經(jīng)驗的基礎(chǔ)之上的，但這有很大的局限性，而人工神經(jīng)網(wǎng)絡(luò)可以充分逼近任意復(fù)雜的時變非線性系統(tǒng)，采用并行分布處理方法，可學習和自適應(yīng)不確定系統(tǒng)。利用神經(jīng)網(wǎng)絡(luò)可以幫助模糊控制器進行學習，模糊邏輯可以幫助神經(jīng)網(wǎng)絡(luò)初始化及加快學習過程。通常神經(jīng)網(wǎng)絡(luò)的基本構(gòu)架如下所示：
? ? ? 整個神經(jīng)網(wǎng)絡(luò)結(jié)構(gòu)為五層，其中第一層為“輸入層“，第二層為“模糊化層”，第三層為“模糊推理層”，第四層為“歸一化層”，第五層為“解模糊輸出層”。?
? ? ? 第一層為輸入層，其主要包括兩個節(jié)點，所以第一層神經(jīng)網(wǎng)絡(luò)的輸入輸出可以用如下的式子表示：
? ? ? ??第二層為輸入變量的語言變量值，通常是模糊集中的n個變量，它的作用是計算各輸入分量屬于各語言變量值模糊集合的隸屬度。用來確定輸入在不同的模糊語言值對應(yīng)的隸屬度，以便進行模糊推理，如果隸屬函數(shù)為高斯函數(shù)，那么其表達式為：
其中變量的具體含義和第一層節(jié)點的變量含義相同。
第三層是比較關(guān)鍵的一層，即模糊推理層，這一層的每個節(jié)點代表一條模糊規(guī)則，其每個節(jié)點的輸出值表示每條模糊規(guī)則的激勵強度。該節(jié)點的表達式可用如下的式子表示：
?
第四層為歸一化層，其輸出是采用了Madmdani模糊規(guī)則，該層的表達式為：?
第五層是模糊神經(jīng)網(wǎng)絡(luò)的解模糊層，即模糊神經(jīng)網(wǎng)絡(luò)的清晰化.?
3.算法的simulink建模
? ? ? ? 為了對比加入FNN控制器后的性能變化，我們同時要對有FNN控制器的模型以及沒有FNN控制器的模型進行仿真，仿真結(jié)果如下所示：
? ? ? ? 非FNN控制器的結(jié)構(gòu)：
其仿真結(jié)果如下所示：
FNN控制器的結(jié)構(gòu)：
??? 其仿真結(jié)果如下所示：
前面的是訓(xùn)練階段，后面的為實際的輸出，為了能夠體現(xiàn)最后的性能，我們將兩個模型的最后輸出進行對比，得到的對比結(jié)果所示：
?? 從上面的仿真結(jié)果可知，PID的輸出值范圍降低了很多，性能得到了進一步提升。
調(diào)速TS模型，該模型最后的仿真結(jié)果如下所示：
??? 從上面的仿真結(jié)果可知，采用FNN控制器后，其PID的輸出在一個非常小的范圍之內(nèi)進行晃動，整個系統(tǒng)的性能提高了80%。這說明采用模糊神經(jīng)網(wǎng)絡(luò)后的系統(tǒng)具有更高的性能和穩(wěn)定性。
4.部分程序
Mamdani模糊控制器的S函數(shù)
function [out,Xt,str,ts] = Sfunc_fnn_Mamdani(t,Xt,u,flag,Learn_rate,coff,lamda,Number_signal_in,Number_Fuzzy_rules,x0,T_samples)
%輸入定義
% t,Xt,u,flag :S函數(shù)固定的幾個輸入腳
% Learn_rate :學習度
% coff :用于神經(jīng)網(wǎng)絡(luò)第一層的參數(shù)調(diào)整
% lamda :神經(jīng)網(wǎng)絡(luò)的學習遺忘因子
% Number_signal_in :輸入的信號的個數(shù)
% Number_Fuzzy_rules :模糊控制規(guī)則數(shù)
% T_samples :模塊采樣率
%輸入信號的個數(shù)
Number_inport = Number_signal_in;
%整個系統(tǒng)的輸入x，誤差輸入e，以及訓(xùn)練指令的數(shù)組的長度
ninps = Number_inport+1+1;
NumRules = Number_Fuzzy_rules;
Num_out1 = 3*Number_signal_in*Number_Fuzzy_rules + ((Number_signal_in+1)*NumRules)^2 + (Number_signal_in+1)*NumRules;
Num_out2 = 3*Number_signal_in*Number_Fuzzy_rules + (Number_signal_in+1)*NumRules;
%S函數(shù)第一步，參數(shù)的初始化
if flag == 0
out = [0,Num_out1+Num_out2,1+Num_out1+Num_out2,ninps,0,1,1];
str = [];
ts = T_samples;
Xt = x0;
%S函數(shù)的第二步，狀態(tài)的計算
elseif flag == 2
%外部模塊的輸出三個參數(shù)變量輸入x，誤差輸入e，以及訓(xùn)練指令的數(shù)組的長度
x = u(1:Number_inport);%輸入x
e = u(Number_inport+1:Number_inport+1);%誤差輸入e
learning = u(Number_inport+1+1);%訓(xùn)練指令的數(shù)組的長度
%1的時候為正常工作狀態(tài)
if learning == 1
Feedfor_phase2;
%下面定義在正常的工作狀態(tài)中，各個網(wǎng)絡(luò)層的工作
%層1：
In1 = x*ones(1,Number_Fuzzy_rules);
Out1 = 1./(1 + (abs((In1-mean1)./sigma1)).^(2*b1));
%層2：
precond = Out1';
Out2 = prod(Out1)';
S_2 = sum(Out2);
%層3：
if S_2~=0
Out3 = Out2'./S_2;
else
Out3 = zeros(1,NumRules);
end
%層4：
Aux1 = [x; 1]*Out3;
%訓(xùn)練數(shù)據(jù)
a = reshape(Aux1,(Number_signal_in+1)*NumRules,1);
%參數(shù)學習
P = (1./lamda).*(P - P*a*a'*P./(lamda+a'*P*a));
ThetaL4 = ThetaL4 + P*a.*e;
ThetaL4_mat = reshape(ThetaL4,Number_signal_in+1,NumRules);
%錯誤反饋
e3 = [x' 1]*ThetaL4_mat.*e;
denom = S_2*S_2;
%下面自適應(yīng)產(chǎn)生10個規(guī)則的模糊控制器
Theta32 = zeros(NumRules,NumRules);
if denom~=0
for k1=1:NumRules
for k2=1:NumRules
if k1==k2
Theta32(k1,k2) = ((S_2-Out2(k2))./denom).*e3(k2);
else
Theta32(k1,k2) = -(Out2(k2)./denom).*e3(k2);
end
end
end
end
e2 = sum(Theta32,2);
%層一
Q = zeros(Number_signal_in,Number_Fuzzy_rules,NumRules);
for i=1:Number_signal_in
for j=1:Number_Fuzzy_rules
for k=1:NumRules
if Out1(i,j)== precond(k,i) && Out1(i,j)~=0
Q(i,j,k) = (Out2(k)./Out1(i,j)).*e2(k);
else
Q(i,j,k) = 0;
end
end
end
end
Theta21 = sum(Q,3);
%自適應(yīng)參數(shù)調(diào)整
if isempty(find(In1==mean1))
deltamean1 = Theta21.*(2*b1./(In1-mean1)).*Out1.*(1-Out1);
deltab1 = Theta21.*(-2).*log(abs((In1-mean1)./sigma1)).*Out1.*(1-Out1);
deltasigma1 = Theta21.*(2*b1./sigma1).*Out1.*(1-Out1);
dmean1 = Learn_rate*deltamean1 + coff*dmean1;
mean1 = mean1 + dmean1;
dsigma1 = Learn_rate*deltasigma1 + coff*dsigma1;
sigma1 = sigma1 + dsigma1;
db1 = Learn_rate*deltab1 + coff*db1;
b1 = b1 + db1;
for i=1:Number_Fuzzy_rules-1
if ~isempty(find(mean1(:,i)>mean1(:,i+1)))
for i=1:Number_signal_in
[mean1(i,:) index1] = sort(mean1(i,:));
sigma1(i,:) = sigma1(i,index1);
b1(i,:) = b1(i,index1);
end
end
end
end
%完成參數(shù)學習過程
%并保存參數(shù)學習結(jié)果
Xt = [reshape(mean1,Number_signal_in*Number_Fuzzy_rules,1);reshape(sigma1,Number_signal_in*Number_Fuzzy_rules,1);reshape(b1,Number_signal_in*Number_Fuzzy_rules,1);reshape(P,((Number_signal_in+1)*NumRules)^2,1);ThetaL4;reshape(dmean1,Number_signal_in*Number_Fuzzy_rules,1);reshape(dsigma1,Number_signal_in*Number_Fuzzy_rules,1);reshape(db1,Number_signal_in*Number_Fuzzy_rules,1);dThetaL4;];
end
out=Xt;
%S函數(shù)的第三步，定義各個網(wǎng)絡(luò)層的數(shù)據(jù)轉(zhuǎn)換
elseif flag == 3
Feedfor_phase;
%定義整個模糊神經(jīng)網(wǎng)絡(luò)的各個層的數(shù)據(jù)狀態(tài)
%第一層
x = u(1:Number_inport);
In1 = x*ones(1,Number_Fuzzy_rules);%第一層的輸入
Out1 = 1./(1 + (abs((In1-mean1)./sigma1)).^(2*b1));%第一層的輸出，這里，這個神經(jīng)網(wǎng)絡(luò)的輸入輸出函數(shù)可以修改
%第一層
precond = Out1';
Out2 = prod(Out1)';
S_2 = sum(Out2);%計算和
%第三層
if S_2~=0
Out3 = Out2'./S_2;
else
Out3 = zeros(1,NumRules);%為了在模糊控制的時候方便系統(tǒng)的運算，需要對系統(tǒng)進行歸一化處理
end
%第四層
Aux1 = [x; 1]*Out3;
a = reshape(Aux1,(Number_signal_in+1)*NumRules,1);%控制輸出
%第五層，最后結(jié)果輸出
outact = a'*ThetaL4;
%最后的出處結(jié)果
out = [outact;Xt];
else
out = [];
endTS模糊控制器的S函數(shù)文章來源：http://www.zghlxwxcb.cn/news/detail-404837.html
function [out,Xt,str,ts] = Sfunc_fnn_TS(t,Xt,u,flag,Learn_rate,coffa,lamda,r,vigilance,coffb,arate,Number_signal_in,Number_Fuzzy_rules,x0,Xmins,Data_range,T_samples)
%輸入定義
% t,Xt,u,flag :S函數(shù)固定的幾個輸入腳
% Learn_rate :學習度
% coffb :用于神經(jīng)網(wǎng)絡(luò)第一層的參數(shù)調(diào)整
% lamda :神經(jīng)網(wǎng)絡(luò)的學習遺忘因子
% Number_signal_in :輸入的信號的個數(shù)
% Number_Fuzzy_rules :模糊控制規(guī)則數(shù)
% T_samples :模塊采樣率
Data_in_numbers = Number_signal_in;
Data_out_numbers = 1;
%整個系統(tǒng)的輸入x，誤差輸入e，以及訓(xùn)練指令的數(shù)組的長度
ninps = Data_in_numbers+Data_out_numbers+1;
Number_Fuzzy_rules2 = Number_Fuzzy_rules;
Num_out1 = 2*Number_signal_in*Number_Fuzzy_rules + ((Number_signal_in+1)*Number_Fuzzy_rules2)^2 + (Number_signal_in+1)*Number_Fuzzy_rules2 + 1;
Num_out2 = 2*Number_signal_in*Number_Fuzzy_rules + (Number_signal_in+1)*Number_Fuzzy_rules2;
%S函數(shù)第一步，參數(shù)的初始化
if flag == 0
out = [0,Num_out1+Num_out2,1+Num_out1+Num_out2,ninps,0,1,1];
str = [];
ts = T_samples;
Xt = x0;
%S函數(shù)的第二步，狀態(tài)的計算
elseif flag == 2
x1 = (u(1:Data_in_numbers) - Xmins)./Data_range;
x = [ x1; ones(Data_in_numbers,1) - x1];
e = u(Data_in_numbers+1:Data_in_numbers+Data_out_numbers);
learning = u(Data_in_numbers+Data_out_numbers+1);
%1的時候為正常工作狀態(tài)
if learning == 1
NumRules = Xt(1);
NumInTerms = NumRules;
Feedfor_phase;
%最佳參數(shù)搜索
New_nodess = 0;
reass = 0;
Rst_nodes = [];
rdy_nodes = [];
while reass == 0 && NumInTerms<Number_Fuzzy_rules
%搜索最佳點
N = size(w_a,2);
node_tmp = x * ones(1,N);
A_AND_w = min(node_tmp,w_a);
Sa = sum(abs(A_AND_w));
Ta = Sa ./ (coffb + sum(abs(w_a)));
%節(jié)點歸零
Ta(Rst_nodes) = zeros(1,length(Rst_nodes));
Ta(rdy_nodes) = zeros(1,length(rdy_nodes));
[Tamax,J] = max(Ta);
w_J = w_a(:,J);
xa = min(x,w_J);
%最佳節(jié)點測試
if sum(abs(xa))./Number_signal_in >= vigilance,
reass = 1;
w_a(:,J) = arate*xa + (1-arate)*w_a(:,J);
elseif sum(abs(xa))/Number_signal_in < vigilance,
reass = 0;
Rst_nodes = [Rst_nodes J ];
end
if length(Rst_nodes)== N || length(rdy_nodes)== N
w_a = [w_a x];
New_nodess = 1;
reass = 0;
end
end;
%節(jié)點更新
u2 = w_a(1:Number_signal_in,:);
v2 = 1 - w_a(Number_signal_in+1:2*Number_signal_in,:);
NumInTerms = size(u2,2);
NumRules = NumInTerms;
if New_nodess == 1
ThetaL5 = [ThetaL5; zeros(Number_signal_in+1,1)];
dThetaL5 = [dThetaL5; zeros(Number_signal_in+1,1)];
P = [ P zeros((Number_signal_in+1)*(NumRules-1),Number_signal_in+1);
zeros(Number_signal_in+1,(Number_signal_in+1)*(NumRules-1)) 1e6*eye(Number_signal_in+1); ];
du2 = [du2 zeros(Number_signal_in,1);];
dv2 = [dv2 zeros(Number_signal_in,1);];
end
%層2：
x1_tmp = x1;
x1_tmp2 = x1_tmp*ones(1,NumInTerms);
Out2 = 1 - check(x1_tmp2-v2,r) - check(u2-x1_tmp2,r);
%層3：
Out3 = prod(Out2);
S_3 = sum(Out3);
%層4：
if S_3~=0
Out4 = Out3/S_3;
else
Out4 = zeros(1,NumRules);
end
Aux1 = [x1_tmp; 1]*Out4;
a = reshape(Aux1,(Number_signal_in+1)*NumRules,1);
%層五
P = (1./lamda).*(P - P*a*a'*P./(lamda+a'*P*a));
ThetaL5 = ThetaL5 + P*a.*e;
ThetaL5_tmp = reshape(ThetaL5,Number_signal_in+1,NumRules);
%錯誤反饋
%層4：
e4 = [x1_tmp' 1]*ThetaL5_tmp.*e;
denom = S_3*S_3;
%層3：
Theta43 = zeros(NumRules,NumRules);
if denom~=0
for k1=1:NumRules
for k2=1:NumRules
if k1==k2
Theta43(k1,k2) = ((S_3-Out3(k2))./denom).*e4(k2);
else
Theta43(k1,k2) = -(Out3(k2)./denom).*e4(k2);
end
end
end
end
e3 = sum(Theta43,2);
%層2
Q = zeros(Number_signal_in,NumInTerms,NumRules);
for i=1:Number_signal_in
for j=1:NumInTerms
for k=1:NumRules
if j==k && Out2(i,j)~=0
Q(i,j,k) = (Out3(k)./Out2(i,j)).*e3(k);
else
Q(i,j,k) = 0;
end
end
end
end
Thetass = sum(Q,3);
Thetavv = zeros(Number_signal_in,NumInTerms);
Thetauu = zeros(Number_signal_in,NumInTerms);
for i=1:Number_signal_in
for j=1:NumInTerms
if ((Out2(i)-v2(i,j))*r>=0) && ((Out2(i)-v2(i,j))*r<=1)
Thetavv(i,j) = r;
end
if ((u2(i,j)-Out2(i))*r>=0) && ((u2(i,j)-Out2(i))*r<=1)
Thetauu(i,j) = -r;
end
end
end
%根據(jù)學習結(jié)果辨識參數(shù)計算
e3_tmp = (e3*ones(1,Number_signal_in))';
du2 = Learn_rate*Thetavv.*e3_tmp.*Thetass + coffa*du2;
dv2 = Learn_rate*Thetauu.*e3_tmp.*Thetass + coffa*dv2;
v2 = v2 + du2;
u2 = u2 + dv2;
if ~isempty(find(u2>v2))
for i=1:Number_signal_in
for j=1:NumInTerms
if u2(i,j) > v2(i,j)
temp = v2(i,j);
v2(i,j) = u2(i,j);
u2(i,j) = temp;
end
end
end
end
if ~isempty(find(u2<0)) || ~isempty(find(v2>1))
for i=1:Number_signal_in
for j=1:NumInTerms
if u2(i,j) < 0
u2(i,j) = 0;
end
if v2(i,j) > 1
v2(i,j) = 1;
end
end
end
end
%WA由學習結(jié)果更新
w_a = [u2; 1-v2];
%上面的結(jié)果完成學習過程
Xt1 = [NumRules;reshape(w_a,2*Number_signal_in*NumInTerms,1);reshape(P,((Number_signal_in+1)*NumRules)^2,1); ThetaL5;reshape(du2,Number_signal_in*NumInTerms,1);reshape(dv2,Number_signal_in*NumInTerms,1);dThetaL5;];
ns1 = size(Xt1,1);
Xt = [Xt1; zeros(Num_out1+Num_out2-ns1,1);];
end
out=Xt;
%S函數(shù)的第三步，定義各個網(wǎng)絡(luò)層的數(shù)據(jù)轉(zhuǎn)換
elseif flag == 3
NumRules = Xt(1);
NumInTerms = NumRules;
Feedfor_phase;
u2 = w_a(1:Number_signal_in,:);
v2 = 1 - w_a(Number_signal_in+1:2*Number_signal_in,:);
%層1輸出
x1 = (u(1:Data_in_numbers) - Xmins)./Data_range;
%層2輸出
x1_tmp = x1;
x1_tmp2 = x1_tmp*ones(1,NumInTerms);
Out2 = 1 - check(x1_tmp2-v2,r) - check(u2-x1_tmp2,r);
%層3輸出
Out3 = prod(Out2);
S_3 = sum(Out3);
%層4輸出.
if S_3~=0
Out4 = Out3/S_3;
else
Out4 = zeros(1,NumRules);
end
%層5輸出
Aux1 = [x1_tmp; 1]*Out4;
a = reshape(Aux1,(Number_signal_in+1)*NumRules,1);
outact = a'*ThetaL5;
out = [outact;Xt];
else
out = [];
end
function y = check(s,r);
rows = size(s,1);
columns = size(s,2);
y = zeros(rows,columns);
for i=1:rows
for j=1:columns
if s(i,j).*r>1
y(i,j) = 1;
elseif 0 <= s(i,j).*r && s(i,j).*r <= 1
y(i,j) = s(i,j).*r;
elseif s(i,j).*r<0
y(i,j) = 0;
end
end
end
return
A05-04文章來源地址http://www.zghlxwxcb.cn/news/detail-404837.html
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