【模糊神经网络】基于simulink的模糊神经网络控制器设计(模糊数学神经网络)

【模糊神经网络】基于simulink的模糊神经网络控制器设计 1.软件版本

推荐整理分享【模糊神经网络】基于simulink的模糊神经网络控制器设计(模糊数学神经网络)，希望有所帮助，仅作参考，欢迎阅读内容。

文章相关热门搜索词:模糊rbf神经网络,模糊神经网络训练数据量多少合适,模糊神经网络原理,模糊神经网络和神经网络区别,模糊神经网络pid,模糊神经网络应用,模糊神经网络和神经网络区别,模糊神经网络和神经网络区别,内容如对您有帮助，希望把文章链接给更多的朋友！

MATLAB2010b

2.模糊神经网络理论概述

        由于模糊控制是建立在专家经验的基础之上的，但这有很大的局限性，而人工神经网络可以充分逼近任意复杂的时变非线性系统，采用并行分布处理方法，可学习和自适应不确定系统。利用神经网络可以帮助模糊控制器进行学习，模糊逻辑可以帮助神经网络初始化及加快学习过程。通常神经网络的基本构架如下所示：

      整个神经网络结构为五层，其中第一层为“输入层“，第二层为“模糊化层”，第三层为“模糊推理层”，第四层为“归一化层”，第五层为“解模糊输出层”。 

      第一层为输入层，其主要包括两个节点，所以第一层神经网络的输入输出可以用如下的式子表示：

        第二层为输入变量的语言变量值，通常是模糊集中的n个变量，它的作用是计算各输入分量属于各语言变量值模糊集合的隶属度。用来确定输入在不同的模糊语言值对应的隶属度，以便进行模糊推理，如果隶属函数为高斯函数，那么其表达式为：

其中变量的具体含义和第一层节点的变量含义相同。

第三层是比较关键的一层，即模糊推理层，这一层的每个节点代表一条模糊规则，其每个节点的输出值表示每条模糊规则的激励强度。该节点的表达式可用如下的式子表示：

 

第四层为归一化层，其输出是采用了Madmdani模糊规则，该层的表达式为： 

第五层是模糊神经网络的解模糊层，即模糊神经网络的清晰化. 

3.算法的simulink建模

        为了对比加入FNN控制器后的性能变化，我们同时要对有FNN控制器的模型以及没有FNN控制器的模型进行仿真，仿真结果如下所示：

        非FNN控制器的结构：

其仿真结果如下所示：

FNN控制器的结构：

    其仿真结果如下所示：

前面的是训练阶段，后面的为实际的输出，为了能够体现最后的性能，我们将两个模型的最后输出进行对比，得到的对比结果所示：

   从上面的仿真结果可知，PID的输出值范围降低了很多，性能得到了进一步提升。

调速TS模型，该模型最后的仿真结果如下所示：

    从上面的仿真结果可知，采用FNN控制器后，其PID的输出在一个非常小的范围之内进行晃动，整个系统的性能提高了80%。这说明采用模糊神经网络后的系统具有更高的性能和稳定性。

4.部分程序

Mamdani模糊控制器的S函数

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)%输入定义% t,Xt,u,flag :S函数固定的几个输入脚% Learn_rate :学习度% coff :用于神经网络第一层的参数调整% lamda :神经网络的学习遗忘因子% Number_signal_in :输入的信号的个数 % Number_Fuzzy_rules :模糊控制规则数% T_samples :模块采样率%输入信号的个数 Number_inport = Number_signal_in;%整个系统的输入x，误差输入e，以及训练指令的数组的长度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函数第一步，参数的初始化if flag == 0out = [0,Num_out1+Num_out2,1+Num_out1+Num_out2,ninps,0,1,1]; str = []; ts = T_samples; Xt = x0;%S函数的第二步，状态的计算elseif flag == 2%外部模块的输出三个参数变量输入x，误差输入e，以及训练指令的数组的长度x = u(1:Number_inport);%输入xe = u(Number_inport+1:Number_inport+1);%误差输入elearning = u(Number_inport+1+1);%训练指令的数组的长度%1的时候为正常工作状态if learning == 1 Feedfor_phase2; %下面定义在正常的工作状态中，各个网络层的工作%层1：In1 = x*ones(1,Number_Fuzzy_rules);Out1 = 1./(1 + (abs((In1-mean1)./sigma1)).^(2*b1));%层2：precond = Out1'; Out2 = prod(Out1)';S_2 = sum(Out2);%层3：if S_2~=0 Out3 = Out2'./S_2;else Out3 = zeros(1,NumRules);end %层4：Aux1 = [x; 1]*Out3;%训练数据a = reshape(Aux1,(Number_signal_in+1)*NumRules,1); %参数学习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);%错误反馈e3 = [x' 1]*ThetaL4_mat.*e;denom = S_2*S_2;%下面自适应产生10个规则的模糊控制器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 endende2 = sum(Theta32,2);%层一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 endTheta21 = sum(Q,3);%自适应参数调整 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 endendend%完成参数学习过程%并保存参数学习结果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;];endout=Xt;%S函数的第三步，定义各个网络层的数据转换elseif flag == 3Feedfor_phase;%定义整个模糊神经网络的各个层的数据状态%第一层x = u(1:Number_inport);In1 = x*ones(1,Number_Fuzzy_rules);%第一层的输入Out1 = 1./(1 + (abs((In1-mean1)./sigma1)).^(2*b1));%第一层的输出，这里，这个神经网络的输入输出函数可以修改%第一层precond = Out1'; Out2 = prod(Out1)';S_2 = sum(Out2);%计算和%第三层if S_2~=0 Out3 = Out2'./S_2;else Out3 = zeros(1,NumRules);%为了在模糊控制的时候方便系统的运算，需要对系统进行归一化处理end%第四层Aux1 = [x; 1]*Out3;a = reshape(Aux1,(Number_signal_in+1)*NumRules,1);%控制输出%第五层，最后结果输出outact = a'*ThetaL4;%最后的出处结果out = [outact;Xt]; elseout = [];end

TS模糊控制器的S函数

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)%输入定义% t,Xt,u,flag :S函数固定的几个输入脚% Learn_rate :学习度% coffb :用于神经网络第一层的参数调整% lamda :神经网络的学习遗忘因子% Number_signal_in :输入的信号的个数 % Number_Fuzzy_rules :模糊控制规则数% T_samples :模块采样率 Data_in_numbers = Number_signal_in;Data_out_numbers = 1;%整个系统的输入x，误差输入e，以及训练指令的数组的长度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函数第一步，参数的初始化if flag == 0out = [0,Num_out1+Num_out2,1+Num_out1+Num_out2,ninps,0,1,1]; str = []; ts = T_samples; Xt = x0;%S函数的第二步，状态的计算elseif flag == 2x1 = (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的时候为正常工作状态if learning == 1 NumRules = Xt(1);NumInTerms = NumRules;Feedfor_phase; %最佳参数搜索New_nodess = 0;reass = 0;Rst_nodes = []; rdy_nodes = [];while reass == 0 && NumInTerms<Number_Fuzzy_rules %搜索最佳点 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))); %节点归零 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); %最佳节点测试 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; endend; %节点更新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%层2：x1_tmp = x1;x1_tmp2 = x1_tmp*ones(1,NumInTerms);Out2 = 1 - check(x1_tmp2-v2,r) - check(u2-x1_tmp2,r);%层3： Out3 = prod(Out2); S_3 = sum(Out3);%层4：if S_3~=0 Out4 = Out3/S_3;else Out4 = zeros(1,NumRules); endAux1 = [x1_tmp; 1]*Out4;a = reshape(Aux1,(Number_signal_in+1)*NumRules,1);%层五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);%错误反馈%层4：e4 = [x1_tmp' 1]*ThetaL5_tmp.*e;denom = S_3*S_3;%层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 endende3 = sum(Theta43,2);%层2Q = 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 endThetass = 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 endend%根据学习结果辨识参数计算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 endendif ~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 endend%WA由学习结果更新w_a = [u2; 1-v2];%上面的结果完成学习过程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函数的第三步，定义各个网络层的数据转换elseif flag == 3NumRules = 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,:);%层1输出x1 = (u(1:Data_in_numbers) - Xmins)./Data_range; %层2输出x1_tmp = x1; x1_tmp2 = x1_tmp*ones(1,NumInTerms); Out2 = 1 - check(x1_tmp2-v2,r) - check(u2-x1_tmp2,r);%层3输出Out3 = prod(Out2); S_3 = sum(Out3);%层4输出.if S_3~=0 Out4 = Out3/S_3;else Out4 = zeros(1,NumRules); end%层5输出Aux1 = [x1_tmp; 1]*Out4;a = reshape(Aux1,(Number_signal_in+1)*NumRules,1);outact = a'*ThetaL5;out = [outact;Xt]; elseout = [];endfunction 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 endendreturn

A05-04