www.pudn.com > nnctrl_v5.zip > special1.m, change:1997-10-28,size:10538b


% ---------------------------------     SPECIAL1     ------------------------------ 
% 
%  Program for training an inverse model of a system by so-called specialized 
%  training (see Psaltis, Sideris & Yamamura: "A Multilayered Neural Network 
%  Controller"). 
%   
%  The inverse model is trained with a recursive back-propagation algorithm. 
% 
%  The user must provide a neural network model of the process to be controlled 
%  and an initial inverse model. This can be created by choosing the weights at 
%  random or by training the network with general training. The latter is 
%  recommended when possible.  
% 
%  All parameters associated with the training procedure are set in the 
%  file 'invinit1.m' 
% 
%  Made by Magnus Norgaard IAU, Technical University of Denmark. 
%  LastEditDate: Oct. 28, 1997.  
 
 
%---------------------------------------------------------------------------------- 
%-------------------         >>>  INITIALIZATIONS  <<<        --------------------- 
%---------------------------------------------------------------------------------- 
 
%>>>>>>>>>>>>>>>>>>>>>>      READ VARIABLES FROM FILE       <<<<<<<<<<<<<<<<<<<<<<< 
clear plot_a plot_b 
global ugl 
invinit1                                 % Run user sepcified initializations 
eval(['load ' nninv]);                   % Load inverse neural model 
 
 
% >>>>>>>>>>>>>>>>>>   DETERMINE STRUCTURE OF FORWARD MODEL    <<<<<<<<<<<<<<<<<<<< 
outputs   = 1;                           % # of outputs 
eval(['load ' nnforw]);                  % Load forward neural model of system 
hiddenf   = length(NetDeff(1,:));        % Number of hidden neurons 
L_hiddenf = find(NetDeff(1,:)=='L')';    % Location of linear hidden neurons 
H_hiddenf = find(NetDeff(1,:)=='H')';    % Location of tanh hidden neurons 
L_outputf = find(NetDeff(2,:)=='L')';    % Location of linear output neurons 
H_outputf = find(NetDeff(2,:)=='H')';    % Location of tanh output neurons 
y1f       = [zeros(hiddenf,1);1];        % Hidden layer outputs 
yhat      = zeros(outputs,1);            % Network output 
 
 
% >>>>>>>>>>>>>>>>>>>>>>>>   DETERMINE REGRESSOR STRUCTURE   <<<<<<<<<<<<<<<<<<<<<<    
na        = NN(1);                       % # of past y's to be used in TDL 
nb        = NN(2);                       % # of past u's to be used in TDL 
nk        = NN(3);                       % Time delay in system 
nab       = na+sum(nb);                  % Number of "inputs" to each net 
inputs    = nab;                         % # of inputs 
phi       = zeros(inputs+1,1);           % Initialize regressor vector 
 
 
% >>>>>>>>>>>>>>>>>>    DETERMINE STRUCTURE OF INVERSE MODEL    <<<<<<<<<<<<<<<<<<< 
hiddeni   = length(NetDefi(1,:));        % Number of hidden neurons 
L_hiddeni = find(NetDefi(1,:)=='L')';    % Location of linear hidden neurons 
H_hiddeni = find(NetDefi(1,:)=='H')';    % Location of tanh hidden neurons 
L_outputi = find(NetDefi(2,:)=='L')';    % Location of linear output neurons 
H_outputi = find(NetDefi(2,:)=='H')';    % Location of tanh output neurons 
y1i       = [zeros(hiddeni,1);1];        % Hidden layer outputs 
delta1    = zeros(hiddeni,1);            % "Back-propagated error" 
delta2    = zeros(1,1);                  % "Back-propagated error" 
d21 = W2f(1:hiddenf);                    % Derivative if linear output 
d10 = W1f(:,na+1);                       % Derivative if linear hidden units 
d20       = 0;                           % Derivative of output w.r.t. control 
 
%>>>>>>>>>>>>>>>>>    CALCULATE REFERENCE SIGNAL & FILTER IT     <<<<<<<<<<<<<<<<<< 
if strcmp(refty,'siggener'), 
  ref = zeros(samples+1,1); 
  for ii = 1:samples+1, 
    ref(ii) = siggener(Ts*(ii-1),sq_amp,sq_freq,sin_amp,sin_freq,dc,sqrt(Nvar)); 
  end 
else 
  eval(['ref = ' refty ';']); 
  ref=ref(:); 
  i=length(ref); 
  if i>samples+1, 
    ref=ref(1:samples+1); 
  else 
    ref=[ref;ref(i)*ones(samples+1-i,1)]; 
  end 
end 
ym = filter(Bm,Am,ref);               % Filter the reference 
ym(samples+1) = ym(1);                % Necessary because the reference is repeated 
ref(samples+1) = ref(1); 
 
 
%>>>>>>>>>>>>>>>>>>>>>>>>        INITIALIZE VARIABLES        <<<<<<<<<<<<<<<<<<<<<< 
% Initialization of vectors containing past signals 
maxlength = 5; 
y_old     = zeros(maxlength,1); 
u_old     = zeros(maxlength,1); 
 
% Initialization of Simulink system 
if strcmp(simul,'simulink') 
  simoptions = simset('Solver',integrator,'MaxRows',0); % Set integrator opt. 
  eval(['[sizes,x0] = ' sim_model '([],[],[],0);']);    % Get initial states 
end 
 
% Initializations of vectors used for storing old data 
ref_data    = [ref(1:samples)]; 
ym_data     = [ym(1:samples)]; 
u_data      = zeros(samples,1); 
y_data      = zeros(samples,1); 
yhat_data   = zeros(samples,1); 
 
 
% Miscellanous initializations 
maxiter = maxiter*samples;            % Number of iterations 
u      = 0; 
y      = 0; 
t      = -Ts; 
i      = 0;                           % Iteration in current epoch counter 
SSE    = 0;                           % Sum of squared error in current epoch 
first  = max(na,nb+nk-1)+10;          % Update weights when iteration>first 
epochs = 0;                           % Epoch counter 
fighandle=progress; 
 
%---------------------------------------------------------------------------------- 
%---------------------         >>>   MAIN LOOP   <<<           -------------------- 
%---------------------------------------------------------------------------------- 
for iter=1:maxiter, 
  i = i+1; 
  t = t + Ts; 
 
 
  %>>>>>>>>>>>>>>  PREDICT OUTPUT OF SYSTEM USING THE FORWARD MODEL   <<<<<<<<<<<<< 
  phi = [y_old(1:na);u_old(1:nb);1]; 
  h1f = W1f*phi; 
  y1f(H_hiddenf)  = pmntanh(h1f(H_hiddenf)); 
  y1f(L_hiddenf)  = h1f(L_hiddenf);     
  h2f = W2f*y1f; 
  yhat(H_outputf) = pmntanh(h2f(H_outputf)); 
  yhat(L_outputf) = h2f(L_outputf); 
 
 
  %>>>>>>>>>>>>>>>>>>>>  READ OUTPUT FROM THE PHYSICAL SYSTEM   <<<<<<<<<<<<<<<<<<< 
  if strcmp(simul,'simulink') 
    utmp=[t-Ts,u_old(1);t,u_old(1)]; 
    simoptions.InitialState=x0; 
    [time,x0,y] = sim(sim_model,[t-Ts t],simoptions,utmp); 
    x0 = x0(size(x0,1),:)'; 
    y  = y(size(y,1),:)'; 
  elseif strcmp(simul,'matlab') 
    ugl = u_old(1); 
    [time,x] = ode45(mat_model,[t-Ts t],x0); 
    x0 = x(length(time),:)'; 
    eval(['y = ' model_out '(x0);']); 
  elseif strcmp(simul,'nnet') 
    y = yhat; 
  end 
   
   
  %>>>>>>>>>>>>>>>>>>>>>>>    CALCULATE PREDICTION ERROR    <<<<<<<<<<<<<<<<<<<<<<< 
  ey = ym(i) - y;                          % prediction error (a priori) 
 
 
  %>>>>>>>>>>>>  COMPUTE DERIVATIVE OF PREDICTED OUTPUT W.R.T. CONTROL <<<<<<<<<<<< 
  if iter >first,                          % wait a few samples before updating 
    % Matrix containing the partial derivative of the output w.r.t 
    % each of the outputs from the hidden units 
    if H_outputf, 
      d21 = (1-yhat*yhat)*W2f(1:hiddenf); 
    end 
 
    % Matrix containing partial derivatives of the output from each hidden unit 
    % w.r.t the most recent control input: 
    d10(H_hiddenf) = (1-y1f(H_hiddenf).*y1f(H_hiddenf)).*W1f(H_hiddenf,na+1); 
 
    % Partial derivative of output w.r.t the most recent control input 
    d20 = d21(1:hiddenf)*d10; 
 
 
    %>>>>>>>>>>>>>>>>>>>>>>   UPDATE WEIGHTS BY BACK-PROP    <<<<<<<<<<<<<<<<<<<<<< 
    E = d20*ey;                           % "Virtual" error on control signal 
                                          % Delta for output layer 
    delta2(H_outputi) = (1-u(H_outputi).*u(H_outputi)).*E(H_outputi); 
    delta2(L_outputi) = E(L_outputi); 
                                          % delta for hidden layer 
    E1 = W2i(:,1:hiddeni)'*delta2;  
    delta1(H_hiddeni) = (1-y1i(H_hiddeni).*y1i(H_hiddeni)).*E1(H_hiddeni); 
    delta1(L_hiddeni) = E1(L_hiddeni); 
    
    W2i = W2i + eta*delta2*y1i';          % Update weights between hidden and ouput 
    W1i = W1i + eta*delta1*phii';         % Update weights between input and hidden 
     
   SSE = SSE + ey*ey;                     % Update performance index (SSE) 
  end 
 
 
  %>>>>>>>>>>>>>>>>>>>>>>     DETERMINE CONTROL SIGNAL      <<<<<<<<<<<<<<<<<<<<<<<  
  % Control using the inverse model 
  phii= [ref(i+1);y;y_old(1:na-1);u_old(1:nb-1);1]; 
  h1i = W1i*phii;   
  y1i(H_hiddeni) = pmntanh(h1i(H_hiddeni)); 
  y1i(L_hiddeni) = h1i(L_hiddeni);     
  h2i = W2i*y1i; 
  u(H_outputi)   = pmntanh(h2i(H_outputi)); 
  u(L_outputi)   = h2i(L_outputi); 
  
   
  %>>>>>>>>>>>>>>>>>>       COPY DATA INTO THE DATA VECTORS       <<<<<<<<<<<<<<<<< 
  u_data(i)    = u; 
  y_data(i)    = y; 
  yhat_data(i) = yhat; 
 
 
  %>>>>>>>>>>>>>>>>>>>>>>>>         TIME OPDATES          <<<<<<<<<<<<<<<<<<<<<<<<< 
  y_old = shift(y_old,y); 
  u_old = shift(u_old,u); 
 
 
  %>>>>>>>>>>>>>>>>>>>>      PRINT %-AGE OF EPOCH COMPLETED      <<<<<<<<<<<<<<<<<< 
  progress(fighandle,floor(100*i/samples)); 
 
  %>>>>>>>>>>>>>>>>>>>>>>>>>>>        DRAW PLOTS       <<<<<<<<<<<<<<<<<<<<<<<<<<<< 
  if i==samples, 
    epochs = epochs+1; 
    figure(gcf) 
     
    % Plot A 
    if(exist('plot_a')==1), 
      if epochs==1, 
        [a_plots,dummy]=size(plot_a);      % # of plots in plot A 
        plmata = zeros(samples,a_plots);   % Collect vectors in plmat 
      end 
      for nn = 1:a_plots,  
        plmata(:,nn) = eval(plot_a(nn,:));    
      end 
      subplot(2,1,1); 
      plot([0:samples-1],plmata);          % Plot plmata 
      xlabel('Samples'); 
      set(gca,'Xlim',[0 samples-1]);       % Set x-axis 
      title(['Specialized Training  (SSE = ' num2str(SSE) ... 
                                         ',    epoch = ' num2str(epochs) ')']); 
      grid on 
    end 
   
    % Plot B 
    if(exist('plot_b')==1), 
      if epochs==1, 
        [b_plots,dummy]=size(plot_b);      % # of plots in plot B 
        plmatb = zeros(samples,b_plots);   % Collect the vectors in plmat 
      end 
      for nn = 1:b_plots,  
        plmatb(:,nn) = eval(plot_b(nn,:));    
      end 
      subplot(2,1,2); 
      plot([0:samples-1],plmatb);          % Plot plmatb 
      xlabel('Samples');  
      set(gca,'Xlim',[0 samples-1]);       % Set x-axis 
      grid on 
    end 
    figure(gcf); drawnow 
    i   = 0; 
    SSE = 0; 
    if iter<maxiter, fighandle=progress; end 
  end 
end 
%---------------------------------------------------------------------------------- 
%------------------         >>>   END OF MAIN LOOP   <<<        ------------------- 
%---------------------------------------------------------------------------------- 
subplot(111)