special3.m

基于神经网络的控制工具箱

% ---------------------------------     SPECIAL3     ------------------------------
%
%  Program for training an inverse model of a process by so-called specialized
%  training (see Psaltis, Sideris & Yamamura: "A Multilayered Neural Network
%  Controller").
%  
%  The inverse model is trained with a recursive Gauss-Newton algorithm
%  ("recursive prediction error method"). Three different versions have been
%  implemented: Exponential forgetting, constant trace, and the
%  exponential forgetting and resetting algorithm (EFRA).
%
%  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 'invinit2.m'
%
%  See the program "special2" for an implementation inspired by recursive
%  pseudo-linear regression.
%
%  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
invinit2                                 % 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 "signal 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
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,
    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);

% Variables associated with the weight update algorithm
SSE = 0;                                % Sum of squared error in current epoch
epochs = 0;                             % Epoch counter
first = max(na,nb+nk-1)+10;             % Update weights when iteration>first
index = (hiddeni+1) + 1 + [0:hiddeni-1]*(inputs+1); % A useful vector!
parameters1= hiddeni*(inputs+1);        % # of input-to-hidden weights
parameters2= (hiddeni+1);               % # of hidden-to-output weights
parameters = parameters1 + parameters2; % Total # of weights
PSI        = zeros(parameters,1);       % Deriv. of inv. net output w.r.t. weights
PSIold     = zeros(parameters,nb-1);    % Past PSI vectors
PSI_red    = zeros(parameters,1);       % Deriv. of forw. net output w.r.t. weights
PSIold_red = zeros(parameters,na);      % Past PSI_red vectors
                                        % Parametervector containing all weights
theta = [reshape(W2i',parameters2,1) ; reshape(W1i',parameters1,1)];
index3= 1:(parameters+1):(parameters^2);% Yet another useful vector
if strcmp(method,'ff'),                 % Forgetting factor method
  mflag     = 1;                        % Method flag
  lambda    = trparms(1);               % Forgetting factor
  p0        = trparms(2);               % Diagonal element of covariance matrix
  P         = p0 * eye(parameters);     % Initialize covariance matrix
elseif strcmp(method,'ct'),             % Constant trace method
  mflag     = 2;                        % Method flag
  lambda    = trparms(1);               % Forgetting factor
  alpha_max = trparms(2);               % Max. eigenvalue
  alpha_min = trparms(3);               % Min. eigenvalue
  P      = alpha_max * eye(parameters); % Initialize covariance matrix
  Pbar      = P;                        % Initialize covariance matrix
elseif strcmp(method,'efra'),           % EFRA method
  mflag     = 3;                        % Method flag
  alpha     = trparms(1);               % EFRA parameters
  beta      = trparms(2);
  delta     = trparms(3);
  lambda    = trparms(4);
  gamma     = (1-lambda)/lambda;
  maxeig = gamma/(2*delta)*(1+sqrt(1+4*beta*delta/(gamma*gamma)));% Max. eigenvalue
  P      = maxeig * eye(parameters);    % Initialize covariance matrix
  betaI     = beta*eye(parameters);     % Useful diagonal matrix
end

% 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
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;


  %>>>>>>>>>>>>  COMPUTE DERIVATIVE OF PREDICTED OUTPUT W.R.T. CONTROL <<<<<<<<<<<<

   % 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);