## Set up u_star
  u_star = ppp_ustar(A_u_sim,1,t,0,0,n_u-n_U);

  ## Simulate
  par(i_ppp_sim(:,3)) = U;		# Update the simulation ppp weights
  [y_sim,x] = eval(sprintf("%s_sim(x_0_sim, par, simpar_sim, u_star);", \
			   system_name_sim));
  x_0_sim  = x(n_t,:)';		# Extract state for next time
  u_sim = (u_star*U);
endfunction

    extras.alpha = 0.1;
    extras.criterion = 1e-5;
    extras.emulate_timing = 0;
    extras.max_iterations = 10;
    extras.simulate = 1;
    extras.v = 1e-5;
    extras.verbose = 0;
    extras.visual = 0;
  endif

  ##Estimate if we have some adjustable parameters
  estimating_parameters = (length(i_par)>0);
  
  ## Names
  s_system_name = sprintf("s%s", system_name);

  ## System details -- defines simulation within ol interval
  par = eval(sprintf("%s_numpar;", system_name));
  simpar = eval(sprintf("%s_simpar;", system_name));

      ## Generate input to actual system
      u_star_t = ppp_ustar(A_u,1,t_ol',0,0,n_u-n_U);

      ## Tune parameters/states
      if (estimating_parameters==1)
	## Save up the estimated parameters
	par_est = pars(i_par(:,1));
	p = [p; par_est'];

	## Set up according to interval length
	if (T_ol>T_ol_0) ## Truncate data
	  simpar_est.last = T_ol_0;
	  y_est = y_ol(1:n_t+1,:);
	else
	  simpar_est.last = T_ol;
	  y_est = y_ol;
	endif

	simpar_pred.last = T_ol_0; # Predicted length of next interval
	pars(i_ppp(:,1)) = U_old; # Update the simulation ppp weights
	
	## Optimise
	tick = time;
	[pars,Par,Error,Y,its] = \
	    ppp_optimise(s_system_name,x_0_models,pars,simpar_est,u_star_t,y_est,i_par,extras);
	
	if extras.visual
	  figure(2);
	  title("Parameter optimisation"); 
	  II = [1:length(y_est)]; plot(II,y_est,"*", II,Y);
	endif
	
	est_time = time-tick;  
	t_est = [t_est;est_time];
	its_est = [its_est; its-1];
      endif

      ## Update internal model
      par(i_ppp(:,3)) = U_old; # Update the internal model ppp weights

      if (estimating_parameters==1)
	par(i_par(:,3)) = pars(i_par(:,1)); # Update the internal model params
      endif

      simpar_model.last = T_ol;
      [y_model,x_model] = eval(sprintf("%s_sim(x_0_model, par, simpar_model, \
 					       u_star_t);",system_name));

      x_0 = x_model(n_ol+1,:)';	# Initial state of next interval
##      x_0 = x_model(n_ol-1,:)';	# Initial state of next interval
      x_0_model = x_0;
      x_0_models(1:2:(2*n_x)-1) = x_0_model;

      ## Compute U by optimisation
      tick = time;

      ## Predict state at start of next interval
      par(i_ppp(:,3)) = U;
      [y_next,x_next] = eval(sprintf("%s_sim(x_0, par, simpar, \
					     u_star_t);",system_name));
      x_next = x_next(n_t+1,:)'; # Initial state for next time
      x_nexts(1:2:(2*n_x)-1) = x_next; # And for internal sensitivity model
      
      ## Optimize for next interval      
      U_old = U;		# Save previous value
      U = expm(A_u*T_ol)*U;	# Initialise from continuation trajectory
      pars(i_ppp(:,1)) = U;	# Put initial value of U into the parameter vector
      [U, U_all, Error, Y, its] = ppp_nlin(system_name,x_nexts,pars,simpars,u_star_tau,w_s,i_ppp,extras);
      if extras.visual
	figure(3);
	title("PPP optimisation");
	II = [1:length(w_s)]; plot(II,w_s,"*", II,Y);
	figure(1);
	endif

      ppp_time = time-tick;  
      t_ppp = [t_ppp;ppp_time];
      its_ppp = [its_ppp; its-1];

      ## Total execution time
      T_total = time - t_start;

  ######################################
  
  ###############################################################
  ## Version control history
  ###############################################################
  ## $Id$
  ## $Log$
  ## Revision 1.8  2002/04/23 17:50:39  gawthrop
  ## error --> err to avoid name clash with built in function
  ##
  ## Revision 1.7  2001/08/10 16:19:06  gawthrop
  ## Tidied up the optimisation stuff
  ##
  ## Revision 1.6  2001/07/03 22:59:10  gawthrop
  ## Fixed problems with argument passing for CRs
  ##
  ## Revision 1.5  2001/06/06 07:54:38  gawthrop

  ## Revision 1.1  2000/12/28 11:58:07  peterg
  ## Put under CVS
  ##
  ###############################################################


  ## Copyright (C) 1999,2000 by Peter J. Gawthrop

  sim_command = sprintf("%s_ssim(x_0,par,simpar,u,i_s)", system_name);

  ## Extract indices
  i_t = free(:,1);		# Parameters
  i_s = free(:,2)';		# Sensitivities

  if nargin<8

    if (N_y!=n_y)
      mess = sprintf("n_y (%i) in data not same as n_y (%i) in model", n_y,N_y);
      error(mess);
    endif
    
    ## Use the last part of the simulation to compare with data
    y = y(N_data-n_data:N_data-1,:);
    y_par = y_par(N_data-n_data:N_data-1,:);






    ##Evaluate error, cost derivative J and cost second derivative JJ
    err = 0; 
    J = zeros(n_th,1);
    JJ = zeros(n_th,n_th);
    
    for i = 1:n_y
      E = y(:,i) - y_0(:,i);	#  Error in ith output