Overview
Comment:Added terminal cost for w
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SHA3-256: bf8c1313054692b34d2cb72afefdcbd4d4c86f41733521c42c9946e98a619bbf
User & Date: gawthrop@users.sourceforge.net on 2002-12-20 12:48:41
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Context
2002-12-23
11:17:47
Now GPL only check-in: 731d6ee8b5 user: gawthrop@users.sourceforge.net tags: origin/master, trunk
2002-12-20
12:48:41
Added terminal cost for w check-in: bf8c131305 user: gawthrop@users.sourceforge.net tags: origin/master, trunk
10:44:23
Don't augment A_u with A_w - do it externally check-in: 56129bf804 user: gawthrop@users.sourceforge.net tags: origin/master, trunk
Changes

Modified mttroot/mtt/lib/control/PPP/ppp_lin.m from [db890617e0] to [badb5c2ae2].

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  ## Exit if badly conditioned
  cond_uu = cond(J_uu);
  if cond_uu>max_cond
    error(sprintf("J_uu is badly conditioned. Condition number = 10^%i",log10(cond_uu)));
  endif

  ## Terminal constraint
  tau_last = tau(m_t);
  x_x_t = expm(A*tau_last);	# deriv. of x*(tau_2) wrt x(0)
  J_ux = J_ux + x_u_t'*P*x_x_t;
  J_uu = J_uu + x_u_t'*P*x_u_t;

  ## w bits
  if n_W>0
    for i = 1:n_y			# For each output
      QQ = ones(n_U,1)*Q(i,:);	# Resize Q
      J_uw = J_uw + (QQ .* y_u(:,i:n_y:n_yu)') * Ws (:,i:n_y:n_yw);
      QQ = ones(n_x,1)*Q(i,:);	# Resize Q
      J_xw = J_xw + (QQ .* y_x(:,i:n_y:n_yx)') * Ws (:,i:n_y:n_yw);
      QQ = ones(n_W,1)*Q(i,:);	# Resize Q
      J_ww = J_ww + (QQ .* Ws (:,i:n_y:n_yw)') * Ws (:,i:n_y:n_yw);
    endfor
  endif





















  ## Compute the open-loop gains
  K_w = J_uu\J_uw;
  K_x = J_uu\J_ux;

  ## U*(tau) at tau=0 
  Us0 = ppp_ustar(A_u,n_u,0);		
  







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  ## Exit if badly conditioned
  cond_uu = cond(J_uu);
  if cond_uu>max_cond
    error(sprintf("J_uu is badly conditioned. Condition number = 10^%i",log10(cond_uu)));
  endif







  ## w bits
  if n_W>0
    for i = 1:n_y			# For each output
      QQ = ones(n_U,1)*Q(i,:);	# Resize Q
      J_uw = J_uw + (QQ .* y_u(:,i:n_y:n_yu)') * Ws (:,i:n_y:n_yw);
      QQ = ones(n_x,1)*Q(i,:);	# Resize Q
      J_xw = J_xw + (QQ .* y_x(:,i:n_y:n_yx)') * Ws (:,i:n_y:n_yw);
      QQ = ones(n_W,1)*Q(i,:);	# Resize Q
      J_ww = J_ww + (QQ .* Ws (:,i:n_y:n_yw)') * Ws (:,i:n_y:n_yw);
    endfor
  endif

  ## Terminal constraint 
  tau_last = tau(m_t);
  x_x_t = expm(A*tau_last);	# deriv. of x*(tau_2) wrt x(0)
  J_ux = J_ux + x_u_t'*P*x_x_t;
  J_uu = J_uu + x_u_t'*P*x_u_t;

  ## Terminal constraint - w bits
  ## NB SISO ONLY at the moment
  C = C(1,:);			# REMOVE ME

  ## deriv of x* wrt W
  if (cond(A)<1e10)		# Finite ss gain
    x_W_t =  (A\B)*inv(C*(A\B));
  else				# Infinite ss gain
    Y_0 = zeros(n_x,n_y); Y_0(1,:) = ones(1,n_y);
    x_W_t =  obsv(A,C)\Y_0;
  endif

  J_uw = J_uw + x_u_t'*P*x_W_t;

  ## Compute the open-loop gains
  K_w = J_uu\J_uw;
  K_x = J_uu\J_ux;

  ## U*(tau) at tau=0 
  Us0 = ppp_ustar(A_u,n_u,0);		
  


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