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Comment:Don't use terminal weighting if no P argument
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SHA3-256: 082eb03c4c567ade3aa6285dd4b91b5f22902cc3416e45ad5f005a7ce4a59097
User & Date: gawthrop@users.sourceforge.net on 2003-05-15 08:09:13
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Context
2003-05-16
11:16:28
Fixed bug with multiports check-in: 303b24d0d7 user: gawthrop@users.sourceforge.net tags: origin/master, trunk
2003-05-15
08:09:13
Don't use terminal weighting if no P argument check-in: 082eb03c4c user: gawthrop@users.sourceforge.net tags: origin/master, trunk
2003-05-14
09:01:18
*** empty log message *** check-in: a3ddb77db1 user: gawthrop@users.sourceforge.net tags: origin/master, trunk
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Modified mttroot/mtt/lib/control/PPP/ppp_lin.m from [2951f6d250] to [a5131f4e21].

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  if nargin<9
    R = zeros(n_u,1);
  endif

  ## Default P (terminal weight)
  if nargin<10
    P = zeros(n_x,n_x);
    P_weighting = 0
  else
    P_weighting = 1
  endif

  ## Default condittion number
  if nargin<11
    max_cond = 1e20;
  endif
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      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

  if P_weighting
  ## 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;

    ## 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;
  endif
  
  ## 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)));
    error(sprintf("J_uu is badly conditioned. Condition number = \
	10^%i",log10(cond_uu)));
  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);		
  
  ## Compute the closed-loop gains
  k_x = Us0*K_x;
  k_w = Us0*K_w;

endfunction

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