function [u,U,J] = ppp_qp (x,W,J_uu,J_ux,J_uw,Us0,Gamma,gamma)
## usage: [u,U] = ppp_qp (x,W,J_uu,J_ux,J_uw,Gamma,gamma)
## INPUTS:
## x: system state
## W: Setpoint vector
## J_uu,J_ux,J_uw: Cost derivatives (see ppp_lin)
## Us0: value of U* at tau=0 (see ppp_lin)
## Gamma, gamma: U constrained by Gamma*U <= gamma
## Outputs:
## u: control signal
## U: control weight vector
##
## Predictive pole-placement of linear systems using quadratic programming
## Use ppp_input_constraint and ppp_output_constraint to generate Gamma and gamma
## Use ppp_lin to generate J_uu,J_ux,J_uw
## Use ppp_cost to evaluate resultant cost function
## Copyright (C) 1999 by Peter J. Gawthrop
## $Id$
## Check the sizes
n_x = length(x);
[n_U,m_U] = size(J_uu);
if n_U != m_U
error("J_uu must be square");
endif
[n,m] = size(J_ux);
if (n != n_U)||(m != n_x)
error("J_ux should be %ix%i not %ix%i",n_U,n_x,n,m);
endif
if length(gamma)>0 # Constraints exist: do the QP algorithm
U = qp(J_uu,(J_ux*x - J_uw*W),Gamma,gamma); # QP solution for weights U
#U = pd_lcp04(J_uu,(J_ux*x - J_uw*W),Gamma,gamma); # QP solution for weights U
u = Us0*U; # Control signal
else # Do the unconstrained solution
## Compute the open-loop gains
K_w = J_uu\J_uw;
K_x = J_uu\J_ux;
## Closed-loop control
U = K_w*W - K_x*x; # Basis functions weights - U(t)
u = Us0*U; # Control u(t)
endif
endfunction