function [Gamma,gamma] = ppp_input_constraint (A_u,Tau,Min,Max,Order,i_u,n_u)
## usage: [Gamma,gamma] = ppp_input_constraint (A_u,Tau,Min,Max,Order)
##
## Derives the input constraint matrices Gamma and gamma
## For Constraints Min and max at times Tau
## Order=0 - input constraints
## Order=1 - input derivative constraints
## etc
## i_u: Integer index of the input to be constrained
## n_u: Number of inputs
## NOTE You can stack up Gamma and gamma matrices for create multi-input constraints.
## Copyright (C) 1999 by Peter J. Gawthrop
## $Id$
## Sizes
[n_U,m_U] = size(A_u); # Number of basis functions
[n,N_t] = size(Tau); # Number of constraint times
## Defaults
if nargin<5
Order = zeros(1,N_t);
endif
if nargin<6
i_u = 1;
n_u = 1;
endif
if N_t==0 # Nothing to be done
Gamma = [];
gamma = [];
return
endif
if n != 1
error("Tau must be a row vector");
endif
n = length(Min);
m = length(Max);
o = length(Order);
if (n != N_t)||(m != N_t)||(o != N_t)
error("Tau, Min and max must be the same length");
endif
## Extract the A_i matrix for this input
A_i = ppp_extract(A_u,i_u);
## Create the constraints in the form: Gamma*U < gamma
Gamma = [];
gamma = [];
one = ones(m_U,1);
i=0;
zero_l = zeros(1,(i_u-1)*m_U); # Pad left-hand
zero_r = zeros(1,(n_u-i_u)*m_U); # Pad right-hand
for tau = Tau # Stack constraints for each tau
i++;
Gamma_tau = ( A_i^Order(i) * expm(A_i*tau) * one )';
Gamma_tau = [ zero_l Gamma_tau zero_r ]; # Only for i_uth input
Gamma = [Gamma;[-1;1]*Gamma_tau]; # One row for each of min and max
gamma_tau = [-Min(i);Max(i)];
gamma = [gamma;gamma_tau];
endfor
endfunction