ctr_norm is a row of real numbers scaling the contraints'vector :
[ctr_norm(1)*X(1)-Xh(1); ...]
the size of ctr_norm is the size of X0; c,rho are the well known parameters used in dual lagrangian problems;
Non-linear optimization routine for discret Lagrange problem without contraints or only with bound contraints imposed to the command u :
min J(u) = sum L(u(t),X(t),t) + phi(X(T),T) ub<u<uh t=0..T-1
for a control u(t) defined on {0..T-1} the state X of the system is the solution of the system of equations
X(0)=X0 , X(t+1)=f(u(t),X(t),t)
BEWARE L is a matrix of three strings : name of the cost function, name of the partial derivative of the cost with respect to u, and name of the partial derivative of the cost with respect to X. The declarations of f and phi follow the same syntax.
DEFAULT PARAMETERS
stop parameters
nap = 200; iter= 200; epsf= 0.000E+00; epsg= 0.4441E-15;
epsx= is a vector (or matrix) of zeros, which size is the size of the initial command u0 ;
lag parameters k is a vector (or matrix) of ones, which size is the size of the initial state X0 ;
c=100; r=50;
uzawa parameters
maxiter=10; stop=0.001;