dynoptimsc - the discret optimal command tool with state contraints

Calling Sequence

[uopt,Xopt,critopt,gradopt]=dynoptim(L,f,phi,ub,u0,uh,Xinf,X0,Xsup,[stop],[lag],[uzawa],[algo])

Parameters

• L,f,phi : string matrices giving name of scilab macros (see below)
• ub,u0,uh : three scalar matrices of the same size. u0 is an initial guess for the optimal control, ub and uh are respectively a lower bound and an upper bound for u. Let [n_u,step] be the size of matrix u. n_u is the command size and step is the number of time steps (I.e the horizon time T)
• X0 : a column vector which gives the initial state value.
• Xinf, Xsup : the state upper and lower bounds vectors
• stop : a sequence of optional parameters controlling the convergence of the algorithm. This sequence has the same meaning as the corresponding sequence in the optim man pages. stop= 'ar',nap, iter ,epsg ,epsf ,epsx,info
• algo : specify the algorithm to be used, quasi newton, or conjuged gradient algo='gc' or algo='qn'
• lag : lag parameter of the lagrangian cost function used to incorporate the state bounds contraints lag='lag',ctr_norm,c,rho

  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;

• uzawa : sequence of optional parameters controlling the convergence of the uzawa algorithm algo='usawa',maxiter,stop maxiter is the maximal alowed number of dual steps stop is the threshol\ d of gradient

Description

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;
   

See Also

dynoptim  optim  

Author

Sebastien Berthaud, J.Ph.Chancelier