Reference
Category : GAMS NOA library
Mainfile : control3.gms
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Optimal control problem with a nonlinear dynamic constraint and boundary
conditions solved as a General Nonlinear Programming Problem.
Divya Garg, et al., Direct trajectory optimization and costate estimation of
finite-horizon and infinite-horizon optimal control problems using a
Radau pseudospectral method. Computational optimization and Applications,
vol.49, nr. 2, June 2011, pp. 335-358.
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Sets n states / state1 /
set k /t1*t100/
ku(k) control horizon
ki(k) initial period
kt(k) terminal period ;
ku(k) = yes$(ord(k) lt card(k));
ki(k) = yes$(ord(k) eq 1);
kt(k) = not ku(k);
Display k, ki, kt, ku;
Parameter rk penalty control / 0.01 /
xinit(n) initial value / state1 2 / ;
Variables x(n,k) state variable
u(k) control variable
j criterion
Equations cost criterion definition
stateq(n,k) state equation ;
cost..
j =e= .5*sum((k,n), (x(n,k)) +
.5*sum((ku), (u(ku))*rk*(u(ku))) );
stateq(n,k+1)..
x(n,k+1) =e= 2*x(n,k) + 2*u(k)*sqrt(x(n,k)) ;
Model control3 /all/;
$ifThenI x%mode%==xbook
x.l(n,k) = xinit(n);
x.fx(n,ki) = xinit(n);
x.fx(n,kt) = 2;
$endIf
Solve control3 minimizing j using nlp;
Display x.l, u.l;
$ifThenI x%mode%==xbook
file res1 /control3.dat/;
put res1
loop(k, put x.l('state1',k):10:5,',', put/)
loop(k, put u.l(k):10:5,',', put/)
$endIf
* End Control3