$*************************************************************
$ Cart on a Track
$
$ R. F. Stengel, "Optimal Control and Estimation", Dover
$   Publications, 1994, p. 196.
$
$ Optimal solution:  2307.69
$*************************************************************

OPTION {{
  FTOL = "1e-6";
  OTOL = "1e-6";
}}

DECLARATION {{
  PARA q = 1;
  PARA r = 100;
  XVAR {j,k1,k2};
  ZVAR {x,v,u,int};
  ISPE {x,v,int};
  XUBD {1e6,100,100};
  XSTP {0,0,0};
  XLBD {-1e6,-100,-100};
  ZINC {0,0,0,0};
  TIME {0,10};
}}

MODEL {{
  MIN:  j;
  dae1: x' =e= v;
  dae2: v' =e= u;
  dae3: u =e= k1 + k2*t;
  dae4: int' =e= u*u;
  obj1[1]: j =e= q*(x - 100)*(x - 100) + r*int;
}}