$*************************************************************
$  Parameter Estimation for a Simple Batch
$  Reactor System
$  L. T. Biegler and I. B. Tjoa
$
$ CACHE Process Design Case Studies
$ M. Morari and I.E. Grossmann
$
$  Optimal solution:  1.1858e-06
$*************************************************************

OPTION {{
#Note that the tolerances have a large affect
#on the solution of this problem.
  FTOL = 1e-10;
  OTOL = 1e-10;
}}

DECLARATION {{
  INDEX {i};
  SET I = |1:10|;

#Data
  PARA yhata(I) = {0.606,0.368,0.223,0.135,0.082,
                   0.050,0.030,0.018,0.011,0.007};
  PARA yhatb(I) = {0.373,0.564,0.647,0.669,0.656,
                   0.624,0.583,0.539,0.494,0.451};

  XVAR {p1,p2,  #parameters to be estimated
        diff(I) #differences between modeled and measured values
       };

  ZVAR {ya,yb};
  ISPE {ya,yb};
  ZINC {1,0};
  TIME {0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0};
}}

MODEL {{
  MIN:  <<i E I| diff(i)>>;
  dae1: ya' =e= -p1*ya;
  dae2: yb' =e= p1*ya - p2*yb;
  err(i E I)[i]:  diff(i) =e= (ya - yhata(i))^2 + (yb - yhatb(i))^2;
}}