Difference between revisions of "Isomerization of Alpha-Pinene problem (TACO)"

# ----------------------------------------------------------------
# Insomerization of Alpha-Pinene problem using AMPL and TACO
# (c) Christian Kirches, Sven Leyffer
#
# Source: COPS 3.1 collocation formulation - March 2004
#         Alexander S. Bondarenko - Summer 1998
# ----------------------------------------------------------------
include OptimalControl.mod;
 
param ne > 0, integer;               # number of differential equations
param np > 0, integer;               # number of ODE parameters
param nm > 0, integer;               # number of measurements
 
param bc {1..ne};                    # boundary conditions
param tau {1..nm};                   # times at which observations made
 
var t;
var tf := tau[nm];
 
param z {1..nm,1..ne};               # observations
var theta {1..np} >= 0, <= 100;      # ODE parameters
 
var u{1..ne} >= 0, <= 200;
 
minimize l2error{i in 1..nm}:
	eval ( sum {s in 1..ne} (u[s] - z[i,s])^2, tau[i] );
 
subject to theta_bounds {i in 1..np}: theta[i] >= 0.0;      
 
subject to ode_bc {s in 1..ne}:  eval(u[s], 0.0) = bc[s];
 
subject to de1:
	diff (u[1], t) = - (theta[1]+theta[2])*u[1];
 
subject to de2:
	diff (u[2], t) = theta[1]*u[1];
 
subject to de3:
	diff (u[3], t) = theta[2]*u[1] - (theta[3]+theta[4])*u[3] + theta[5]*u[5];
 
subject to de4:
	diff (u[4], t) = theta[3]*u[3];
 
subject to de5:
	diff (u[5], t) = theta[4]*u[3] - theta[5]*u[5];
 
data pinene_taco.dat;
 
option solver ...;
 
solve;

param ne := 5;  
param np := 5;
param nm := 8;
 
# Time measurements
 
param tau :=
  1     1230.0
  2     3060.0
  3     4920.0
  4     7800.0
  5    10680.0
  6    15030.0
  7    22620.0
  8    36420.0;
 
# Concentrations
 
param z :
        1       2       3       4       5   := 
  1   88.35    7.3     2.3     0.4     1.75
  2   76.4    15.6     4.5     0.7     2.8
  3   65.1    23.1     5.3     1.1     5.8
  4   50.4    32.9     6.0     1.5     9.3
  5   37.5    42.7     6.0     1.9    12.0
  6   25.9    49.1     5.9     2.2    17.0
  7   14.0    57.4     5.1     2.6    21.0
  8    4.5    63.1     3.8     2.9    25.7;
 
param bc := 
  1  100.0  
  2   0.0  
  3   0.0  
  4   0.0
  5   0.0;
 
# Initial values
 
let {i in 1..np} theta[i] := 0.0;