View source for Isomerization of Alpha-Pinene problem (TACO)

This page contains a model of the [[Isomerization of Alpha-Pinene problem]] in [http://www.ampl.org AMPL] format, making use of the TACO toolkit for AMPL control optimization extensions. This problem is due to <bibref>Box1973</bibref>. The original model using a collocation formulation can be found in the [http://www.mcs.anl.gov/~more/cops/ COPS library].
Note that you will need to include a generic [[support AMPL files|AMPL/TACO support file]], OptimalControl.mod.
To solve this model, you require an optimal control or NLP code that uses the TACO toolkit to support the AMPL optimal control extensions.

=== AMPL ===

This is the source file pinene_taco.mod
<source lang="AMPL">
# ----------------------------------------------------------------
# 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;

</source>

This is the data file pinene_taco.dat
<source lang="AMPL">
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;

</source>

== Other Descriptions ==

Other descriptions of this problem are available in

* Mathematical notation at [[Isomerization of Alpha-Pinene problem]]
* [[:Category:AMPL | AMPL]] (using a fixed discretization) at the [http://www.mcs.anl.gov/~more/cops/ COPS library]

== References ==
<bibreferences/>
 
[[Category:AMPL/TACO]]