Catalyst mixing problem (TACO)

This page contains a model of the Catalyst mixing problem in AMPL format, making use of the TACO toolkit for AMPL control optimization extensions. This problem is due to [Stryk1999]Author: Stryk, O. von
Institution: Technische Universit\"at M\"unchen, Germany
Title: User's guide for DIRCOL (Version 2.1): A direct collocation method for the numerical solution of optimal control problems
Year: 1999
. The original model using a collocation formulation can be found in the COPS library. Note that you will need to include a generic 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 catmix_taco.mod

# ----------------------------------------------------------------
# Catalyst mixing problem using AMPL and TACO
# (c) Christian Kirches, Sven Leyffer
#
# Source: COPS 3.1 collocation formulation - March 2004
# ----------------------------------------------------------------
include OptimalControl.mod;
 
param ne := 2;    	  	# number of differential equations
 
var tf := 1;      		# Final time
var t;
 
param bc {1..ne};    		# Boundary conditions for x
 
var u;
let u.type := "u1";
 
var v {1..ne};
 
minimize objective: eval (-1 + v[1] + v[2], tf);
let objective.scale := 0.01;
 
subject to u_bounds: 0.0 <= u <= 1.0;
 
subject to de1:
  diff(v[1],t) = u*(10*v[2] - v[1]);
 
subject to de2:
  diff(v[2],t) = u*(v[1] - 10*v[2]) - (1 - u)*v[2];
 
subject to b_eqn {s in 1..ne}: eval(v[s],0) = bc[s];
 
data catmix_taco.dat;
 
option solver ...;
 
solve;

This is the data file catmix_taco.dat

# Set the design parameters
 
param bc :=
  1   1
  2   0;

Other Descriptions

Other descriptions of this problem are available in

• Mathematical notation at Catalyst mixing problem
• AMPL (using a fixed discretization) at the COPS library

References

[Stryk1999]

Stryk, O. von (1999): User's guide for DIRCOL (Version 2.1): A direct collocation method for the numerical solution of optimal control problems. Technische Universit\"at M\"unchen, Germany.