# 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 + v, tf);
let objective.scale := 0.01;

subject to u_bounds: 0.0 <= u <= 1.0;

subject to de1:
diff(v,t) = u*(10*v - v);

subject to de2:
diff(v,t) = u*(v - 10*v) - (1 - u)*v;

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