# 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. |