Catalytic cracking problem

Catalytic cracking problem
State dimension:	1
Differential states:	2
Discrete control functions:	1
Interior point equalities:	2

This problem tries to determine "reaction coefficients for the catalytic cracking of gas oil into gas and other byproducts." (Cite and problem taken from the COPS library)

Mathematical formulation

The problem is given by

$\begin{array}{ll}\underset{\theta }{\min }& \sum _{j=1}^{21}||y({\tau }_j;\theta )-z_j|{|}^2\\ \text{s.t.}& {\dot{y}}_1& =& -({\theta }_1+{\theta }_3)y_1^2,\\ & {\dot{y}}_2& =& {\theta }_1{y}_1^2-{\theta }_2{y}_2.\\ \end{array}$

Parameters

The values $z_j$ are measurements for the concentration for $y$ at time points ${\tau }_1,...,{\tau }_{2}1$.

Source Code

Model descriptions are available in

• AMPL/TACO code at Catalyst cracking problem (TACO)