Catalytic cracking problem

Catalytic cracking problem
Algebraic states:	2
Continuous control values:	3

The Catalytic cracking 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

$\begin{array}{llcl}\underset{\theta }{\min }& \sum _{j=1}^{21}& & ||y({\tau }_j;\theta )-z_j|{|}^2\\ \text{s.t.}& {\dot{y}}_1& =& -({\theta }_1+{\theta }_3)y_1^2,\\ & {\dot{y}}_2& =& {\theta }_1{y}_1^2-{\theta }_2{y}_2,\\ & {\theta }_i& \ge & 0.\end{array}$

Parameters

The values $z_j$ are measurements for the concentration for $y$ at time points ${\tau }_1,...,{\tau }_{21}$ and initial conditions are known.

Source Code

Model descriptions are available in

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