# Difference between revisions of "Catalytic cracking problem"

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

$\begin{array}{llcl} \displaystyle \min_{\theta} &\sum\limits_{j=1}^{21} &&||y(\tau_j; \theta) - z_j||^2 \\[1.5ex] \mbox{s.t.} & \dot{y}_1 & = & -(\theta_1 + \theta_3) y_1^2, \\ & \dot{y}_2 & = & \theta_1 y_1^2 - \theta_2 y_2, \\ & \theta_i & \geq & 0 \quad i = 1,...,3. \end{array}$

## 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