Difference between revisions of "Catalytic cracking problem"
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FelixMueller (Talk | contribs) (→Mathematical formulation) |
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<math> | <math> | ||
\begin{array}{llcl} | \begin{array}{llcl} | ||
| − | \displaystyle \min_{\theta} &\sum\limits_{j=1}^{21} &||y(\tau_j; \theta) - z_j||^2 \\[1.5ex] | + | \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, \\ | \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. \\ | & \dot{y}_2 & = & \theta_1 y_1^2 - \theta_2 y_2. \\ | ||
Revision as of 18:24, 5 May 2016
| 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}{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. \\
\end{array}](https://mintoc.de/images/math/2/8/8/2885d8750238867231e6b5daac178415.png)
Parameters
The values 
are measurements for the concentration for 
at time points 
.
Source Code
Model descriptions are available in
