Difference between revisions of "Isomerization of Alpha-Pinene problem"
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& \dot{y}_4 & = & \theta_3 y_3, \\ | & \dot{y}_4 & = & \theta_3 y_3, \\ | ||
& \dot{y}_5 & = & \theta_4 y_3 - \theta_5 y_5, \\ | & \dot{y}_5 & = & \theta_4 y_3 - \theta_5 y_5, \\ | ||
| − | & \theta_i & \geq & 0. | + | & \theta_i & \geq & 0 \quad i = 1,...,5. |
\end{array} | \end{array} | ||
</math> | </math> | ||
Revision as of 09:32, 27 July 2016
| Isomerization of Alpha-Pinene problem | |
|---|---|
| Algebraic states: | 5 |
| Continuous control values: | 5 |
| Path constraints: | 5 |
The Isomerization of Alpha-Pinene problem tries to determine "reaction coefficients in the thermal isometrization of 
-Pinene." (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}^{8} &&||y(\tau_j; \theta) - z_j||^2 \\[1.5ex]
\mbox{s.t.}
& \dot{y}_1 & = & -(\theta_1 + \theta_2) y_1, \\
& \dot{y}_2 & = & \theta_1 y_1, \\
& \dot{y}_3 & = & \theta_2 y_1 - (\theta_3 + \theta_4) y_3 + \theta_5 y_5, \\
& \dot{y}_4 & = & \theta_3 y_3, \\
& \dot{y}_5 & = & \theta_4 y_3 - \theta_5 y_5, \\
& \theta_i & \geq & 0 \quad i = 1,...,5.
\end{array}](https://mintoc.de/images/math/2/7/e/27e9cac630d2bee3b9c7a252f363678e.png)
Parameters
The values 
are measurements for the concentration for 
at time points 
and initial conditions are known.
Source Code
Model descriptions are available in
