Difference between revisions of "Catalyst mixing problem"
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& \dot{x}_2 & = & u ( x_1 - 10 x_2) - (1 - u \, x_2) , \\ | & \dot{x}_2 & = & u ( x_1 - 10 x_2) - (1 - u \, x_2) , \\ | ||
& x(t_0) &=& (1, 0)^T, \\ | & x(t_0) &=& (1, 0)^T, \\ | ||
| − | |||
\end{array} | \end{array} | ||
</math> | </math> | ||
Revision as of 10:47, 10 April 2016
| Catalyst mixing problem | |
|---|---|
| State dimension: | 1 |
| Differential states: | 3 |
| Discrete control functions: | 1 |
| Interior point equalities: | 3 |
The Catalyst mixing problem seeks an optimal policy for mixing two catalysts "along the length of a tubular plug ow reactor involving several reactions". (Cite and problem taken from the COPS library)
Mathematical formulation
The problem is given by
![\begin{array}{llcl}
\displaystyle \min_{x, u} &-1 + x_1(t_f) + x_2(t_f) \\[1.5ex]
\mbox{s.t.} & \dot{x}_1 & = & u ( 10 x_2 - x_1), \\
& \dot{x}_2 & = & u ( x_1 - 10 x_2) - (1 - u \, x_2) , \\
& x(t_0) &=& (1, 0)^T, \\
\end{array}](https://mintoc.de/images/math/c/7/5/c75df9a53c1af824d06d285dac040c99.png)
Parameters
In this model the parameters used are 
.
Source Code
Model descriptions are available in
