Difference between revisions of "Catalyst mixing problem"
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\displaystyle \min_{x, u} &-1 + x_1(t_f) + x_2(t_f) \\[1.5ex] | \displaystyle \min_{x, u} &-1 + x_1(t_f) + x_2(t_f) \\[1.5ex] | ||
\mbox{s.t.} | \mbox{s.t.} | ||
| − | & \dot{x}_1 & = & u ( 10 x_2 - x_1), \\ | + | & \dot{x}_1 & = & u ( 10 x_2(t) - x_1(t)), \\ |
| − | & \dot{x}_2 & = & u ( x_1 - 10 x_2) - (1 - u \, x_2) , \\ | + | & \dot{x}_2 & = & u ( x_1(t) - 10 x_2(t)) - (1 - u(t)) \, x_2(t) , \\ |
& x(t_0) &=& (1, 0)^T, \\ | & x(t_0) &=& (1, 0)^T, \\ | ||
| − | & u(t) &\in& | + | & u(t) &\in& \{0,1\}. |
\end{array} | \end{array} | ||
</math> | </math> | ||
Revision as of 19:47, 12 January 2018
| Catalyst mixing problem | |
|---|---|
| State dimension: | 1 |
| Differential states: | 2 |
| Continuous control functions: | 1 |
| Path constraints: | 2 |
| Interior point equalities: | 2 |
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(t) - x_1(t)), \\
& \dot{x}_2 & = & u ( x_1(t) - 10 x_2(t)) - (1 - u(t)) \, x_2(t) , \\
& x(t_0) &=& (1, 0)^T, \\
& u(t) &\in& \{0,1\}.
\end{array}](https://mintoc.de/images/math/e/9/4/e94553dfd2fab04f8dd7e1b9eea94142.png)
Parameters
In this model the parameters used are 
.
Source Code
Model descriptions are available in
