Difference between revisions of "Catalyst mixing problem"
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| − | \displaystyle \min_{x, | + | \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), \\ | \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) , \\ | & \dot{x}_2 & = & u ( x_1 - 10 x_2) - (1 - u \, x_2) , \\ | ||
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
Failed to parse (lexing error): \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, \\ & u(t) &\in& \[0,1\]. \end{array}
Parameters
In this model the parameters used are 
.
Source Code
Model descriptions are available in
