Difference between revisions of "Oil Shale Pyrolysis"
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| − | The following problem is an example from the global optimal control literature and was introduced in < | + | The following problem is an example from the global optimal control literature and was introduced in <bib id="Wen1977" />. |
Revision as of 21:32, 30 December 2015
| Oil Shale Pyrolysis | |
|---|---|
| State dimension: | 1 |
| Differential states: | 2 |
| Continuous control functions: | 1 |
| Discrete control functions: | 0 |
| Interior point equalities: | 2 |
The following problem is an example from the global optimal control literature and was introduced in [Wen1977]The entry doesn't exist yet..
Mathematical formulation
![\begin{array}{ll}
\displaystyle \min_{u} & \displaystyle -x_1(t_N)^2 \\[1.5ex]
\mbox{s.t.} & \displaystyle \dot{x}_0(t) = -k_0x_0(t)-(k_2+k_3+k_4)x_0(t)x_1(t)\\
& \displaystyle \dot{x}_1(t) = k_0x_0(t)-k_1x_1(t) + k_2x_0(t)x_1(t)\\
& \displaystyle k_i = a_i e^{-u(t)\frac{b_i}{R}},\quad \forall i\in \{1,\dots,5\} \\ [1.5ex]
& \displaystyle t \in \left[t_0,t_N\right] \\
& \displaystyle u(t) \in \left[698.15/748.15,1\right]\\
& \displaystyle x(t_0) = (1,0)^T\\
\end{array}](https://mintoc.de/images/math/1/f/1/1f15d56c53ab5cb4f754b96f88544de2.png)
where this is the normalized form with
, with
![u_{temp} \in \left[698.15,748.15\right]](https://mintoc.de/images/math/9/8/a/98ac80bcd09490e8b25c526ea84b2ce9.png)
Parameters
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[698.15/748.15,1] |
Measurement grid
Reference solution
Coming soon.
References
| [Wen1977] | The entry doesn't exist yet. |
