View source for Tubular Reactor

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|nd        = 1
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|nw        = 1
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The '''Tubular Reactor problem''' is a two-dimensional [[:Category:ODE model|ODE model]]. It aims to maximize the value of the second differential state at the end of the time interval.

The optimal integer control functions exhibits a [[:Category:Sensitivity-seeking arcs|singular arc]].

== Mathematical formulation ==
<p>
<math>
 \begin{array}{lll}
 \displaystyle \min_{w} && -x_2(1) \\
 \text{subject to} \\
\quad \dot{x_1}(t) & = & -(w(t) + \frac{1}{2} \cdot w(t)^2) \cdot x_1(t),\\
\quad \dot{x_2}(t) & = & w(t) \cdot x_1(t), \\
\quad x(0) &=& (1, 0)^T, \\
\quad w(t) & \in & [0, 5] 
  \end{array}
</math>
</p>

== Reference Solutions ==

Here is one local solution to the above control problem.

<gallery caption="Reference solution plots" widths="500px" heights="300px" perrow="1">
 Image:Tubular_Reactor.png| States and discretized control for a local optimum.
</gallery>

== Miscellaneous and Further Reading ==
This formulation and a detailed description can be found in [[#apmonitor|[1]]].

== References ==
<span id="apmonitor">[1]</span> https://apmonitor.com/do/index.php/Main/DynamicOptimizationBenchmarks  <br>


[[Category:MIOCP]]
[[Category:Sensitivity-seeking arcs]]