Difference between revisions of "Catalytic cracking problem"

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(Mathematical formulation)
(Mathematical formulation)
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<math>
 
<math>
 
\begin{array}{llcl}
 
\begin{array}{llcl}
  \displaystyle \min_{\theta} &\sum\limits_{j=1}^{21} &||y(\tau_j; \theta) - z_j||^2  \\[1.5ex]
+
  \displaystyle \min_{\theta} &\sum\limits_{j=1}^{21} &&||y(\tau_j; \theta) - z_j||^2  \\[1.5ex]
 
  \mbox{s.t.} & \dot{y}_1 & = &  -(\theta_1 + \theta_3) y_1^2, \\
 
  \mbox{s.t.} & \dot{y}_1 & = &  -(\theta_1 + \theta_3) y_1^2, \\
 
  & \dot{y}_2 & = & \theta_1 y_1^2 - \theta_2 y_2.  \\
 
  & \dot{y}_2 & = & \theta_1 y_1^2 - \theta_2 y_2.  \\

Revision as of 18:24, 5 May 2016

Catalytic cracking problem
State dimension: 1
Differential states: 2
Discrete control functions: 1
Interior point equalities: 2

This problem tries to determine "reaction coefficients for the catalytic cracking of gas oil into gas and other byproducts." (Cite and problem taken from the COPS library)


Mathematical formulation

The problem is given by


\begin{array}{llcl}
 \displaystyle \min_{\theta} &\sum\limits_{j=1}^{21} &&||y(\tau_j; \theta) - z_j||^2   \\[1.5ex]
 \mbox{s.t.} & \dot{y}_1 & = &  -(\theta_1 + \theta_3) y_1^2, \\
 & \dot{y}_2 & = & \theta_1 y_1^2 - \theta_2 y_2.  \\
\end{array}

Parameters

The values  z_j are measurements for the concentration for  y at time points  \tau_1, ..., \tau_21 .

Source Code

Model descriptions are available in