Difference between revisions of "Catalyst mixing problem"

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\begin{array}{llcl}
 
\begin{array}{llcl}
 
  \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.} & \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) ,  \\
 
  & x(t_0) &=& (1, 0)^T, \\
 
  & x(t_0) &=& (1, 0)^T, \\

Revision as of 19:03, 5 May 2016

Catalyst mixing problem
State dimension: 1
Differential states: 2
Discrete control functions: 1
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 - 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  t_0 = 0, \, \, t_f = 1 .

Source Code

Model descriptions are available in