Catalyst mixing problem

Catalyst mixing problem
State dimension:	1
Differential states:	2
Continuous 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

• AMPL/TACO code at Catalyst mixing problem (TACO)