Catalyst mixing problem

Catalyst mixing problem
State dimension:	1
Differential states:	2
Continuous control functions:	1
Path constraints:	2
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

$\begin{array}{ll}\underset{x,u}{\min }& -1+x_1(t_f)+x_2(t_f)\\ \text{s.t.}& {\dot{x}}_1& =& u(10x_2-x_1),\\ & {\dot{x}}_2& =& u(x_1-10x_2)-(1-u{x}_2),\\ & x(t_0)& =& (1,0{)}^T,\\ & u(t)& \in & [0,1].\end{array}$

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)