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

$\begin{array}{llcl} \min_{x, u} & - 1 + x_{1} (t_{f}) + x_{2} (t_{f}) \\ s.t. & {\dot{x}}_{1} & = & u (10 x_{2} (t) - x_{1} (t)), \\ {\dot{x}}_{2} & = & u (x_{1} (t) - 10 x_{2} (t)) - (1 - u (t)) x_{2} (t), \\ x (t_{0}) & = & (1, 0)^{T}, \\ u (t) & \in & {0, 1} . \end{array}$

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)