Methanol to Hydrocarbons problem

Methanol to Hydrocarbons problem
Algebraic states:	3
Continuous control values:	5

The Methanol to Hydrocarbons problem tries to determine "reaction coefficients for the conversion of methanol into various hydrocarbons." (Cite and problem taken from the COPS library)

Mathematical formulation

The problem is given by

$\begin{array}{llcl}\underset{\theta }{\min }& \sum _{j=1}^{16}& & ||y({\tau }_j;\theta )-z_j|{|}^2\\ \text{s.t.}& {\dot{y}}_1& =& -(2{\theta }_2-\frac{{\theta }_1{y}_2}{({\theta }_2+{\theta }_5)y_1+y_2}+{\theta }_3+{\theta }_4)y_1,\\ & {\dot{y}}_2& =& \frac{{\theta }_1{y}_1({\theta }_2{y}_1-y_2)}{({\theta }_2+{\theta }_5)y_1+y_2}+{\theta }_3{y}_1,\\ & {\dot{y}}_3& =& \frac{{\theta }_1{y}_1(y_2+{\theta }_5{y}_1}{({\theta }_2+{\theta }_5)y_1+y_2}+{\theta }_4{y}_1,\\ & {\theta }_i& \ge & 0.\end{array}$

Parameters

The values $z_j$ are measurements for the concentration for $y$ at time points ${\tau }_1,...,{\tau }_{16}$ and initial conditions are known.

Source Code

Model descriptions are available in

• AMPL/TACO code at Methanol to Hydrocarbons problem (TACO)