Isomerization of Alpha-Pinene problem

Isomerization of Alpha-Pinene problem
Algebraic states:	5
Continuous control values:	5

The Isomerization of Alpha-Pinene problem tries to determine "reaction coe�cients in the thermal isometrization of $\alpha$-Pinene." (Cite and problem taken from the COPS library)

Mathematical formulation

The problem is given by

$\begin{array}{llcl}\underset{\theta }{\min }& \sum _{j=1}^8& & ||y({\tau }_j;\theta )-z_j|{|}^2\\ \text{s.t.}& {\dot{y}}_1& =& -({\theta }_1+{\theta }_3)y_1^2,\\ & {\dot{y}}_2& =& {\theta }_1{y}_1^2-{\theta }_2{y}_2.\\ & {\dot{y}}_3& =& {\theta }_1{y}_1^2-{\theta }_2{y}_2.\\ & {\dot{y}}_4& =& {\theta }_1{y}_1^2-{\theta }_2{y}_2.\\ & {\dot{y}}_5& =& {\theta }_1{y}_1^2-{\theta }_2{y}_2.\\ \end{array}$

Parameters

The values $z_j$ are measurements for the concentration for $y$ at time points ${\tau }_1,...,{\tau }_8$ and initial conditions are known.

Source Code

Model descriptions are available in

• AMPL/TACO code at Catalytic cracking problem (TACO)