Isomerization of Alpha-Pinene problem

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

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

Mathematical formulation

The problem is given by

$\begin{array}{llcl}\underset{\theta }{\min }& \sum _{j=1}^8& & ||y({\tau }_j;\theta )-z_j|{|}^2\\ \text{s.t.}& {\dot{y}}_1& =& -({\theta }_1+{\theta }_2)y_1,\\ & {\dot{y}}_2& =& {\theta }_1{y}_1,\\ & {\dot{y}}_3& =& {\theta }_2{y}_1-({\theta }_3+{\theta }_4)y_3+{\theta }_5{y}_5,\\ & {\dot{y}}_4& =& {\theta }_3{y}_3,\\ & {\dot{y}}_5& =& {\theta }_4{y}_3-{\theta }_5{y}_5,\\ & {\theta }_i& \ge & 0i=1,...,5.\end{array}$

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 Isomerization of Alpha-Pinene problem (TACO)