Methanol to Hydrocarbons problem

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

$\begin{array}{llcl} \displaystyle \min_{\theta} &\sum\limits_{j=1}^{16} &&||y(\tau_j; \theta) - z_j||^2 \\[1.5ex] \mbox{s.t.} & \dot{y}_1 & = & -( 2 \theta_2 - \frac{\theta_1 y_2}{(\theta_2 + \theta_5) y_1 + y_2} + \theta_3 + \theta_4) y_1, \\[0.3cm] & \dot{y}_2 & = & \frac{\theta_1 y_1 (\theta_2 y_1 - y_2)}{(\theta_2 + \theta_5) y_1 + y_2} + \theta_3 y_1, \\[0.3cm] & \dot{y}_3 & = & \frac{\theta_1 y_1 (y_2 + \theta_5 y_1}{(\theta_2 + \theta_5) y_1 + y_2} + \theta_4 y_1, \\[0.3cm] & \theta_i & \geq & 0 \quad i = 1,...,5. \end{array}$

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)