Using google you will find many open-source toolboxes for solving MPC related optimization problems, for instance ACADO, \muAO-MPC, Forces, ...

However, in order to receive detailed feedback, you should be more specific about what kind of MPC problem (linear or nonlinear, discrete or continuous time, ...) you want to solve and what the computational requirements are. 

Hope this helps

timm

Although old, this paper lists several programs: http://www.scribd.com/doc/16955545/MPC-CEP-Qin-Badgwell

Dear Hassan,

GPOPS-II and GAMS are also suggested for this purpose

Search for them

Hope these points work,

Regards,

Saeed Rahmati,

Much chemical process modelling and/or simulation work can be done with the widely-used Microsoft’s Excel.

Application example ― Simulations carried in Excel 5.0 with Visual Basic for Applications (VBA) macros ― The recursive least squares algorithm (RLS) allows for (real-time) dynamical application of least squares regression to time series. Years ago, while investigating adaptive control and energetic optimization of aerobic fermenters, I have applied RLS with forgetting factor (RLS-FF) to estimate the parameters from the KLa correlation, used to predict the O2 gas-liquid mass-transfer, while giving increased weight to most recent data. Estimates were improved by imposing sinusoidal disturbance to air flow and agitation speed (manipulated variables). The power dissipated by agitation was accessed by a torque meter (pilot plant).

The proposed (adaptive) control algorithm compared favourably with PID.

This investigation was reported at (MSc Thesis):

Thesis Controlo do Oxigénio Dissolvido em Fermentadores para Minimi...