Hello,

As you mentioned MPC is more or less a repetition of an optimal control like problem. However, in MPC the optimization horizon is FINITE in spite of the INFINITE horizon of an optimal control problem. Moreover, the solution of MPC is obtained mostly through numerical optimization, which is unlike the analytical solution to optimal control problems that is done by solving the analytical Ricatti Equation. The implementation of MPC requires updated measures of initial conditions and repeated solution to a constrained and a possibly nonlinear system. This makes it a closed loop control, which compensate for model/plant mismatch by using the updated initial conditions.

I find the following discussion very relevant to your question

https://www.google.com.eg/amp/s/www.researchgate.net/post/What_are_the_advantages_of_Model_Predictive_Control_over_Optimal_Control/amp

All the best,

Mohamed

Dear Jingwen Zhang,

The optimal control is to make an open-loop control and thus remains in real time with an attenuation of the mismatch of the system model and the effects of disturbances. However, in the case of the MPC, this is in a closed loop so the correction is integrated in the calculation of the trajectory with a periodic reset of the initial conditions of this control.

For more details and information about this subject i suggest you to see this book on MPC, here are link :

Model predictive control

Author: Camacho, Eduardo F and Alba, Carlos Bordons

Best regards

@Mohamed-Mourad Lafifi Thanks for your reply. Yes, real-time optimal control is an open-loop control, and MPC is a closed-loop control. However, if I added the initial states corrections into real-time optimal control, is real-time control model same as the MPC? That is to say, can the optimal objectives set the same between real-time control and MPC?

@ Mohamed W. Mehrez Thanks for your reply. Yes, but real-time optimal control could also be solved by numerical optimization. And it is an open-loop control, and MPC is a closed-loop control. However, if I added the initial states corrections into real-time optimal control, is real-time control model same as the MPC? That is to say, can the optimal objectives set the same between real-time control and MPC?

Hi Jingwen,

If you recalculate your optimal sequence after periodically resetting the initial conditions, it's like building your predictive model.

Best regards

Dear Jingwen Zhang,

the answer is yes and no. If you perform real time optimisation with a fixed sampling rate and typically, as Mohamed W. Mehrez mentioned, if the time horizon of that problem is finite, then Mohamed-Mourad Lafifi is right that RTO is equivalent to MPC.

Yet nobody would implement it that way. In MPC, you solve the optimal control problem in a preparation phase ahead of time including the sensitivity regarding the (predicted) initial value. Once the measurement/estimate for the initial value is available, you perform an update step. This way, you have a lot of time for the preparation phase, and can react fast in the update phase. So this is already a partial "no".

The real "no" is that typically you apply RTO to precompute steady state set points for your application. I.e., you split the problem into two layers: On a tactical layer, you use RTO to adapt your problem, on the operational layer, you use MPC to solve and react to it.

In the literature, you will also find the term realtime iterations, which again has a different meaning.

I hope that this helps you with your problem.

Best,

Jürgen

Hi, Mohamed-Mourad Lafifi ,

Thanks for your reply. Actually, I just want to periodically reset the initial conditions for better future optimization, rather than recalculating the optimal sequence.

Best regards,

Hi Jingwen Zhang ,

if you just want to reset that, we don't you use sensitivities? You may want to have a look at

Book Optimal Control of ODEs and DAEs

Best,

Jürgen

Hi, Jürgen Pannek,

Thanks for your detailed answer. It really helped me to understand the difference between RTO and MPC. I do not use sensitivity analysis for initial values.

As you said, "On a tactical layer, you use RTO to adapt your problem, on the operational layer, you use MPC to solve and react to it.", YES. But I thought MPC could do on the tactical and operational layers. Because MPC could do the optimization for the current period. Then, MPC also could adapt the states with the measurements for the optimization of next period. Does MPC work like what I said?

Besides, if I added the adaptation for RTO, i.e. RTO also could do the optimization for the current period and adaption for the next period. I am confused about what you said part "no". Thanks.

Bests,

Jingwen

Hi Jingwen Zhang ,

the point here is that RTO typically has a far longer horizon (planning problem), while the MPC horizon is chosen as short as possible to reduce computing time and thereby increasing the sampling rate (control problem). So the tactical layer will give you the tracking signal, and the operational level tracks that signal.

So yes, you could use MPC also on the tactical layer, but at a different sampling rate. So the question is, why would you want to? Mixing the layers is a very bad idea from the practical point of view: These are different units within companies, with different goals. You can still do all with one MPC though.

Best,

Jürgen

Hi Jürgen,

I finally got it. What I really want to do is to incorporate the real-time data into the real-time optimization model, and MPC could do it with short horizon, but RTO could do it for longer horizon. I think I can set the same horizon and same objectives for tactical and operation layer.

Yes, I think MPC could do it though, so do RTO. Thanks.

Best,

Jingwen

An efficiently functioning control system based on Model Predictive Control could significantly improve the logistics process of production in a dynamic approach taking into account various factors and variables of the environment in many enterprises in the production sector.

Dear Jingwen Zhang

real-time optimal control is an open-loop control, and MPC is a closed-loop control.

Regards

Dear Jingwen Zhang,

beyond the previous answers and comments, we have to classify the denominations:

Real-time Optimization (RTO) and Dynamic Optimization (DO) refer to different classes of activities. RTOs work to find the best process operation at steady-state in a timeframe between hours and days while DOs operate the processes in a timeframe of minutes-hours considering the dynamic responses.

Optimal controls (MPC, NMPC, EMPC, LQR, LQG, etc.) are in the DO group and differentiate themselves in few aspects and elements. For instance, we can assert that the traditional MPC is a type of D-RTO (Dynamic Real-time Optimization). Moreover, optimal controls are designed taking in account the Control Theory field (stability, robustness, tuning methods, analysis in frequency and time domains, etc.).

Regards.