Model Predictive Control is a receding control approach, that basically does online dynamic optmisation on a finite horizon while implementing online, the first control optimal action of the control sequence. The online dynamic optimisation is repeated based on the measure system states with a sliding finite-horizon window.
However, can't we say that in principle due to the finite-horizon nature of MPC, the solution result obtains does not guarantee global optimality in the infinite horizon time scale as the control sequence found between A-B will not be necessarily optimal if the horizon A to C (A-B-C) was considered ? It seems to be some kind of corrective greedy search where the best control sequence at any branch is selected and because the control sequence is not fully implemented at the finite horizon, there is a possibility for escaping a bit the danger of the greedy search at the next iteration?
Dear Yves,
Because in the infinite horizon MPC the resulting problem is an infinite dimensional problem that in most cases is computationally intractable and thus the true "Optimal" solution can only be approximated with the discrete time finite horizon equivalent and under assumptions about the origin of the system and its active sets. There is a very good research in this paper that you might want to look at: Pannocchia, Gabriele, Stephen J. Wright, and James B. Rawlings. "Existence and computation of infinite horizon model predictive control with active steady-state input constraints." IEEE Transactions on Automatic Control 48.6 (2003): 1002-1006.
Best,
vassilis
Thank you Vasillis for the clarification, it really looked too obvious why MPC would not strive for an infinite horizon solution, but I will look into the paper you sent to dig more, Computational intractability is clearly a strong reason.
Thank you very much for the insight
Kind regards
The reason that MPC uses a finite horizon approach is that all chemical processes or any other processes where MPC is applied have finite time to steady state (except for level). If you are using steam to heat a reactor, the temperature will increase and based on heat balance, woudl reach a steady state. So in MPC we take this time to steady state as the finite horizon for the variable to be controlled in MPC. Further, each CV in MPC can have a different time horizon. Level control variables are treated differently as integrators (infinite time horizon) as they dont reach a new steady state value.
On further thoughts, is there any process that requires infinite time horizon to reach a new steady state? If not, then dont thikn it is required to use infinite horizon as it would not represent the process and as well as have computation alissues
Thank you Rakesh,
you again opened my mind the whole idea of having a finite-horizon search,
I will look into it deeper,
Kind regards
Hi Rakesh,
I reasoned around the assertion you have made about processes having a finite time to steady state,
How does one know in the first place the response time of the processes as it uses dependent upon the controller used in a the close loop feedback system (i. e. The forward system, controller plus plant model has an impact on the response of the close loop system)
Is the system steady state response analysed from the open loop plant model?
In the many APC projects that I have been involved with, we do open loop step testing on the plant and from the step test data, identify the process models using ID software tools these days. Further, I have also used closed loop step testing with a MPC already controlling the process is running. The mathematical algorithms have been advanced in these software tools that can make use of closed loop step test data to identify models.
If you look at any of the current MPC design and implementation s/w's such as Aspen DMC Plus or Honeywell Profit Controller or Shell SMOC, all make use of open loop or closed loop data and identification methods to come up with finite horizon models.
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