How to specify time varying constraints(linear combination of input/output variables) using MPC Toolbox?

To clarify the issue: I am working on designing a linear MPC controller. Ideally, I would like to speficy constraints that vary over the prediction horizon.

I know this is possible for simple lower and upper bounds on inputs/outputs (see: https://de.mathworks.com/help/mpc/ug/time-varying-weights-and-constraints.html ), atleast within MPC Designer. I also know that constraints(linear combination of input/output variables) can vary inbetween the solution cycle/at run-time (See: https://de.mathworks.com/help/mpc/ug/run-time-constraint-updating.html ). However, as of today, I could not find any way to vary linear combinations of input/output variables for linear MPC over the prediction horizon.

Is there a way to achieve what I am looking for?

Thanks in advance.

Answer 1

[Kothuri]

Hi Benedikt Schmidt,

To vary the linear combinations of input/output variables over the prediction horizon, you can try NonLinearMPC Design which offers a greater flexibility in defining the constraints.

Below are the documentation links for more information on Non-Linear MPC Design

https://www.mathworks.com/help/mpc/nonlinear-mpc-design.html

https://www.mathworks.com/help/mpc/ug/specify-constraints-for-nonlinear-mpc.html

[Benedikt Schmidt]

Hi Kothuri,

I know that it is possible with Nonlinear MPC, but Nonlinear MPC requires way more computational resources than linear MPC. Nevertheless, I found a workaround to avoid the issue of having to specify constraints that vary over the prediction horizon entirely.

But for anybody else having the same question as me: For linear MPC, there is no way to vary the matrices E, F, G, V and S over the prediction horizon (See: https://de.mathworks.com/help/mpc/ref/mpc.setconstraint.html ). To do that you need Nonlinear MPC, like Kothuri mentioned. What can however vary over the prediction horizon are the input/output/disturbance variables. So, if you have e.g. disturbance variables for which you know in advance what values they will take for future time steps, you can use Signal Previewing (See: https://de.mathworks.com/help/mpc/ug/improve-control-performance-with-look-ahead.html ). If you use previewing for a disturbance variable, the respective variable will vary over the prediction horizon. If you specified a constraint using setconstraint and the S matrix is not a zero matrix, than you get constraints, that vary over the prediction horizon (because of the previewing for that disturbance variable).

In short, you can not vary E, F, G, V or S matrices, but by using Signal Previewing, it's still possible to get constraints( i.e. linear combinations of input/output/disturbance variables) which vary over the prediction horizon.

That beeing said, the above idea (Signal Previewing + setconstraint) to create constraints that vary over the prediction horizon lead to numerical instability, which was caused by the Previewing (atleast I think so). Most of the solutions I got this way were infeasible. I resolved the issue by adding a new state to my state space model which represents the constraint that I want to enforce. For the new state I specified hard lower/upper bounds. So essentially I introduced a slack variable. This worked like a charm even which previewing enabled. Hope this gives people with the same issue some ideas on what to try.

Answer 2

[Jordan Olson]

Hello Benedikt,

The simplest way to implement time-varying constraints for a nonlinear MPC is to use a multistage nonlinear MPC. This is essentially a special formulation of the standard nonlinear MPC where you can explicitly specify the cost and constraint functions separately for each stage from k to , p being the prediction horizon. For more information, please see the following:

• nlmpcMultistage documentation (specifically, see Properties -> Stages -> IneqConFcn): https://www.mathworks.com/help/mpc/ref/nlmpcmultistage.html
• [Example] Truck and Trailer Automatic Parking Using Multistage Nonlinear MPC: https://www.mathworks.com/help/mpc/ug/truck-and-trailer-automatic-parking-using-multistage-mpc.html

[Benedikt Schmidt]

Hi Jordan,

thanks for the answer. I should have specified in the initial question, that what I was looking for was specifically intended for linear MPC. My bad. Nevertheless, my original problem was resolved.