How to optimize a parameter using Nonlinear model predictive controller

Hello everyone,

I am using Nonlinear model predictive controller and I wonder if I can optimize a parameter.

Let's take an example Plan Optimal Trajectory Using Nonlinear MPC on this website (https://www.mathworks.com/help/mpc/ref/nlmpc.nlmpcmove.html). In FlyingRobotStateFcn.m there are 2 given parameters alpha and beta = 0.2. Is there a way to make these paremeters also variables and calculate optimal values of alpha and beta ?

Thank you for your answers

Answer 1

[Emmanouil Tzorakoleftherakis]

Looks like you are referring to parameters defined inside the prediction model/state function of the MPC controller. You can make these variables parameters/arguments to the state function by following the guidelines on this page.

To use MPC for static optimization, one idea is to use the parameter as an MV and set a MVRate constraint to zero. That would basically make this MV constant. That way you could have both dynamically changing MVs and a constant one. If you try it, please let me know if it works.

[Ondrej Zoufaly]

From what I understood there is not an example of optimization a parameter without a dataset. What I want to do is to predict an action and during that optimize a parameter. On the given example of mine I would like to predict a trajectory of the ship and also calculate optimal parameter Alpha for which the fuel consumption would be even smaller. I hope you can understand my question, thank you for your answer.

[Emmanouil Tzorakoleftherakis]

A bit clearer now thanks. Looks like alpha shows up in your dynamics. Can this parameter change over time or is it constant? If it is allowed to vary, you could treat it as an additional input to your system and have MPC calculate that as well

[Ondrej Zoufaly]

That's the problem, it is a constant. In the example the parameters are moment arms of engines, so the optimized value should be as large as possible (so no need for optimiziation). However, I want to use it in my own model, I'm just demonstrating on this example since it is very clear and easy.

[Emmanouil Tzorakoleftherakis]

I see. So basically you have mixed dynamic and static decision variables. I haven't tried it myself, but one idea is to still use the parameter as an MV and set a MVRate constraint to zero. That would basically make this MV constant. That way you could have both dynamically changing MVs and a constant one. If you try it, please let me know if it works.

I also updated my answer accordingly