Can the cost function and constraints for NMPC controller be changed based on the condition given?

Hello,

I am currently working on a path tracking controller for a 4-wheel steering system using the NMPC (Nonlinear Model Predictive Control) toolbox. I would like to inquire about updating the cost function and constraints based on specific conditions or limiting the search area of the manipulated variables in certain situations.

Specifically, I would like to know if it is possible to dynamically update the cost function and constraints during runtime based on real-time conditions or events. For example, can the cost function and constraints be adjusted to prioritize different objectives or penalize certain variables depending on the current state of the system or external factors?

Additionally, I am interested in learning how to limit the search area of the manipulated variables within a certain band or range for particular situations. This would allow me to ensure that the control inputs generated by the NMPC algorithm stay within predefined limits, which may be necessary for safety or operational reasons.

I would greatly appreciate any suggestions, insights, or examples regarding the implementation. Any resources, research papers, or code examples related to this topic would be highly beneficial.

Thank you in advance for your assistance and guidance!

Answer 1

[Akshat Dalal]

Hello Shrinidhi,

I understand that you are implementing nonlinear MPC using the Model Predictive Control Toolbox and have a query regarding creating a cost function which can be dynamically updated during runtime and depends on the current state of simulation. You also want to put constraints on the search area of the manipulated variables.

For the first part, you could implement multistage nonlinear MPC which lets you specify different cost functions for each stage. I hope this would aid you to some extent in having a dynamic cost function. The “LandingRocketWithMPCExample.m” script demonstrates how you can create a dynamic cost function by leveraging multistage nonlinear MPC. The cost function for this example, defined in “LanderVehicleCostFcn.m”, takes the current “stage” of simulation as one of its inputs, and outputs the corresponding cost “J” for that state. The following documentation gives a detailed explanation of the script - https://in.mathworks.com/help/releases/R2022a/mpc/ug/landing-rocket-with-mpc-example.html

The second part of your query can be achieved by creating a NMPC controller using the ‘nlmpc’ function, which lets you specify constraints for manipulated variables.

To read more about multistage nonlinear MPC and related functionalities, please refer the following documentation –

1. https://in.mathworks.com/help/releases/R2022a/mpc/ref/nlmpcmultistage.html
2. https://in.mathworks.com/help/releases/R2022a/mpc/ug/specify-constraints-for-nonlinear-mpc.html

You could also refer the following example to learn more about the implementation –

1. https://in.mathworks.com/help/releases/R2022a/mpc/ug/truck-and-trailer-automatic-parking-using-multistage-mpc.html