Part 1 (Cont'd) | MPC Model Simulation using Runge Kutta Method

NEW: this video shows the MATLAB implementation of the Runge Kutta method for model simulation using Casadi.
This is a workshop on implementing model predictive control (MPC) and moving horizon estimation (MHE) in Matlab. The implementation is based on the Casadi Package which is used for numerical optimization. A non-holonomic mobile robot is used as a system for the implementation.
Full Playlist can be found here:
• MPC and MHE implementa...
You find this workshop useful? you can cite any of my related work here:
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Presenter Website: sites.google.c...
workshop slides and matlab codes can be found here:
github.com/MMe...
Casadi can be downloaded from here:
web.casadi.org...

[@FaGa-sc8mi]

Can you please tell how did you obtain the exact discrete model from continuous one? I can imagine you expanded around theta + sampling time * theta_dot, which is omega, but the confusion arises from the presence of omega(k) in the denominator, for both x(k+1) and y(k+1)...

[@MohamedWMehrez]

By direct integration of the system model. That's not always possible for the dynamical systems in general.

[@muhammadhd8407]

Hi, shouldn't change the computations of the next initial state in the function shift.m to use RK method too? variable f that we have passed to the function is the same for two methods f = Function('f',{states,controls},{rhs});

[@dagobertammersee6948]

I don't understand this either?

[@MohamedWMehrez]

Yeah, you should. I am trying to find sometime to fix this on github.

[@michaelkonig5186]

Hi,
is it possible to get the whole code?
Would like to see how you implemented the OCP in Matlab.

[@MohamedWMehrez]

Hi, Matlab code is linked in the video description. All the best!

[@michaelkonig5186]

@@MohamedWMehrez
Thank you!
I am currently also writing a MPC code. However, I still currently have big problems and can not find my error.
Could you help me with this?
It is the same procedure but it is a different use case

[@hanenyaakoubi294]

👍

[@ylulnlulsYx1]

Hi,
did you also change the shift function with Runge Kutta 4th order? Does it even make any difference?

[@MohamedWMehrez]

No change is needed to the shift function. We simply changed f which we pass to the shift function and works the same way as f from Euler discretization.

[@kechidaoussama3511]

how we can add the arrival cost in this program with EK filter ?

[@MohamedWMehrez]

This can be done by adding (the difference between the estimate of the state at time k-N and the corresponding optimization variable for the state at that time) to the cost variable.

[@dagobertammersee6948]

Dear Mr. Mehrez, could you please explain why we don't adapt the discretization in the shift function as well? In the shift function we compute the initial state also by a euler discretization, so why don't we use RK4 again?