Hello @MIDHUNTA30,

First of all, thank you for making this content available. I am beginning my introduction to NMPC and I have two questions regarding the use of fmincon as an optimization solver. First, the vector z is constructed by aggregating Xk and Uk (states and manipulated variables). When you call fmincon, how does it know that it should solve and find the values of only the inputs U for minimizing the cost function? As it is, won't it find the overall combination of X and U which minimizes the cost function?
Second, can you please explain how you defined the non-linear constraints in NMPC1 and NMPC2? And why you didn't do it in the LMPC examples?

Moreover, I am having working on a problem with eight states and two inputs, all with different lower and upper bounds, and I defined them like this:

lb=[x1minones(1,(N+1)),x2minones(1,(N+1)),x3minones(1,(N+1)),x4minones(1,(N+1)),x5minones(1,(N+1)),x6minones(1,(N+1)),x7minones(1,(N+1)),x8minones(1,(N+1)),u1minones(1,N),u2minones(1,N)];

ub=[x1maxones(1,(N+1)),x2maxones(1,(N+1)),x3maxones(1,(N+1)),x4maxones(1,(N+1)),x5maxones(1,(N+1)),x6maxones(1,(N+1)),x7maxones(1,(N+1)),x8maxones(1,(N+1)),u1maxones(1,N),u2maxones(1,N)];

Is this correct?

Thank you!

First of all, I would like to thank you for your amazing work that as helped me a lot in my MPC internship.
I have a question, especially on the NMPC_2.m code file, if we would like to make trajectory following by changing the reference value over time (example x1 = 0.5kTs, x2 = 1), How should we incorporate theses reference changes? I have tried to do so with a unicycle robot model adding some changes in the nlcon function to adjust the value of the reference with the Prediction horizon location in time but with no successful results. (i can send you my .py file if you want to check)
If you have any code example, it would help me a lot

Thank you Midhun

Hello @MIDHUNTA30 ,

First of all, I am really thankful to you that you uploaded your lectures on YouTube. They were of great help to me. After going through your lectures I wanted to try implementing the code myself, but I think there is some inconsistency between the dimensions of the block-diagonal matrices that you have and that I came up with. If you refer to your code LMPC_1.m. The dimension of the variable FX comes out to be 24x12 but when I tried it on my own to verify the dimension, I get it to be 48x24. And this is how I am calculating the dimension of FX :

Since FX is a block diagonal consisting of Fx matrices which is of dimension 4x2 as its diagonal elements.

Now FX is to be pre-multiplied with Xk ( as per your notes ) which is of dimension 12x1, so the block diagonal matrix must be of size 12x12.

Since every element of the block diagonal matrix of size 4x2, therefore the dimension of the block diagonal should be 48x24.

I am not sure if I am calculating the dimensions in the correct manner , Can you please let me know where i am going wrong ?

Thank you.