Hi, I am struggling with HW3. I am doing this with information from the lectures and the dimensions of my matrices are incorrect somehow. I need to double check this. Matrix H is computed with a matrix multiplication C~'*Q~*C~. The dimensionality of Q_ is given by the augmented state vector x~ which should have dimensionality 1 x n+m, because it is length of state vector (n) + length of a single input (m), so in here it could be 6. Matrix C~ however does not correspond to this, as it has dimensionality 60x20. Can someone advise in this situation? Surely I just do not understand correctly. Thanks!
You write "the augmented state vector x~ which should have dimensionality 1 x n+m, because it is length of state vector (n) + length of a single input (m), so in here it could be 6". Is this correct?
it probably isnt, but in the video you specify that x~ = [x;delta u(t-1)]. I though ti should be 1 x m+n. Is this wrong assumption?
It may help if you mention the time within the video.
Anyway, I guess that x~ should denote stacked vectors (actually both state vectors and control vectors) over the time horizon. Therefore its dimension should certainly depend on N as well. Indeed, Kajetán states this correctly in his response.
I do not exclude the possibility that I have some omission in the videos though.
Anyway, I guess that x~ should denote stacked vectors (actually both state vectors and control vectors) over the time horizon. Therefore its dimension should certainly depend on N as well. Indeed, Kajetán states this correctly in his response.
I do not exclude the possibility that I have some omission in the videos though.
There was just a mistake within the declaration of matrix Qdoublebar in the video, but that is fixed in the texts from the videos. And as you said in the video, the x~ is augmented state vector over the time horizon of size N. The most important thing here is not to mix notations of variables eg. x~ vs. x~_k, size N*(m+n) vs. size m+n.
Indeed, besides the (unfortunately) inevitable typos, deciding on a systematic and descriptive yet robust notation is a challenge. While working on those online lecture notes on github I am trying to fine-tune the notation a bit.
The issue is solved. It was as Kajetán mentioned the incorrect formula for Q double bar.
Qdouble bar is given by C~'*Q*C~ that is in dimension C~ - p x m+n and Q - p x p so the dimension of C~'*Q*C~ is m+n x m+n. In result Qdoublebar is then square matrix N*(m+n) and that is valid with the dimension of matrix Cdoublebar that you mentioned as 60x20.