Question about EDMD fit function

[kiranvodrahalli]

Hi,

I was confused by the following line in the fit function:
W = concatenate((Z_dot, X), axis=0) (line 56 in core/learning/edmd.py).
As I understand the EDMD algorithm, W is supposed to be the lifted version of the next predicted state -- why is it the concatenation of the derivative of the lifted Xs (Zs) and X? In particular, it does not seem like this is what https://arxiv.org/pdf/1611.03537.pdf does (referring to pg 8, eqs 16-21) -- it seems like W should be Y_lift. Am I missing something?

Thanks!

[Cafolkes]

Hi Kiran, sorry for the late reply and thank you for the interest in our work. I believe your understanding is correct but we are implementing a slight variation of the method described in the Korda, Mezic paper. First, we implement a *continuous-time *version of the framework described in the paper. The main implication of this is that Y_lift = Z_dot as we seek to find A, B that minimize the objective ||Z_dot - (AZ + BU)||. This hopefully answers the first part of your question. Second, we implement the general input-output version of the framework (similar to pg 16, eqs 39-40). This allows any output to be predicted. However, we are interested in the case where the states (X) are the outputs of interest. We seek to find C that minimizes the objective ||X - CZ|| in addition to finding A, B as described above. In the implementation, we solve these regression problems simultaneously. As a result, W is the concatination of Z_dot (Y_lift) and X (the output). You can see that the A, B, and C correspond to different parts of the M-matrix in lines 64-69 in core/learning/edmd.py. I hope this answers your question, let me know if anything is still unclear. Best, Carl tor. 9. apr. 2020 kl. 05:40 skrev Kiran Vodrahalli <notifications@github.com

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: Hi, I was confused by the following line in the fit function: W = concatenate((Z_dot, X), axis=0) (line 56 in core/learning/edmd.py). As I understand the EDMD algorithm, W is supposed to be the lifted version of the next predicted state -- why is it the concatenation of the derivative of the lifted Xs (Zs) and X? In particular, it does not seem like this is what https://arxiv.org/pdf/1611.03537.pdf does (referring to pg 8, eqs 16-21) -- it seems like W should be Y_lift. Am I missing something? Thanks! — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub <#67>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AGIOQYXWOXF2B3OPTLRCNZLRLU7S3ANCNFSM4MENE37Q> .

-- Kind regards Carl Folkestad PhD Candidate, Control and Dynamical Systems California Institute of Technology Mobile: (626) 689-5272 carl.folkestad@caltech.edu <cfolkest@caltech.edu>