I don't really agree - the xkcd cartoon is about physicists naively going from real-world phenomena to mathematical models, without understanding what is important or already known about the problem domain.
In his case, a physicist is looking at a problem that already has a standard mathematical formalism in control theory, and is suggesting new theoretical approaches to apply to it that he claims provides additional insights.
And, whereas in the cartoon the physicist says, "why does <your field> need a whole journal, anyway", the author of this monograph publishes in existing control theory journals (e.g., [1] in IEEE Transactions on Automatic Control).
I made the remark based on "Its natural audience would be control theorists, but they may find the level of abstraction very challenging" which sounds a bit condescending even if true.
Agreed, but note (afaik) group theory is not usually applied in Control Theory, so it does seem it would be a challenge to someone in the field (maybe just a helpful disclaimer).
From a quick skim, it certainly looks like advanced mathematics is at use, but control theorists that deal with nonlinear systems have been using this kind of formalism already. Lie groups are even used in robotics to write down kinematics of serial chains.
I would counter that a minority of control engineers are using Lie groups and that a lot of people who have got by with linear methods so far might end up needing the conclusions in this book.
