I am working on the control of underactuated mechanical systems (UMSs) using backstepping method. UMSs are classified into triangular normal forms (strict-feedback and strict-feedforward) and nontriangular form (byrnes-isidori normal form). In particular, a strict-feedback system permits applying backstepping method. How about nontriangular form? Is it possible to apply backstepping to this class? Can anyone help me?
I think that you might find interesting the Phd thesis (and corresponding publications) of R. Olfati-Saber that studies the question of normal forms and (backstepping,forwarding, and other) control of UMS: Article Nonlinear Control of the Under-actuated Mechanical System wi...
Hope this is helpful. Regards!
Thanks very much. I studied his thesis but Olfati-saber has said stabilization of a nontriangular form is in general much more diffcult than that of a triangular form. For example, backstepping or forwarding is not applicable. But in some papers, examples of nontriangular form have been controlled using backstepping!
https://www.sciencedirect.com/science/article/pii/S0273117715005384
I think that there should be a way to design backstepping for nontriangular form but i don't know in which conditions it is possible.
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