Consider a notation change to support output feedback

[russtedrake]

Consider a notation change to support output feedback

[RussTedrake]

@TobiaMarcucci -- any opinions on this one?

[TobiaMarcucci]

As you say, using f(x,u) for the dynamics and h(x,u) for the output is not unusual. For example Khalil does that in "Nonlinear systems" and Isidori does that in "Nonlinear control systems". However, they both do that to save g(x) for the coefficient of u in the dynamics (i.e. xdot = f(x,u) + g(x)u). So I agree that the current solution is not super clean. I'd also go for xdot = f(x,u), y = g(x,u) as long as control-affine dynamics do not appear too often.

Regarding the running cost in the OCPs. In dynamic programming, e.g. Bertsekas' book, I've seen g(x,u) as you are using right now. However, in most of the modern "analytical optimal control" books I've read, the integrand term is l(x,u) or L(x,u) (e.g., Liberzon's and Bressan and Piccoli's). Could l(x,u) be better than c(x,u), provided that no other conflicts arise?

[RussTedrake]

thanks! I've done xdot = f1(x,u) + f2(x)u for control affine in the intro, so that overlap is not a big concern.

yes, I could be happy, I think, with l(x,u) for the running cost.