You might also want to check out Infinite-Dimensional Systems Theory by Curtain and Zwart for an account of linear systems theory developed for separable Hilbert spaces. And for nonsmooth control, check out Nonsmooth Analysis And Control by Francis Clarke.
So you might need to blend a couple existing ideas together. Give it a shot!
Not much use for that kind of math whatsoever, but it’s fun
Immediately, I think it would have uses in quantum computing (where the state space can be an infinite-dimensional Hilbert space) and fluid dynamics (which are governed by partial differential equations, which can be represented as abstract differential equations on suitable function spaces).
What part of control theory are you focused on?
PM me for more details since I don’t wanna doxx myself, but my interest is in nonlinear high-dimensional dynamical systems.
Check out the book Mathematical Control Theory: Deterministic Finite-Dimensional Systems by Eduardo Sontag. A lot of his results take place in general metric spaces. Make sure to read the Appendix first, because this dude is absolutely next-level with the math. You’ll see.
You might also want to check out Infinite-Dimensional Systems Theory by Curtain and Zwart for an account of linear systems theory developed for separable Hilbert spaces. And for nonsmooth control, check out Nonsmooth Analysis And Control by Francis Clarke.
So you might need to blend a couple existing ideas together. Give it a shot!
Immediately, I think it would have uses in quantum computing (where the state space can be an infinite-dimensional Hilbert space) and fluid dynamics (which are governed by partial differential equations, which can be represented as abstract differential equations on suitable function spaces).
PM me for more details since I don’t wanna doxx myself, but my interest is in nonlinear high-dimensional dynamical systems.