I'm interested in getting a better understanding of optimal control theory including the HJB equation and the Maximum principle. Most of the books/notes I've seen do not seem to use a normed space approach with Fréchet derivatives. The story is similar in books on calculus of variations, but I eventually found a nice derivation of the Euler Lagrange equation using Fréchet derivatives, and I now would like this for control too.
Can someone point me to a book or notes on control theory that uses Fréchet derivatives on normed function spaces? An answer to another question on this topic recommended Sontag Mathematical Control Theory, but that doesn't seem to be using Fréchet derivatives much.
Thanks.