I am using optimal control for mathematical economics. However, many books by Kamien and Schwarz, Sydsaeter et Sierstad do not always enter into mathematical foundations of optimal control and give some toolbox and in many parts of these books (which are quite rigorous by the way), I feel like I am given some recipes. I have searched for previously asked questions on the topic but did not find what I am looking for.
Are there any references dealing with the foundations of optimal control, and dynamic optimization by referring to the calculus of variations or analysis?