Yes, that is what I meant [1]. For example, you can use ideas from differential equations/analysis to determine say, the existence and uniqueness of solutions f

Yes, that is what I meant [1]. For example, you can use ideas from differential equations/analysis to determine say, the existence and uniqueness of solutions for continuous ODEs. Pontryagin's Principle and the calculus of variations in general gives you theoretical machinery for working with models in analytic form. Some problems such as minimum time optimization are more tractable in continuous time form than in discrete time. You can also in some simple cases derive the set of closed-form optimal solution trajectories (unconstrained case) and analyze that directly. Once the models are transformed into discrete form for numerical solution, the tools used lie more in the realm of linear algebra (positive definiteness of Hessians, etc.) [1] https://en.wikipedia.org/wiki/Mathematical_analysis https://en.wikipedia.org/wiki/Mathematical_analysis