Section: Application Domains
Applications to some domains of mathematics
Control theory (in particular thinking in terms of inputs and reachable set) has brought novel ideas and progresses to mathematics. For instance, some problems from classical calculus of variations have been revisited in terms of optimal control and Pontryagin's Maximum Principle  ; also, closed geodesics for perturbed Riemannian metrics where constructed in  ,  using control techniques.
Inside McTAO, a work like  ,  is definitely in this line, applying techniques from control to construct some perturbations under constraints of Hamiltonian systems to solve longstanding open questions in the field of dynamical systems. Also, in  , geometric control is applied successfully to obtain genericity properties for Hamiltonian systems.