In this talk, we consider the class of optimal control problems, where the control system is given by a controlled second order differential equation. Such control systems naturally appear in mechanics in the form of controlled Euler-Lagrange equations. Classically, Pontryagin’s maximum principle gives necessary optimality conditions for the optimal control problem, or alternatively, a variational approach based on an augmented objective for smooth problems. We propose a new Lagrangian approach leading to equivalent optimality conditions in the form of Euler-Lagrange equations and show its geometrical characterization. As a result, the differential geometric structure (similar to classical Lagrangian dynamics) can be exploited in the framework of optimal control problems. In particular, the formulation enables the symplectic discretization of the optimal control problem via variational integrators in a straightforward way. 

https://indico.math.cnrs.fr/event/12751/