Salle Coriolis (bât. Galois)
Abstract. In this talk, I will propose a framework to better understand turnpike phenomena in optimal control problems. I first review the notion of invariant manifold including stable manifold method to compute infinite horizon optimal control solution as well as its applications in mechatronics control. Then, I will show that the turnpike-like behavior can be seen in general nonlinear dynamical systems under hyperbolic assumption and then this is used to analyze Hamiltonian systems associated with optimal control problems. Conditions for turnpike are described in terms of the geometry of stable and unstable manifolds.