Mini-class of Franco Rampazzo (University of Padova, Italia) on optimal control: June 19, 21, 24, 26 and 27, from 2pm to 4pm in room Bichat - ENSEM

Nonlinear Optimal Control: an introduction to necessary conditions for minima, Hamilton-Jacobi equations, and geometric controllability.
This course is conceived for graduate students in Mathematics, Engineering, and Physics. No particular prerequisites are required. The course will focus maily on the celebrated Pontryagin Maximum Principle, which consists in some general necessary conditions for minima of Optimal Control problems. On one hand the latter are strongly motivated by applications (e.g. aerospace engineering, mechanics, finance, medicine). On the other hand, they generalize Calculus of Variations' problems, in that the velocities are dynamically constrained by ODE's with control parameters. The main proof we will present relies on a strong, intuitive, geometric idea, namely set-separation, which in turn is made precise by a suitable application of general tools such as cones' transversality and a suitable directional open mapping theorem. Other subjects of the course will include some connections with Hamilton-Jacobi PDE's as well as basic tools from Geometric Control (e.g. Lie brackets, Frobenius Theorem, Chow's Theorem.)
Detailed lecture notes will be available since the beginning of the course.