PhD in Pure and Applied Mathematics

This course is conceived for graduate students in Mathematics, Engeneering, and Physics. It focuses on the celebrated Pontryagin Maximum Principle, a set of general necessary conditions for minima of Optimal Control problems. The latter generalize Calculus of Variations' problems, in that the velocities are dynamically constrained by ODE's with control parameters.

The approach we 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 directional open mapping theorem.

Time permitting, some issues from Geometric Control theory will be mentioned (e.g. Lie brackets), as well as connections with Hamilton-Jacobi PDE's.

Since the beginning of the course detailed lecture notes will be available.

 

5 CFU [25 ore]