01220nas a2200121   4500008004100000245009100041210006900132260001000201520080700211653002801018100001601046856003601062       2014                        en  d00aThe curvature of optimal control problems with applications to sub-Riemannian geometry0 acurvature of optimal control problems with applications to subRi  bSISSA3 aOptimal control theory is an extension of the calculus of variations, and deals with the optimal behaviour of a system under a very general class of constraints. This field has been pioneered by the group of mathematicians led by Lev Pontryagin in the second half of the 50s and nowadays has countless applications to the real worlds (robotics, trains, aerospace, models for human behaviour, human vision, image reconstruction, quantum control, motion of self-propulsed micro-organism).

In this thesis we introduce a novel definition of curvature for an optimal control problem. In particular it works for any sub-Riemannian and sub-Finsler structure. Related problems, such as comparison theorems for sub-Riemannian manifolds, LQ optimal control problem and Popp's volume and are also investigated.10aSub-Riemannian geometry1 aRizzi, Luca  uhttp://hdl.handle.net/1963/7321