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Bounds on the loss of regularity of time-optimal trajectories of generic control affine systems

Francesco Boarotto
Institution: 
Laboratorie Jacques-Louis Lion & INRIA
Location: 
A-134
Schedule: 
Thursday, November 23, 2017 - 15:00 to 16:30
Abstract: 

In this talk we consider the control system \dot{q}=f_0(q)+uf_1(q), with |u|\leq 1 in an n-dimensional manifold M.

We study the non-smoothness set \Sigma of time-extremal trajectories coming from the associated time-optimal problem. We prove that, for the generic choice of the fields f_0 and f_1, \Sigma can be written as a finite union of discrete sets, whose number is bounded above by n^2. In particular, all extremal trajectories are smooth out of a countable set. Joint work with M. Sigalotti.

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