2017/05/29 by Francesco Boarotto, Boarotto, Francesco, Mario Sigalotti +1 · 1 citation
Computer Science · Engineering · #Control and Stability of Dynamical Systems #Differential Geometry (math.DG) #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · doi:10.48550/arxiv.1705.10055
openalex publication_date 2017/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider in this paper the regularity problem for time-optimal trajectories of a single-input control-affine system on a n-dimensional manifold. We prove that, under generic conditions on the drift and the controlled vector field, any control u associated with an optimal trajectory is smooth out of a countable set of times. More precisely, there exists an integer K, only depending on the dimension n, such that the non-smoothness set of u is made of isolated points, accumulations of isolated points, and so on up to K-th order iterated accumulations.