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Геометрическая теория оптимального управления
10 июня 2020 г. 16:45–18:15, г. Москва, The seminar take place online via skype, from the user "msu.opu@gmail.com"
 


A bound on the iteration order of Fuller singularities for generic control-affine time-optimal systems

M. Sigalotti

Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste

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Аннотация: It is known that a time-optimal control-affine system can have any kind of singularity. It is also known that the Fuller phenomenon (i.e., the accumulation of switching times) occurs generically for extremal trajectories of control-affine time-optimal systems if the dimension of the manifold is large enough and the control takes values in a polytope. In this talk we consider the case where the control takes values in a m-dimensional ball. We present recent results stating that, for generic systems with m=1 or m even, the control u associated with an extremal trajectory is smooth out of a countable set of times. More precisely, there exists an integer K, only depending on m and the dimension of the ambient manifold, 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. The talk is based on joint works with F. Boarotto and Y. Chitour.

Website: http://opu.math.msu.su/node/587

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