Dynamical Systems Seminar: David Simpson
Noisy Sliding Motion
,Ìý
Date and time:Ìý
Thursday, May 28, 2015 - 2:00pm
³¢´Ç³¦²¹³Ù¾±´Ç²Ô:Ìý
ECCR 257
´¡²ú²õ³Ù°ù²¹³¦³Ù:Ìý
The problem of quantitatively determining the effects of small noise on a periodic orbit of a nonsmooth system that has sliding segments is surprisingly complex.Ìý Understanding stochastic dynamics for sliding segments, non-sliding segments, and transitions from sliding to non-sliding segments, requires completely different methods, and much of the theory of stochastic differential equations is simply not applicable to systems with discontinuities.
In this talk I will describe various basic results for stochastic perturbations of nonsmooth systems with sliding.Ìý We will encounter stochastic averaging, asymptotics for the Fokker-Planck equation, the Feynman-Kac formula, and PDE boundary value problems.Ìý I will describe how the results apply to an example in relay control for which small noise induces an unexpectedly large increase in the frequency of oscillations.