Dynamical Systems Seminar: David Simpson

Noisy Sliding Motion

David Simpson

Institute of Fundamental Sciences, Massey University

Date and time: 

Thursday, May 28, 2015 - 2:00pm

Location: 

ECCR 257

Abstract: 

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.  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.  We will encounter stochastic averaging, asymptotics for the Fokker-Planck equation, the Feynman-Kac formula, and PDE boundary value problems.  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.