Universality and Control of Fat Tails
arXiv:2303.09635 · doi:10.1109/LCSYS.2023.3279248
Abstract
Motivated by applications in hydrodynamics and networks of thermostatically-control loads in buildings we study control of linear dynamical systems driven by additive and also multiplicative noise of a general position. Utilizing mathematical theory of stochastic multiplicative processes we present a universal way to estimate fat, algebraic tails of the state vector probability distributions. This prompts us to introduce and analyze mean-q-power stability criterion, generalizing the mean-square stability criterion, and then juxtapose it to other tools in control.
6 pages, 1 figure, L-CSS/CDC 2023 (+ corrected missprints)