Universality and Control of Fat Tails

Michael Chertkov

doi:10.1109/lcsys.2023.3279248

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arXiv · 2303.09635

Universality and Control of Fat Tails

Michael Chertkov

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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.

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eess.SY cond-mat.stat-mech cs.SY nlin.CD stat.AP

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Michael Chertkov. 2023-03-16. Universality and Control of Fat Tails. https://doi.org/10.1109/lcsys.2023.3279248

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