Wasserstein Contraction Bounds on Closed Convex Domains with Applications to Stochastic Adaptive Control

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

This paper is motivated by the problem of quantitatively bounding the convergence of adaptive control methods for stochastic systems to a stationary distribution. Such bounds are useful for analyzing statistics of trajectories and determining appropriate step sizes for simulations. To this end, we extend a methodology from (unconstrained) stochastic differential equations (SDEs) which provides contractions in a specially chosen Wasserstein distance. This theory focuses on unconstrained SDEs with fairly restrictive assumptions on the drift terms. Typical adaptive control schemes place constraints on the learned parameters and their update rules violate the drift conditions. To this end, we extend the contraction theory to the case of constrained systems represented by reflected stochastic differential equations and generalize the allowable drifts. We show how the general theory can be used to derive quantitative contraction bounds on a nonlinear stochastic adaptive regulation problem.

Original languageEnglish (US)
Title of host publication60th IEEE Conference on Decision and Control, CDC 2021
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages366-371
Number of pages6
ISBN (Electronic)9781665436595
DOIs
StatePublished - 2021
Event60th IEEE Conference on Decision and Control, CDC 2021 - Austin, United States
Duration: Dec 13 2021Dec 17 2021

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2021-December
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370

Conference

Conference60th IEEE Conference on Decision and Control, CDC 2021
Country/TerritoryUnited States
CityAustin
Period12/13/2112/17/21

Bibliographical note

Publisher Copyright:
© 2021 IEEE.

Fingerprint

Dive into the research topics of 'Wasserstein Contraction Bounds on Closed Convex Domains with Applications to Stochastic Adaptive Control'. Together they form a unique fingerprint.

Cite this