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 language | English (US) |
---|---|
Title of host publication | 60th IEEE Conference on Decision and Control, CDC 2021 |
Publisher | Institute of Electrical and Electronics Engineers Inc. |
Pages | 366-371 |
Number of pages | 6 |
ISBN (Electronic) | 9781665436595 |
DOIs | |
State | Published - 2021 |
Event | 60th IEEE Conference on Decision and Control, CDC 2021 - Austin, United States Duration: Dec 13 2021 → Dec 17 2021 |
Publication series
Name | Proceedings of the IEEE Conference on Decision and Control |
---|---|
Volume | 2021-December |
ISSN (Print) | 0743-1546 |
ISSN (Electronic) | 2576-2370 |
Conference
Conference | 60th IEEE Conference on Decision and Control, CDC 2021 |
---|---|
Country/Territory | United States |
City | Austin |
Period | 12/13/21 → 12/17/21 |
Bibliographical note
Publisher Copyright:© 2021 IEEE.