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Distributionally Robust Covariance Steering with Optimal Risk Allocation

Renganathan, Venkatraman LU ; Pilipovsky, Joshua and Tsiotras, Panagiotis (2023)
Abstract
This article extends the optimal covariance steering (CS) problem for discrete time linear stochastic systems modeled using moment-based ambiguity sets. To hedge against the uncertainty in the state distributions while performing covariance steering, distributionally robust risk constraints are employed during the optimal allocation of the risk. Specifically, a distributionally robust iterative risk allocation (DR-IRA) formalism is used to solve the optimal risk allocation problem for the CS problem using a two-stage approach. The upper-stage of DR-IRA is a convex problem that optimizes the risk, while the lowerstage optimizes the controller with the new distributionally robust risk constraints. The proposed framework results in solutions... (More)
This article extends the optimal covariance steering (CS) problem for discrete time linear stochastic systems modeled using moment-based ambiguity sets. To hedge against the uncertainty in the state distributions while performing covariance steering, distributionally robust risk constraints are employed during the optimal allocation of the risk. Specifically, a distributionally robust iterative risk allocation (DR-IRA) formalism is used to solve the optimal risk allocation problem for the CS problem using a two-stage approach. The upper-stage of DR-IRA is a convex problem that optimizes the risk, while the lowerstage optimizes the controller with the new distributionally robust risk constraints. The proposed framework results in solutions that are robust against arbitrary distributions in the considered ambiguity set. Finally, we demonstrate our proposed approach using numerical simulations. Addressing the covariance steering problem through the lens of distributional robustness marks the novel contribution of this article. (Less)
Please use this url to cite or link to this publication:
author
; and
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
in press
subject
host publication
American Control Conference
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • scopus:85167779091
project
Scalable Control of Interconnected Systems
language
English
LU publication?
yes
id
fea30cb2-4218-45e0-a666-5a90711b56d1
date added to LUP
2023-04-06 13:28:30
date last changed
2023-12-19 15:14:34
@inproceedings{fea30cb2-4218-45e0-a666-5a90711b56d1,
  abstract     = {{This article extends the optimal covariance steering (CS) problem for discrete time linear stochastic systems modeled using moment-based ambiguity sets. To hedge against the uncertainty in the state distributions while performing covariance steering, distributionally robust risk constraints are employed during the optimal allocation of the risk. Specifically, a distributionally robust iterative risk allocation (DR-IRA) formalism is used to solve the optimal risk allocation problem for the CS problem using a two-stage approach. The upper-stage of DR-IRA is a convex problem that optimizes the risk, while the lowerstage optimizes the controller with the new distributionally robust risk constraints. The proposed framework results in solutions that are robust against arbitrary distributions in the considered ambiguity set. Finally, we demonstrate our proposed approach using numerical simulations. Addressing the covariance steering problem through the lens of distributional robustness marks the novel contribution of this article.}},
  author       = {{Renganathan, Venkatraman and Pilipovsky, Joshua and Tsiotras, Panagiotis}},
  booktitle    = {{American Control Conference}},
  language     = {{eng}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  title        = {{Distributionally Robust Covariance Steering with Optimal Risk Allocation}},
  url          = {{https://lup.lub.lu.se/search/files/142814004/2210.00050_2.pdf}},
  year         = {{2023}},
}