Guaranteed Privacy-Preserving $\mathcal{H}_{\infty}$-Optimal Interval Observer Design for Bounded-Error LTI Systems

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Khajenejad, Mohammad, Martinez, Sonia
Format: Preprint
Published: 2023
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866912021524512768
author Khajenejad, Mohammad
Martinez, Sonia
author_facet Khajenejad, Mohammad
Martinez, Sonia
contents This paper furthers current research into the notion of guaranteed privacy, which provides a deterministic characterization of the privacy of output signals of a dynamical system or mechanism. Unlike stochastic differential privacy, guaranteed privacy offers strict bounds on the proximity between the ranges of two sets of estimated data. Our approach relies on synthesizing an interval observer for a perturbed linear time-invariant (LTI) bounded-error system. The design procedure incorporates a bounded noise perturbation factor computation and observer gains synthesis. Consequently, the observer simultaneously provides guaranteed private and stable interval-valued estimates for a desired variable. We demonstrate the optimality of our design by minimizing the $\mathcal{H}_{\infty}$ norm of the observer error system. Furthermore, we assess the accuracy of our proposed mechanism by quantifying the loss incurred when considering guaranteed privacy specifications. Finally, we illustrate the outperformance of the proposed approach to differential privacy through simulations.
format Preprint
id arxiv_https___arxiv_org_abs_2309_13873
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Guaranteed Privacy-Preserving $\mathcal{H}_{\infty}$-Optimal Interval Observer Design for Bounded-Error LTI Systems
Khajenejad, Mohammad
Martinez, Sonia
Systems and Control
This paper furthers current research into the notion of guaranteed privacy, which provides a deterministic characterization of the privacy of output signals of a dynamical system or mechanism. Unlike stochastic differential privacy, guaranteed privacy offers strict bounds on the proximity between the ranges of two sets of estimated data. Our approach relies on synthesizing an interval observer for a perturbed linear time-invariant (LTI) bounded-error system. The design procedure incorporates a bounded noise perturbation factor computation and observer gains synthesis. Consequently, the observer simultaneously provides guaranteed private and stable interval-valued estimates for a desired variable. We demonstrate the optimality of our design by minimizing the $\mathcal{H}_{\infty}$ norm of the observer error system. Furthermore, we assess the accuracy of our proposed mechanism by quantifying the loss incurred when considering guaranteed privacy specifications. Finally, we illustrate the outperformance of the proposed approach to differential privacy through simulations.
title Guaranteed Privacy-Preserving $\mathcal{H}_{\infty}$-Optimal Interval Observer Design for Bounded-Error LTI Systems
topic Systems and Control
url https://arxiv.org/abs/2309.13873