McGlinchey, Aisling and Mason, Oliver (2017) Differential Privacy and the l1 Sensitivity of Positive Linear Observers. IFAC-PapersOnLine, 50 (1). pp. 3111-3116. ISSN 2405-8963

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Abstract

We consider the design of differentially private observers for positive linear systems in discrete time. In particular, we first provide a general bound for the l1 sensitivity of the map defined by a Luenberger observer for a linear time invariant (LTI) system and show that this can be tight as well as describing how it relates to previous work. We then define an optimisation problem for minimising this bound for positive linear observers and provide a characterisation of optimal solutions for systems with a single measured output. Finally we show how the addition of Laplacian noise can violate positivity, even for the optimally designed positive observer and discuss directions for future work.

Item Type:	Article
Keywords:	Positive systems; linear time-invariant systems; observers for linear systems; differential privacy; optimization;
Academic Unit:	Faculty of Science and Engineering > Mathematics and Statistics Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID:	12006
Identification Number:	https://doi.org/10.1016/j.ifacol.2017.08.317
Depositing User:	Oliver Mason
Date Deposited:	06 Dec 2019 12:06
Journal or Publication Title:	IFAC-PapersOnLine
Publisher:	Elsevier
Refereed:	Yes
URI:	Publisher
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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