Differential Privacy and the l1 Sensitivity of Positive Linear Observers*. Issue 1 (July 2017)

• Record Type: Journal Article
• Authors: McGlinchey, Aisling; Mason, Oliver
• Is Part Of: IFAC-PapersOnLine. Volume 50:Issue 1(2017)
• Page Start: 3111
• Page End: 3116
• Publication Date: 2017-07
• Subjects: Positive systems -- linear time-invariant systems -- observers for linear systems -- differential privacy -- optimization; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2017.08.317
• Languages: English
• ISSNs: 2405-8963

Abstract

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 l 1 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.