Mathematics > Optimization and Control
[Submitted on 19 Dec 2018 (v1), last revised 31 Mar 2021 (this version, v6)]
Title:Observability Robustness under Sensor Failures: a Computational Perspective
View PDFAbstract:This paper studies the robustness of observability of a linear time-invariant system under sensor failures from a computational perspective. To be precise, the problem of determining the minimum number of sensors whose removal can destroy system observability, as well as the problem of determining the minimum number of state variables that need to be prevented from being directly measured by the existing sensors to destroy observability, is investigated. The first one is closely related to the ability of unique state reconstruction of a system under adversarial sensor attacks, and the dual of both problems are in the opposite direction of the well-studied minimal controllability problems. It is proven that all these problems are NP-hard, both for a numerical system and a structured system, even restricted to some special cases. It is also shown that the first problems both for a numerical system and a structured one share a cardinality-constrained submodular minimization structure, for which there is no known constant or logarithmic factor approximation in general. On the other hand, for the first two problems, under a reasonable assumption often met by practical systems, that the eigenvalue geometric multiplicities of the numerical systems or the matching deficiencies of the structured systems are bounded by a constant, by levering the rank-one update property of the involved rank function, it is possible to obtain the corresponding optimal solutions by traversing a subset of the feasible solutions. We show such a method has polynomial time complexity in the system dimensions and the number of sensors.
Submission history
From: Yuan Zhang Dr [view email][v1] Wed, 19 Dec 2018 03:56:45 UTC (119 KB)
[v2] Sun, 20 Oct 2019 06:03:53 UTC (163 KB)
[v3] Wed, 4 Dec 2019 02:44:25 UTC (165 KB)
[v4] Fri, 3 Jan 2020 03:44:55 UTC (161 KB)
[v5] Mon, 22 Mar 2021 14:26:06 UTC (80 KB)
[v6] Wed, 31 Mar 2021 06:53:26 UTC (81 KB)
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