Distributed Resilient State Estimation for Cyber-Physical Systems Against Bit Errors: A Zonotopic Set-Membership Approach

Abstract

This paper addresses the distributed resilient state estimation issue for a class of large-scale cyber-physical systems (CPSs) against bit errors. Owing to the reliability of the binary data, a novel binary encoding-decoding scheme is developed to enable digital communication of the CPSs. We consider the situation where the transmitted binary bits may be flipped over noisy communication channels. The primary purpose of this paper is to design a distributed resilient estimation scheme under a bit-flipped detection mechanism to achieve a reliable estimation of the CPSs. First, by means of the Minkowski sum of sets, a novel distributed zonotopic resilient estimation scheme is proposed where the optimal estimator gain is obtained in the minimum <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$F$</tex-math></inline-formula> -radius sense. Furthermore, a two-stage bit-flipped detection scheme is developed by taking advantage of 1) the prediction output zonotope and 2) the intersection between the prediction zonotope and the estimation zonotope. Furthermore, in order to improve the algorithm efficiency, a reduction operator is introduced to reduce the order of the zonotope. Finally, the IEEE 30-bus systems are applied to verify theoretical results of the developed distributed resilient estimation algorithm.