Event-Based Distributed Set-Membership Estimation for Complex Networks Under Deception Attacks

Abstract

This paper addresses the problem of event-based distributed set-membership estimation for complex networks with unknown but bounded (UBB) disturbances. To reflect the compromised data transmissions in cyber security, deception attacks are taken into consideration. Meanwhile, a novel estimation model is proposed against UBB disturbances. In order to schedule the signal transmissions between nodes and remote estimators, a novel decentralized dynamic periodic event-triggered mechanism (DPETM) with a time-varying threshold is developed for each node of the complex networks, which reduces the waste of communication resources and the complexity of computation. Thereafter, a series of distributed set-membership estimators are designed, whose parameters are explicitly determined in terms of the resolution of a particular linear matrix inequality (LMI) related to the information of the communication topology. An optimized ellipsoid estimation set is obtained by applying a recursive optimization algorithm. Finally, the simulation results are shown to demonstrate the viability of the proposed method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper is motivated by set-membership state estimation problem of complex networks in practical missions, such as military, environment, industry, etc. The set-membership estimation of complex networks provides a reliable confidence region for each system node. Event-triggered control is an effective method for the design of set-membership estimator. But the common results require the systems to monitor the measurements point-to-point, which leads to the huge consumption of calculation and communication resources. For this reason, this paper originally extends the DPETM to the discrete-time version from the field of continuous-time systems. Meanwhile, this paper considers the deception attacks in communication channels, and the generic framework established earlier can tackle simultaneously sector-bounded nonlinearity, UBB disturbances, and deception attacks. The main difficulty of this paper lies in the analysis for the sawtooth constraint of periodic samplings. For this difficulty, we introduce a piecewise auxiliary function, which is similar with the loop-function in the field of continuous-time systems. Together with recursive optimization algorithm, the detailed analysis method is proposed for the reliable confidence regions of each set-membership estimator.