Network security issues are significant for cyber-physical systems while existing wireless networks are vulnerable to cyber-attacks. This paper proposes a novel detector for stealthy attacks in distributed consensus-based filtering, which has fewer objects to detect and thus can reduce the time consumption of the detector. Based on the proposed detector, we can analyze the estimated performance of the distributed estimator under a stealthy attack. The purpose of this study is to analyze the properties and performance of the estimator equipped with the proposed detector depending on the adversary’s available resources. First, we study the sufficient condition for distributed state estimation to be resilient based on the assumption that the adversary has sufficient resources. With limited adversary resources, the optimal Kalman gain can be obtained by minimizing state estimation error covariance. Furthermore, a sufficient condition is presented to guarantee the convergence of the estimation error covariance in the estimator equipped with the proposed detector. Finally, a simulation example is provided to demonstrate the effect of the detector on the distributed estimator.

In this paper, spatial diffusions are introduced to fractional-order coupled networks and the problem of synchronization is investigated for fractional-order coupled neural networks with reaction-diffusion terms. First, a new fractional-order inequality is established based on the Caputo partial fractional derivative. To realize asymptotical synchronization, two types of adaptive coupling weights are considered, namely: 1) coupling weights only related to time and 2) coupling weights dependent on both time and space. For each type of coupling weights, based on local information of the node's dynamics, an edge-based fractional-order adaptive law and an edge-based fractional-order pinning adaptive scheme are proposed. Furthermore, some new analytical tools, including the method of contradiction, L'Hopital rule, and Barbalat lemma are developed to establish adaptive synchronization criteria of the addressed networks. Finally, an example with numerical simulations is provided to illustrate the validity and effectiveness of the theoretical results.