This article investigates resilient distributed online estimation (DOE) in unreliable directed networks with differential privacy requirements. In the network considered, some agents are subject to Byzantine attacks and thus could send arbitrary incorrect messages to their neighbors. The remaining agents aim to collaboratively estimate the value of an unknown vector parameter while protecting their private data. In this article, by adding private noises to mask the estimate, a stochastic approximation-type resilient differentially private DOE algorithm is proposed to protect the privacy of sensitive information. A time-varying step size is introduced to attenuate the divergence caused by the private noise, and furthermore, guarantees the convergence of the algorithm.When the directed graph is (2F+1)-robust, the algorithm is shown to be both mean square and almost sure convergence in the sense of 𝜖-differential privacy. A simulation example is given to verify the effectiveness and superiority of the algorithm.
In this paper, the consensus problem for a class of interconnected systems with different cyber‐physical topologies is investigated. A two‐layer control framework is proposed where two different connections exist among the systems in physical and cyber layers, respectively. The former directly reflects the physical coupling among systems, while the latter uses the states' information transferred by communication channels to generate control. The physical and cyber topologies are undirected and not required to be connected. An event‐triggered protocol based on cyber local sampled information is designed with no need to solve any matrix equation or inequality. Theoretical sufficient conditions for consensus are derived in terms of algebraic inequality and Zeno behavior is excluded. A novel expandable construction scheme is proposed to construct switching topologies for cyber layer. Numerical simulation and comparison show the effectiveness of the proposed control method and the advantage on saving communication network constructions.
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