Joint Estimation of States, Sparse Sensor Attacks, and Unknown Inputs in Discrete-Time Cyber–Physical Systems
针对离散时间信息物理系统在稀疏攻击和未知扰动下的安全状态估计问题，通过构建增广系统消除扰动影响，设计嵌入投影算子的Luenberger观测器，实现系统状态、扰动和攻击信号的渐近估计，且能实时估计当前状态而非延迟状态。
This article studies the problem of secure state estimation (SSE) with disturbance decoupling for discrete-time cyber-physical systems (CPSs) under sparse attacks and unknown disturbances. Under the premise that partial output measurements are reliable, an augmented system that incorporates unknown disturbances and attacks into its state vector is constructed, thereby eliminating their impact on estimation performance. A necessary and sufficient condition for the observability of the augmented system is given. Subsequently, a Luenberger-like observer based on the augmented system is designed, where a projection operator is embedded to ensure sparsity in attack estimation. It is proven that this observer achieves asymptotic estimation of the original system states, disturbances, and attack signals. Furthermore, leveraging the observability property of the augmented system, a method for reconstructing the system states is proposed. Unlike the existing approaches, the proposed methods effectively estimate the current-time system states (rather than delayed states) even under the influence of dynamically switched sparse attacks and unknown disturbances. Finally, two examples are provided to clearly demonstrate the effectiveness and superiority of the proposed methods.