Joint Estimation of States, Sparse Sensor Attacks, and Unknown Inputs in Discrete-Time Cyber–Physical Systems

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.