Efficient resilient dynamic co-estimation framework for cyber-physical systems under sensor attacks

In this study, a novel co-estimation approach is proposed for dynamic state estimation of cyber-physical systems (CPSs) subjected to sensor attacks. In the proposed approach, the sensory measurements are preprocessed to extract some valuable information about the launched cyber-attack. This information is then manipulated to form new state equations, which are augmented with the CPS model. The newly obtained model effectively represents the behaviour of both the CPS states as well as the launched cyber-attack, and can be used for their co-estimation. Two structures are suggested for the preprocessing of the sensory measurements that deploy Kalman filter (KF) and two-step KF for co-estimation of the states and cyber-attacks. To effectively handle the concurrent effects of cyber-attacks and unknown inputs on the CPS co-estimation process, some auxiliary outputs are generated using high-gain approximate differentiators to realise the required matching conditions. The proposed dynamic co-estimation approach improves accuracy via considering the inter-correlation between the CPS states and the cyber-attacks. To demonstrate the viability of the proposed co-estimation method, thorough stability and feasibility analysis are provided. Furthermore, extensive simulations are performed on a well-known CPS-the IEEE 14-bus test system- to demonstrate the effectiveness of the proposed approach.