Resilient Reinforcement in Secure State Estimation against Sensor Attacks with a priori Information

Recent control systems severe depend on information technology infrastructures, especially the Internet of things (IoT) devices, which create many opportunities for the interaction between the physical world and cyberspace. Due to the tight connection, however, cyber attacks have the potential to generate evil consequences for the physical entities, and therefore, securing control systems is a vital issue to be addressed for building smart societies. To this end, this paper especially deals with the state estimation problem in the presence of malicious sensor attacks. Unlike the existing work, in this paper, we consider the problem with a priori information of the state to be estimated. Specifically, we address three prior knowledge—the sparsity information, $ (\alpha, \bar{n}_0)$ -sparsity information, and side information, and in each scenario, we show that the state can be reconstructed even if more sensors are compromised. This implies that the prior information reinforces the system resilience against malicious sensor attacks. Then, an estimator under sensor attacks considering the information is developed and, under a certain condition, the estimator can be relaxed into a tractable convex optimization problem. Further, we extend this analysis to systems in the presence of measurement noises, and it is shown that the prior information reduces the state-estimation error caused by the noise. The numerical simulations in a diffusion process finally illustrate the reinforcement and error-reduction results with the information.