Secure state estimation for cyber-physical systems under network attacks

Abstract

This thesis is concerned with the secure state estimation problem for Cyber-Physical Systems (CPSs) under network attacks. The research is carried out from multiple perspectives such as single-channel systems to multi-channel systems, single-type attacks to multi-type attacks, traditional independent and identical distributions to complex Markov modelings. At the same time, three types of estimators are designed for different scenarios: optimal estimators (OEs), optimal linear estimators (OLEs), and approximate optimal estimators (AOEs) comprehensive analysis is carried out for the stability and estimation performance of these estimators.

For CPSs under Denial of Service (DoS) attacks, both single-channel and multi-channel scenarios are considered. For single-channel CPSs, the OLE is designed based on the independent and identical distribution model and the Markov chain model, realizing an effective estimation of the system state. It is proved that the OLE is stable if and only if the system is stable. From a mean sense, it is shown that the unobservability of packet losses caused by DoS attacks will degrade the estimation performance, and an upper bound of the performance degradation is obtained. Moreover, how the packet recovery/failure rate affects the estimation performance for the two special cases is analytically characterized. For multi-channel CPSs, the OLE is designed to handle the large-scale distributed configurations. A necessary and sufficient condition for the OLE to remain stable and convergent is first established, and additionally, a tight upper bound on the estimation performance loss caused by attacks is provided and the proportional relationship between the estimator performance and attack success rate is established.

Furthermore, the research expands to more intricate scenarios that encompass mixed attacks. For single-channel CPSs, the OE and OLE are designed. Due to the stealthiness of mixed attacks, the OE consists of an exponentially increasing number of terms, and the OLE is able to address this computation issue with its estimation performance fairly close to the optimal one. Moreover, it is proved that when the system is stable, the exponentially increasing number of terms remain bounded, making the OE stable; and that the OLE is stable if and only if the system is stable. For multi-channel CPSs, the OE and a centralized AOE are designed. This AOE is designed by using the sequential Kalman filtering technique and the generalized Pseudo-Bayesian algorithm, which is not only computationally efficient, but also features theoretically guaranteed performance and stability. Specifically, it is proved when the attack success rate is less than a threshold value, both the OE and the AOE are stable, and the averaged performance deviation between the OE and the proposed AOE remains bounded.