Secure Estimation for Cyber-Physical Systems via Sliding Mode

This paper is concerned with the problem of secure state reconstruction for cyber-physical systems (CPSs). CPSs are more vulnerable to the cyber world yet to attackers, who can attack any sensor of the considered systems and modify values of attacked sensors to be arbitrary ones. In the design process, both malicious attacks on sensors and unknown input are taken into consideration. First, a linear discrete-time state-space model is utilized to describe such systems, and then a sparse vector is adopted to model attacks. By collecting sensor measurements and using an iterative approach, a new model in descriptor form is obtained, which paves the way for estimating system states under an unknown input situation. Second, the problem of secure state estimation is transformed into an optimal version. A novel sliding-mode observer is proposed to estimate system states from collected sensor measurements corrupted by malicious attacks. In order to guarantee the estimations to be sparse, a projection operator is designed. Third, a projected sliding-mode observer-based estimation algorithm is developed to reconstruct system states, where an event-triggered scheme is integrated to save limited computational resource. In addition to propose such an algorithm, the effectiveness of both projection operator and sliding-mode observer is analyzed. Furthermore, the convergence of the proposed secure estimation algorithm is proved. Finally, some simulation results are given to demonstrate the effectiveness of the proposed algorithm.