Secure Switched Observers for Cyber-Physical Systems Under Sparse Sensor Attacks: A Set Cover Approach

Secure state estimation for cyber-physical systems under sparse sensor attacks is the problem of estimating the state from the corrupted measurements. Although such problem can be addressed by brute force search, combinatorial candidates lead to excessive time requirement, which hinders the scalability. For reducing the computational complexity, this paper provides an alternative approach (called set cover approach) to reduce the number of candidates by at least half with the help of a greedy algorithm. Then, a switched observer, with less candidate observers, is designed to estimate the state from the corrupted measurements under the basic observability requirement. Meanwhile, a modified greedy algorithm is proposed to reduce the number of candidates further based on the observer design conditions. Finally, the effectiveness of the proposed set cover approach is demonstrated by two simulations showing an order of magnitude decrease in execution time.