Centralized approximate optimal estimation for cyber-physical systems under joint cyber-attacks

This paper studies the state estimation for cyber-physical systems with multiple channels under joint Denial-of-Service and deception attacks. We show that the optimal estimator (OE) cannot be implemented in practice, as its computational complexity exponentially grows with respect to time. Then, we develop a centralized approximate optimal estimator (AOE) by using a generalized pseudo-Bayesian algorithm. This AOE 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. Finally, simulation examples are provided to illustrate the obtained results.