On Finite-State Stochastic Modeling and Secure Estimation of Cyber-Physical Systems

The problem of secure state estimation and attack detection in cyber-physical systems is considered in this paper. A stochastic modeling framework is first introduced, based on which the attacked system is modeled as a finite-state hidden Markov model with switching transition probability matrices controlled by a Markov decision process. Based on this framework, a joint state and attack estimation problem is formulated and solved. Utilizing the change of probability measure approach, we show that an unnormalized joint state and attack distribution conditioned on the sensor measurement information evolves in a linear recursive form, based on which the optimal estimates can be further calculated by evaluating the normalized marginal conditional distributions. The estimation results are further applied to secure estimation of stable linear Gaussian systems, and extensions to more general systems are also discussed. The effectiveness of the results are illustrated by numerical examples and comparative simulation.