Resilient State Estimation and Control of Cyber-Physical Systems Against False Data Injection Attacks on Both Actuator and Sensors

This article studies the secure state estimation and control problem of cyber-physical systems, where there are multiple heterogeneous sensing nodes and one actuator which are both under the threat of intermittent false data injection attacks. A specific filter gain is proposed by solving the equality constrained optimization problem so that the attack on the actuator does not affect the a posteriori estimation error of the system. A new method to construct $\chi ^2$ detection variables is proposed, which does not require that the covariance matrix be invertible, and then the actuator and sensor attack detection schemes are developed, respectively. Based on the detection results, a multiple information fusion algorithm is developed and an estimator-based controller with the compensator, which can compensate for the actuator attack in the previous step, is further designed. A necessary and sufficient condition for complete compensation is provided, and the stability of the filter and the control system is proved. Finally, the effectiveness of the estimation algorithm and control algorithm is verified by numerical simulation.