Resilient State and Input Estimation for Complex Network Subject to Cyber Attack: A Set-Membership Method

This article is concerned with resilient state estimation for a class of complex network with the vulnerable communication channel from the sensor to estimator, where both transmitted input and output signals are susceptible to malicious attacks. To overcome these challenges, a novel set-membership filter framework integrated with an unknown input estimator is designed. This framework enables the joint estimation of states and unknown inputs and actively mitigates the adverse impact of corrupted input signals. Furthermore, it circumvents the practical difficulties of direct input measurement in applications. Through rigorous mathematical induction, sufficient conditions are derived to guarantee the state remains bounded within an ellipsoid centered at its estimation, even in the presence of malicious attacks. The input filter gain is determined to decouple the state estimation error from unknown input, while the state filter gain is optimized to minimize the ellipsoid. The proposed framework is subsequently extended to the complex networks with direct feedthrough. Finally, numerical simulations and battery experiments are conducted to validate the resilience and effectiveness of the designed set-membership estimators.