A Robust and Resilient State Estimation for Linear Systems

Abstract

This article is concerned with the state estimation of linear dynamic systems when some sensors are corrupted by attackers. This problem is known as resilient state estimation (RSE), and aims to achieve, under some conditions, the estimation of the true state despite the malicious attacks on sensors. The state-of-art RSE methods provides a bound on estimation errors when external disturbance exists. However, it is shown in this article that the effect of the disturbance on estimation error may be larger than that for conventional observers, or even worse, resiliency may be lost for the disturbance that exceeds the bound. To resolve this issue, unknown input observer (UIO) mechanism is adopted in RSE for the purpose of estimating true plant state under both sensor attacks and external disturbance. Also achieved in this work is the method of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">partial</i> state UIO synthesis, which relaxes the design requirement for full state UIO. In relation to resiliency, it is shown that 2 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$q$</tex-math></inline-formula> redundant detectability is a necessary condition for robust and resilient state estimator in order to tolerate up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$q$</tex-math></inline-formula> sensor attacks. Numerical examples are given to validate the effectiveness of the proposed method.