Secure estimation against non-fixed channel attacks in cyber-physical systems

This article studies the secure estimation problem for cyber-physical systems (CPSs) with sparse attacks and noises. Instead of fixed attacked sensor channels, the malicious attack investigated in this work is s$$ s $$-sparse and the set of attacked sensor channels is time-varying. A novel l1$$ {l}_1 $$-minimization based on QR decomposition, rather than minimizing the row support of the attack matrix directly, is designed to reconstruct malicious attacks. Furthermore, considering that the presence of Gaussian noises may produce estimation errors, a secure conservative estimation method based on Kalman filter is proposed to estimate the consolidated signal consisting of sparse attacks and measurement noises. Moreover, it is proved that robustness of the proposed estimation algorithm can be guaranteed with the upper bound of estimation error covariance. An illustrative example is utilized to show the effectiveness of the proposed methods.