Iteration-Form Multiplicative Watermarking for Quantization-Involved Networked Control Systems

Multiplicative watermarking can enhance cyber attacks detection capacity of quantization-involved networked control system (QNCSs). This article presents an iteration-form solution to conventional summation-form multiplicative watermarking (SMW). First, limitation of conventional SMW for QNCSs is revealed, where there exists high design complexity whilst decreasing measurement perturbation from SMW and achieving successful replay attacks (RAs) detection. Second, a new iteration-form multiplicative watermarking (IMW) is designed by leveraging a keys transformation to reconstruct SMW with multiple coupled keys, where design complexity is greatly reduced and there are only dual decoupled keys to be designed. Furthermore, a positive correlation between value of one key and measurement perturbation from IMW is provided. Third, a positive correlation between ratio of the other key at different instants and RAs detection performance of IMW is explored by using residual covariance analysis. Finally, experimental results from networked inverted pendulum systems confirm the feasibility and effectiveness of new IMW.