Energy-Constrained Optimal Stealthy Attacks under Sequential State Estimation and Detection

This article investigates the stealthy attack design against the sequential estimation of cyberphysical systems (CPSs), with the aim of providing a theoretical basis for refining defense mechanisms. A multiobjective attack model is proposed under the energy constraint, which comprehensively utilizes available innovations from both reliable and suspicious sensors to disrupt the state estimation performance with the assurance of stealthiness. By deriving the recursion of the error covariance, the optimization objective is formulated as a tradeoff between the terminal and average estimation errors to accommodate different scenarios. The corresponding stealthiness conditions are further analyzed based on an analysis of the statistical characteristics of coupled innovations. Then, according to the properties of orthogonal matrices and the Lagrange multiplier method, closed-form solutions for the optimal attack matrices are derived, which avoid addressing the semidefinite programming problem. Moreover, the optimal scheduling is solved via 0-1 programming after parameter separation. Finally, numerical simulations are provided to validate the results.