Innovation-based optimal linear attacks and detection under K-L divergence detector in cyber-physical systems

In this paper, a Gaussian distributed innovation-based linear attack strategy is considered against the Kullback-Leibler (K-L) divergence detector in cyber-physical systems. In order to find the optimal attack strategy, an optimization problem is formulated to maximize the degradation of system estimation performance without exceeding the threshold of the K-L divergence detector. From the defenders' perspective, a watermark detection strategy is adopted to detect such an attack. We consider a special situation where the optimal strategy is taken. A similar optimization problem is formulated to find the optimal distribution of watermark signal. For the convenience of solving the optimization problem, an inequality constraint is appended to the optimization problem. The new problem is proved to be a convex optimization problem which can be solved with the KKT conditions. Finally, some numerical simulations are provided to illustrate the analytical results.