Optimal innovation-based attacks against remote state estimation with side information and historical data

This work investigates the attack strategy design problem of the false data injection attack against the cyber-physical system. Distinct from the relevant results which utilise the current intercepted data or additionally consider side information, a more universal attack model is proposed which combines historical data and side information with the current intercepted data to synergistically deteriorate the system estimation performance. In order to quantify the impact resulting from the proposed attack strategy, the optimisation objective is characterised by deriving the error covariance matrix under the attacks, which becomes more intricate since the proposed attack model introduces more decision variables and coupled terms. Take the stealthiness which is characterised by Kullback-Leibler divergence as the constraints, the problem investigated in this work is equivalently transformed into the constrained multi-variable non-convex optimisation problems, which are not able to be solved directly by the methods in the relevant results. By utilising the Lagrange multiplier method, the structural characteristic of the optimal mean and the optimal covariance which only related to the Lagrange multiplier are derived, such that the optimal distribution of the modified innovation is able to be obtained by a simple search procedure. Following that, the design of the optimal attack strategy is completed by using semi-definite programming to derive the optimal attack matrices. Finally, the simulation examples are given such that the validity of the results is verified.