Optimal energy constrained deception attacks in cyber–physical systems with multiple channels: A fusion attack approach

This paper studies the issue of developing the optimal deception attacks on the multiple channels in cyber–physical systems, where the attackers are limited by energy constraints. To fully utilize the eavesdropped data, by linearly combining the innovations from the different channels, a fusion attack model is proposed under the stealthiness condition. According to the statistical characteristics of the correlated stochastic variables and the orthogonality principle, the state estimation error is quantified and analyzed by deriving the iteration of the error covariance matrices of the remote estimators under the proposed attack framework. Moreover, by analyzing the correlations of the decision variables in the objective function, it is shown that the attack parameters and energy allocation strategy can be derived by two steps without loss of optimality, such that the optimal attack scheme is acquired by solving a multivariate semi-definite programming (SDP) problem and a linear 0–1 programming problem respectively. Finally, simulation examples are provided to illustrate the effectiveness of the proposed method.