The primary goal of this paper is to analyze the dynamic response of a system under optimal data injection attacks from a control perspective. In this paper, optimal data injection attack design problems are formulated in a similar framework of optimal control. We consider a scenario, where an attacker injects false data to a healthy plant comprising many actuators distributed in different regions. For the case, where an attacker pollutes all actuators, an optimal state feedback injection law is proposed to minimize a quadratic cost functional containing two conflicting objectives. For the case, where the attacker only pollutes partial actuators within a short period, the quadratic programming is employed to solve an optimal switching data injection attack design problem using the technique of embedded transformation. A bang-bang-type solution of the quadratic programming exists on account of the minimum value of the Hamilton functional and is achieved at an extreme point of the convex set. Consequently, a switching condition is derived to obtain the optimal attack sequence. We also introduce a closed-form switching policy for data injection attacks with multiple objectives, which is shown optimal in the sense of minimizing a hybrid quadratic performance criterion. Finally, applications of our approaches to a networked dc motor and a power system are provided to illustrate the effectiveness of the proposed method.

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