## Analytical Severity Analysis of Cyber Attacks on CPSs

Cyber security has emerged as one of the most important issues in the operation of CPSs due to their heavy reliance on the automation and network communications. As the first step to implement a CPS that is robust to possible cyber attacks, we have conducted a study to identify potential cyber threats and vulnerabilities inherent in the given CPS. The main contribution of this research is the development of an *analytical algorithm *that can be used to quantify the severity of a cyber attack on a CPS. For this work, we consider a simplified cyber-physical model where the system and its sensors are assumed to have deterministic linear dynamics with a linear estimator. Based on that set-up, two kinds of models are considered: open-loop and closed-loop models. For the case of a closed-loop model, the system is stabilized by the observer based feedback controller. Then the corrupted data sequences are fed into the given system. Here, our framework includes attacks on both sensor components and control units of the CPS. Thus, the cyber security problem considered in this work is more general than those in most existing research that considers cyber attacks either on sensors or actuators only. To determine whether or not a cyber attack has been successful, we introduce a *linear-quadratic performance* *cost function *as the criteria for attack severity. This cost basically has the same formulation as that of the classical optimal control theory. While the optimal control problem aims at minimizing the cost, the attack sequence in our problem is designed to maximize the cost. Then, through the analytical solution to the maximization problem, we diagnose the system’s vulnerabilities. The performance of our algorithm is demonstrated, specifically for the linearized longitudinal motion of a rotorcraft which is an example of CPSs. For the purpose of comparison, we also run the numerical simulation and obtain the solution numerically for the same attack scenario. Figures 1 plots the analytic solutions representing the most effective attack direction for the CPS’s state estimator. As shown in Figures 2, the numerical process incorporates numerous attack points into its computation set to create the next moment of the cost configuration, i.e., contour map of attack severity. Thus, while maintaining the vital information about attacks, the analytical approach significantly reduces the computation cost.

Figure 1. Analytical Attack Severity Analysis for the State Estimator of Open-Loop System

Figure 2. Numerical Attack Severity Analysis for the State Estimator of Open-Loop System

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