Window-type detector for stealthy false data injection attack in cyber-physical systems

In recent years, the security issues of cyber-physical systems (CPSs) have attracted extensive attention from researchers. In this paper, a novel window-type detector (WTD) is designed for stealthy false data injection (FDI) attack targeted at CPSs. In the absence of attack, the evaluation value of a WTD is $ \chi ^{2} $ χ2 distributed because of the existence of Gaussian noise. In the presence of attack, the evaluation value of the WTD is the result of accumulating the residual data caused by attack signals, which is similar to the mechanism of a summation (SUM) detector. It is proved that when the duration of system operation is much larger than the attack duration squared, evaluation value of an SUM detector is $ \chi ^2 $ χ2 distributed due to the huge number of tolerable historical data. And the structure of finite window size prevents the WTD from failure in such a situation, which equips it with better performance in the detection of attacks with medium duration. Furthermore, it is proved that the closer the window size is to the attack duration, the larger the evaluation value is, which means that the better detection performance could be achieved. Finally, numerical examples are given to verify the characteristics of the WTD.