| Cyber physical system(CPS)is a system that converges sensing devices,communication devices and computing units to realize the interaction between physical facilities and information processes,which is widely used in critical infrastructures such as unmanned vehicles and transportation.Recently,attacks against cyber physical systems have been occurred frequently,which have drawn extensive attention to the security issues of cyber physical systems in academia.Replay attack is the common type of attack in cyber physical systems,in which the attacker only needs to have the ability to eavesdrop and modify the transmitted data to successfully launch the attack without being detected.Hence,it makes economic significance to detect replay attacks in a timely and efficient manner.This paper investigates the problem of replay attack detection in cyber physical systems where the controlled object model is a linear time-invariant model,and achieves the following results.(1)The occurrence of replay attacks can be detected by adding a watermark signal to the control signal,but the control signal under such schemes has deviated from the optimal control signal and the best system control performance cannot be achieved.Therefore,to reduce the performance loss in the normal operation of the system,an attack detection scheme based on watermark signal coding is proposed in this paper,which constructs encoding and decoding signals based on the watermark signal and injects them into the sensor output and state estimator receiver respectively,so as to achieve attack detection and reduce the performance loss caused by the watermark signal.Firstly,the derivation illustrates that the encoded and decoded signals can cancel the effect of the watermark signal on the measured values and residuals.Then,the feasibility of the proposed scheme for replay attack detection is demonstrated,and the optimal choice of the watermark signal covariance for a given detection rate and false alarm rate is achieved by solving an optimization problem.Finally,the simulation experiment with RLC circuit is conducted to show the feasibility of this scheme.(2)The detection approaches for replay attacks that inject watermark signals into control signals are mainly achieved by judging whether the magnitude of the detection function value exceeds a given threshold.These approaches generally need to address the optimization problem about the detection rate and the loss of system control performance.A detection methodology based on periodic control signal coding is proposed in this paper.At first,a selfdesigned periodic random coding signal is added to the control signal,and the corresponding periodic measurement value compensation signal is constructed to demonstrate the periodicity of the compensation signal when the system matrix is stable.Then,the received measurement value signal is compensated using different compensation signals to obtain the position in the period of the compensation signal corresponding to the smallest detection function.The detections of replay attacks are achieved by comparing the relative position in the cycle of this compensation signal with the actual control volume watermark signal.Finally,using a DC motor as the object,the simulation results demonstrate the effectiveness of this scheme. |