Resilient Filter Design Under Cyber Attacks

Nonlinear control systems with communication networks are used in a variety of environments.Except general engineering systems,it plays a pivotal role in economic and military systems.When modeling a nonlinear control system,the Takagi–Sugeno(T-S)fuzzy model is an effective method to represent a class of nonlinear dynamic systems.The T-S fuzzy model is an approximate representation of a nonlinear system with many line segments,fitting a nonlinear system with many linear systems,that is,a complex nonlinear problem is transformed into a linear problem for processing.In recent years,the T-S fuzzy model has been widely used in the filter design of nonlinear control systems,and has achieved fruitful theoretical results.It should be noted that due to the existence of communication networks,the security issues caused by network attacks cannot be ignored when data is transmitted through the network.This paper studies the design problem of security filters in nonlinear systems subject to possible cyber attacks.The main works are listed as follows:First of all,using T-S fuzzy model to describe nonlinear control system.Some assumptions are made appropriately for it to solve the problem of mismatched membership functions caused by network communication.In order to improve the network transmission quality and reduce the network transmission burden,a new event-triggered mechanism(ETM)is proposed.the measurement data are released into the network only when the ETM is violated,and the false data generated by jitter interference can be discarded.This ETM is sensitive to state fluctuations.When the system is disturbed,it can obtain more information from the system and achieve better control performance.At the same time,the possible deception attacks in network are taken into account,a filtering error system is established based on it and the asymptotic stability is proved.Finally a security filter is obtained.Then we also consider the event triggered filter design problem of a multi-sensor nonlinear system under a denial-of-service(DoS)attack.In order to analyze from the perspective of an attacker,the following assumptions are made for the DoS attacks model: DoS attacks are periodic and fixed in period,the periodic intervals include the active periods and the sleeping periods.And data cannot be transmitted to the network during the active periods of the DoS attacks.A new distributed ETM is proposed for each channel under DoS attacks,and a new security criterion is proposed for the design of nonlinear filters.Based on the above assumptions,the filtering error system will adopt a switching model based on the presence or absence of DoS attacks.A series of stability theories are used to obtain sufficient conditions to ensure the exponential stability of the filtering error system and the filter was obtained at last.Finally,a case where a filter is subjected to hybrid attacks in a nonlinear system is studied.Hybrid attacks include randomly deception attacks and DoS attacks,its randomness was described by variable that satisfies the Bernoulli distribution.An ETM is proposed to reduce the transmission of data packets,and based on the proposed ETM,a switching filtering error system under hybrid attacks is established.By using Lyapunov stability theory,sufficient conditions were obtained to ensure the exponential stability of the filtering error system,and the design of the safety filter was completed.The simulation results show the effectiveness of the theoretical analysis and filter design methods.