Research On State Estimation Of Networked Systems In Attack Environment

As a typical complex system,the networked system belongs to a multi-disciplinary research field that has emerged with the accelerated integration of communication,computation and control technologies in recent years,which is widely applied in modern control systems such as smart grids,Internet of Things,and industrial Internets.The networked system transmits and exchanges information through the network,which can achieve complex tasks such as resource sharing,remote monitoring,collaborative control and optimization scheduling.Thus,the networked system has the advantages of high reliability,high flexibility,and scalability,which has attracted extensive attention of researchers.As a major module of networked system,state estimation is mainly used to provide accurate and real-time system states for networked system control.However,due to the incorporation of the communication network,the networkinduced phenomena such as delay,packet loss,and limited bandwidth are inevitable during data transmission,thereby affecting the estimation performance and stability of the state estimator.Meanwhile,the openness of network makes the control system vulnerable to external attacks,and the vulnerability of the networked system itself has great security risks when facing cyber attacks,which may cause economic losses,damage to facilities and even serious threats to life and safety.In addition,the state estimation process of networked systems is always one of the main intrusion objects preferred by attackers.Complex and malicious cyber attacks will affect the operation of state estimators,resulting in performance degradation,operation interruption and even failure.On the other hand,cyber attacks and network communication issues such as packet loss,delay,and limited bandwidth are mutually affected,making the attacks more complex and difficult to detect/defend,and further resulting that the system analysis and design methods of traditional state estimation and safety mechanisms face many challenges and difficulties.In summary,considering the network-induced phenomena such as transmission delay,packet loss,and communication bandwidth constraints,as well as cyber attacks,this paper carried out research on state estimation of networked systems under attack environment,and further research on attack detection and defense methods,which aims to enhance the security of networked system and improve its estimation performance.The main research contents are described as follows:1)The distributed state estimation problem for networked systems under missing measurements is solved.Considering multiple missing measurements and state inequality constraints,an improved distributed Kalman filter is designed to estimate the states of the system.Firstly,the distributed networked system model is constructed by using the internodal transformation theory.Then,by modeling the multiple missing measurement as a random variable that satisfies Bernoulli distributions and constructing a missing measurement matrix,and combined with Kalman filtering algorithm,an improved distributed state estimation method under missing measurements is designed.Finally,considering state inequality constraints,the particle swarm optimization algorithm and probabilitymaximum method are used to solve the distributed estimation problem of networked system under state constraints.2)The distributed consensus estimation problem of networked systems under stochastic cyber attacks is studied.Firstly,considering stochastic cyber attacks that occur between the estimator-estimator channels of distributed networked systems,a random variable satisfying the zero mean Gaussian process and an attack decision variable satisfying a binary distribution are together used to construct the stochastic attack model.On this basis,the communication bandwidth constraint is considered,and an optimal event-triggered distributed Kalman consensus filter is designed to improve the estimation performance of distributed estimator.Then,for scalability considerations,the suboptimal estimator is obtained by an approximation method.Finally,based on the Lyapunov method,the stability analysis of the designed estimator is given.In terms of that,the co-design condition of cyber attacks and the event-triggered mechanism is given,and the influences of stochastic cyber attacks on state estimation algorithm and event-triggered mechanism are further analyzed.3)The distributed consensus estimation problem for networked systems with limited attack energy is investigated.Firstly,considering that the attacker’s energies or resources are limited,a fixed probability random strategy is used to design the attack behavior under limited energy.From the perspective of energies and resources,the distributed consensus estimation algorithm is designed for networked systems with sufficient or limited attack energy.Secondly,the linearization error of the nonlinear networked system is processed based on the variance-constraint method,and then the upper bounds of the estimated error covariance matrices are calculated with sufficient or limited attack energy.Then,by minimizing the trace of upper bound matrix,the filter gain matrix for given the consensus gain matrix is computed.Finally,the stability analysis of distributed consensus estimation algorithm is given with sufficient or limited attack energy.4)The state estimation problem of networked systems with attack detection mechanism is investigated.Firstly,to describe the delay phenomenon of partial measurement data,a random variable satisfying Bernoulli distribution is utilized to construct a delayed measurement matrix.Combined with the standard Kalman filter algorithm,an improved state estimator under measurement delays is designed to obtain the optimal state estimation.Then,considering both cyber attacks and measurement delays,to interfere with the attack detection process,an imperfect data injection attack strategy is designed.In addition,considering the interaction between measurement delays and cyber attacks,an effective attack detection method is designed based on the chi-square detection mechanism and historical secure estimation information to effectively identify attack vectors.5)The state estimation problem of networked systems with attack defense mechanism is investigated.Firstly,in order to effectively resist cyber attacks between estimators,the measurement information of its own nodes is used as a benchmark to design protection decision variables.Then,in order to ensure the estimation accuracy of the distributed estimator and resist the false data injection attack,a defense mechanism is constructed based on the historical secure estimation value by assuming that the historical estimation information of state variables is not affected by the attacker.Moreover,considering the scalability in power systems,a suboptimal distributed Kalman consensus filter with attack defense mechanism is proposed.Finally,a sufficient condition for the stability of distributed estimators with a defense mechanism is given.