Research On State And Attack Variable Estimation Algorithms For Cyber-physical Systems Under False Data Attacks

Cyber-physical systems(CPS)are systems that tightly integrate computing resources,communication resources,and physical resources.Compared to general systems,it has the advantages of faster response,higher precision,and stronger coordination and control functions.At present,CPS have been widely used in smart grids,smart cities,smart medical equipments,intelligent transportation systems,and other fields.Due to the integration of network communication,CPS are very vulnerable to cyber-attack,among which the false data injection(FDI)attacks as a typical attack form have attracted wide attention.FDI attacks mainly access a series of sensors or drive computing platforms through the network,and then inject false data to change the original sensing information or execution information of the system,bringing huge challenges to the security of the system.This dissertation mainly studies the state and attack variable estimation of several kinds of CPS under FDI attacks,and the corresponding estimation algorithms are proposed.The specific contents include:(1)For a class of nonlinear stochastic CPS subjected to actuator FDI attacks,the estimation problems of attack variables are studied.The actuator attack variables are modeled as a class of harmonic-like attack variables with additional random information.Firstly,the harmonic attack model is reconstructed by the Sylvester matrix equation.Based on this,the state variables observer of attack is established under the known and unknown attack model parameters,and the conditions of the existence of the observer are given.Then,an attack variable estimation algorithm is designed under the condition that the attack model parameters are known,and the conditions that the estimation errors can realize mean-square asymptotically bounded and mean-square exponentially stable are given.In addition,for the condition that the attack model parameters are unknown,an adaptive attack variable estimation algorithm is designed,and the conditions that the estimation errors can be mean-square asymptotically bounded and asymptotically stable are given.Finally,two simulation examples are given to verify the validity of the proposed algorithm.(2)For a class of nonlinear stochastic CPS with unknown inputs and sensors subjected to FDI attacks,the estimation problems of system states and time-varying attack variables are studied under known and unknown nonlinear conditions.Firstly,an augmented system equivalent to the dynamic equation of the original system is obtained by augmenting the system state variables and attack variables,and the observability conditions of the system are given.Meanwhile,an intermediate variable is introduced to establish a representation of the unknown inputs.Then,the intermediate variables-based system states and attack variables observers are designed under nonlinear known and unknown conditions,and the anti-disturbances estimation algorithm of system states and time-varying attack variables is designed based on the stability analysis of estimation errors.This algorithm can effectively reduce the influence of difference terms of attack variables and unknown inputs on the estimation performance.Finally,a simulation example is given to verify the correctness of the conclusions obtained under known and unknown nonlinearity.(3)For a class of nonlinear CPS subjected to sensor and actuator(dual-channel)FDI attacks,the estimation problems of system states and dual-channel attack variables are studied in the presence of system disturbances and measurement disturbances.Firstly,the system states and sensor attack variables are augmented to the new states to get a new augmented system.Then,the dynamic proportional-integral-based states and dual-channel attack variables observer is designed by introducing the output estimation errors and their difference terms,and the estimable conditions of the system state and dual-channel attack variables are given.Based on the proposed observer,the estimation algorithm of system states and dual-channel attack variables is given using the stability analysis of the estimation errors.This algorithm can effectively reduce the influence of difference terms of attack variables and disturbances on the estimation performance.Finally,a simulation example is given to verify the effectiveness of the proposed algorithm.(4)For a class of multi-agent CPS subjected to dual-channel FDI attacks,the estimation problems of system states and dual-channel attack variables are studied in the presence of system disturbances and time-varying measurement disturbances.Firstly,the system states,sensor attack variables,and measurement disturbances are augmented to the new states to obtain an augmented system,and an intermediate variable is introduced to establish a reexpression of the actuator attack variables.Then,a distributed observer for system states and dual-channel attack variables is designed by introducing adjustable decentralized and distributed output estimation errors,and a distributed estimation algorithm for system states and dual-channel attack variables is proposed based on the stability analysis of estimation errors.This algorithm can effectively reduce the influence of derivative terms of attack variables and disturbances on the estimation performance,and the calculated amount is not affected by the number of agents.Finally,two simulation examples are given to verify the effectiveness of the presented algorithm.(5)For a class of interconnected CPS subjected to dual-channel FDI attacks,the estimation problems of system states and dual-channel attack variables are studied in the presence of system disturbances and time-varying measurement disturbances.Firstly,the system state,sensor attack variables,and measurement disturbances are augmented to the new states to obtain an augmented system with interconnection terms.Then,a dynamic proportional-integral-based distributed states and attack variables observer is designed by introducing the output estimation errors and its difference terms,and the estimable conditions of the system states and dualchannel attack variables are given.Based on the distributed obsever and the stability analysis of the estimation error system,the distributed estimation algorithm of the system state and dualchannel attack variables is presented.This algorithm can effectively reduce the influence of difference terms of attack variables,disturbances,and interconnection terms on the estimation performance.Finally,a numerical example is given to verify the effectiveness of the proposed algorithm.