Research On Stability Of Networked Control Systems With Quantization Under Attack Environment

Networked Control System（NCS）is a spatially distributed control system consisting of a closed-loop of communication network.NCS is popular in different fields due to its strong flexibility,convenience of development and wide compatibility.However,as a communication medium with low reliability,the network is vulnerable to network attacks and congestion appeared in the process of transmission,which will cause a series of problems,such as network delay,packet loss,failure to operate normally and so on.Therefore,the resource limitation and network security problems in NCS communication need to be solved urgently.Based on the above analysis,aiming at the problem of limited resources,the quantizer is introduced to alleviate the pressure of network communication transmission.At the same time,considering NCS transmission signals are attacked through the network,the stability and performance of the system are studied by designing the controller.The specific contents are as follows:（1）For the NCS with deception attack,the system states are estimated and the output feedback controller is designed.It is assumed that the deception attack occurs in the network channel from the sensor to the controller.The sensor output signal is quantized by a dynamic quantizer to save bandwidth resources.Based on a new set member estimation method--ellipsoid estimation method,the deception data is modeled as unknown but bounded signals,and the closed state estimation ellipsoid set is obtained.Then the parameters of the ellipsoid set of state estimation are minimized so that the estimated state approximates the real state.On the basis of the above work,the output feedback controller is designed and sufficient conditions are obtained to satisfy the stability,so that the closed-loop system can satisfy the asymptotic stability under spoofing attack.The scientific validity of the proposed method is verified by numerical example of MATLAB simulation.（2）For NCS with DoS attack,a new quantization structure for sensor signal is proposed and an H∞output feedback controller is designed.In order to save the limited channel resources,a new quantization structure is used to quantify the sensor signal,which reduces the quantization error compared with the original quantizer.It is assumed that in the network environment,DoS attack exists in the transmission channel from controller to actuator.DoS attack is described as a probability model subject to Bernoulli distribution,and NCS can be modeled as a linear discrete system with random parameters.On the analysis of system stability,different from common quadratic Lyapunov function,this chapter selects a dependent quantization error and attack probability of the Lyapunov function,based on stability theory and linear matrix inequality approach,for which the closed loop system for the sense of mean square exponential stability and satisfies the given H∞performance index of the output feedback controller design method.Finally,an example is given to verify the feasibility of the proposed method.（3）For the NCS with DoS attack and resource constraints,the strong robust control problem of discrete systems is studied.The logarithmic quantizer is introduced into NCS to quantize the sensor signal,so as to reduce the amount of channel transmission.It is assumed that exist DoS attack in the controller-to-actuator transmission channel.The NCS is modeled as a system with random parameters by describing the DoS attack as a probabilistic model subject to Bernoulli distribution.In stability analysis,a Lyapunov function which depends on quantization error and attack probability is selected.The dynamic output feedback controller is designed based on the new model.The controller satisfies the given H∞performance bound normγ_c and makes the closed-loop system satisfies stability and has H∞performance bound normγ_cl under the action of the controller.Finally,the stability of the system is proved by a simulation example,and the effectiveness of the proposed method is verified.