Research On PID Control Methods For Discrete Systems Under Cyber Attacks

With the continuous development of the information society,more attention is paid to security issues caused by cyber attacks.It is an ideal state for signals to be transmitted orderly among the components of networked control systems.However,the actual signal transmission process would be attacked by cyber attacks inevitably,which may affect the overall function of the control system directly.For this reason,it is particularly important to consider the impact of cyber attacks on networked control systems and ensure the working performance of systems.Taking the system mathematical model as the starting point,various cyber attack phenomena are considered in this paper with the event-triggered mechanism being used to alleviate the network communication burden,and the observer-based security-guaranteed H_∞ PID control problem under the event-triggered mechanism is studied via Lyapunov stability theory,stochastic analysis method and matrix inequality technique.The specific work of this paper is as follows.Firstly,an H_∞ PID controller is designed for discrete-time systems based on event-triggered mechanism in the case of random replay attacks.The relative event-triggered mechanism is employed to reduce unnecessary information transmission and save communication energy in the network channel between sensor and observer.The random replay attack is considered in the network channel from the controller to the actuator,and the random variable of Bernoulli distribution is used to describe the randomness.An observer-based PID controller is designed to make the closed-loop system realize exponential stability in the mean square sense and H_∞ disturbance rejection performance.The sufficient condition for the existence of the controller is established in the form of linear matrix inequality,and the gain parameters are calculated of the observer and the PID controller.Secondly,the observer-based H_∞ PID control issue is solved for discrete-time systems using event-triggered mechanism subject to periodic random denial of service(DoS)jamming attacks and infinitely distributed delays.Periodic random DoS jamming attack is considered in the network channel between controller and actuator,and the Kronecker delta function is used to represent the periodic switching between energy-replenishment sleeping period and attack period.An observer-based PID controller is constructed and designed.Sufficient condition is put forward which ensures the existence of the PID controller such that the closed-loop system is exponentially mean-square stable and satisfies the H_∞ performance,and gain expressions are given.Thirdly,the H_∞ PID control is realized of discrete-time systems affected by random deception attacks under event-triggered mechanism.In the network channel from the sensor to the observer,considering that the measurement signal may be subjected to randomly occurring deception attacks after the event is successfully triggered,nonlinear constraints are used to describe the deception signal.Sufficient condition for the existence of H_∞ PID controllers is proposed by analyzing the exponential stability in the mean square sense and H_∞disturbance rejection performance.The unknown gain parameters are obtained by solving a feasible solution of the linear matrix inequality.Finally,the H_∞ PID control problem is addressed of discrete-time systems under event-triggered mechanism and hybrid attack.The event-triggered mechanism is used to judge whether the sensor measurement signal is allowed to enter the network and be transmitted to the observer.The occurrence of hybrid attacks is considered during the transmission process after event triggering.Two sets of independent Bernoulli-distribution random variables are used to describe the randomness of deception attacks and DoS attacks.PID controller is designed to adjust the system to achieve stability and H_∞ disturbance rejection,which is applied to the load rotation angle control of the DC servo motor.The simulation verification of the control method is carried out based on MATLAB software.The simulation results show that the proposed H_∞ PID control method is effective for discrete systems subject to different cyber attacks under the event-triggered mechanism.