Security-Guaranteed PID Control for Discrete-Time Systems Subject to Periodic Dos Attacks

Abstract

This paper is concerned with the observer-based H∞ proportional-integral-derivative (PID) control issue for discrete-time systems using event-triggered mechanism subject to periodic random denial of service (DoS) jamming attacks and infinitely distributed delays. In order to characterize the occurrence of periodic random DoS jamming attacks in the network channel between controller and actuator, the Kronecker delta function is used to represent the periodic switching between the sleeping period and attack period, and a Bernoulli-distributed random variable is utilized to reflect the probabilistic occurrence of DoS attacks. Infinitely distributed delay is involved to reflect actual state lag. The relative event-triggering mechanism is employed to reduce unnecessary information transmission and save communication energy in the network channel between sensor and observer. An observer-based PID controller is constructed for the regulation of the system to achieve an appropriate working effect. The aim of this paper is to design a security-guaranteed PID controller for delayed systems such that both the exponential mean-square stability and the H∞ performance are satisfied. Using the Lyapunov stability theory, stochastic analysis method and matrix inequality technique, a sufficient condition is put forward that ensures the existence of the required observer and PID controller. Gain parameters of the observer and the PID controller are computed by solving a certain matrix inequality. A simulation is carried out to verify the effectiveness of the developed observer-based H∞ PID control method. The obtained H∞ noise rejection level is below 0.85, the average event-based release interval is 13, the absolute values of the maximum estimation error of two elements in the system state are 1.434 and 0.371 using the observer, and two elements of the system state converge to 0.238 and −0.054 at the 41th time step with two elements of the control output being 0.031 and 0.087.