GA‐LMI‐Assisted Event‐Triggered H∞ PID Control for Networked Systems Under Hybrid Cyber Attacks

ABSTRACT This paper addresses the challenge of event‐triggered proportional‐integral‐derivative (PID) control for networked systems under hybrid cyber attacks. The simulation of hybrid attacks involves the use of two groups of Bernoulli variables. Due to the constrained network bandwidth between the controller and actuator, an event‐triggered PID control mechanism is designed to alleviate the network load. By establishing sufficient conditions in matrix inequalities, the closed‐loop system's stability and performance are guaranteed in the mean‐square sense. However, the developed stability conditions include nonlinear terms which are difficult to be solved. To manage the nonlinear constraints during the controller design, a combined GA‐LMI‐based algorithm has been proposed. In addition, an initial value selection method is also presented for the GA‐LMI‐based algorithm in order to provide better algorithm performance. By executing the developed GA‐LMI‐based algorithm, the PID controller gains and the minimal performance can be determined simultaneously. Finally, a numerical example illustrates the reduced conservativeness of the proposed approach, achieving improved performance under varying system parameters. The method's effectiveness is further validated through its application to an unmanned aerial vehicle system.