Design of security aware ESO-based tracking control for singularly perturbed hyperbolic PDE systems under multimodal injection attacks

This article centers on addressing the fault-tolerant tracking control protocol problem for singularly perturbed hyperbolic partial differential equation systems in the midst of probabilistic time delays, multimodal injection attacks, actuator faults, and external disturbances. Succinctly, an improved extended state observer is tailored to yield concurrent and accurate estimation of plant states and external disturbances. Therein, the designated observer is endowed with gain perturbations and multimodal injection attacks to strengthen the resilience of the observer. In the sequel, with the information obtained from the estimator, an improved extended state observer-based fault-tolerant tracking control law is set forth, which greatly assists the analyzed model to attain the steady tracking ability by eliminating the traces of disturbances. Moreover, the actuator faults are considered in the controller channel to enhance the reliability of the tracking performance. Furthermore, through the construction of the Lyapunov-Krasovskii functional, the criteria for ascertaining the tracking objective of the configured system are articulated by means of a linear matrix inequality framework. Subsequently, the desired controller and observer gains are obtained with the aid of established criteria. Ultimately, the significance of the analyzed findings is assured through numerical simulations.