Disturbance rejection-based resilient tracking control for hyperbolic PDE systems with memory-oriented state observer under cyber-attacks

This study addresses the state tracking and disturbance suppression problem for hyperbolic partial differential equations under external disturbances and hybrid cyber-attacks. Precisely, a generalised extended state observer is implemented to simultaneously estimate the system states and external disturbances. Further, capitalising on the estimated data, a memory observer-based resilient tracking controller is designed to reduce disturbance effects and precisely follow the intended reference model. Moreover, the developed controller is equipped with security shields to ward off hybrid cyber-attacks and improve the system's resilience in adversarial circumstances. Added to that, a resilient control mechanism is developed to alleviate gain fluctuations and uphold reliable tracking performance, thus guaranteeing robustness. And, by strategising asymmetric Lyapunov-Krasovskii functional, the adequate requirements for ensuring the stability of the closed-loop system is expressed in the form of linear matrix inequalities. From there, the gains of the developed controller and established observer are computed. At the end, the effectiveness and superior nature of the structured control framework are assessed through two numerical examples which includes the steam-jacketed tubular heat exchanger.