Interconnected disturbance estimator-based security resilient control for semi-Markovian jump PDE systems against multiple attacks

This research aims to address the problem of obtaining resilient secure disturbance rejection control for parabolic partial differential equation systems governed by a semi-Markovian jump process in the presence of parameter uncertainties, multiple cyber attacks, multiple disturbances, additive and multiplicative gain perturbations. In particular, by employing a mode-dependent interconnected disturbance estimator framework, the matched disturbances originating from exogenous systems can be effectively addressed with high estimation accuracy. After that, a resilient secure interconnected disturbance rejection control is designed to accomplish the desired stabilization and disturbance rejection objectives. Therein, multiple cyber attacks encompassing both deception and denial-of-service attacks, along with additive and multiplicative gain perturbations, are incorporated into the controller structure to enhance the system’s protection and resilience. Following that, the necessary criteria for achieving stochastic stabilization of the system under consideration are acquired within the context of linear matrix inequalities through the application of Lyapunov stability theory along with the integral-based Wirtinger’s inequality. In conclusion, two numerical simulations are conducted to confirm the efficiency and applicability of the designed control technique.