Active disturbance rejection hybrid-triggered control for mode-dependent nonlinear PDE systems under resilient disturbance observer

This research focuses on designing a resilient active disturbance rejection hybrid-triggered control scheme for mode-dependent parabolic-type nonlinear PDE systems when subjected to gain fluctuations and multiple disturbances. Specifically, matched disturbances are precisely estimated by using a disturbance observer, while the $ H_{\infty } $ H∞ control strategy mitigates the effects of mismatched disturbances. Further, to alleviate network communication transmission and conserve network resources, the hybrid-triggered technique has been implemented, which encompasses both time-triggered and event-triggered approaches. Here, the switching behaviour within the hybrid mechanism is governed by Bernoulli distributions. From thereon, the resilient hybrid-triggered active disturbance rejection controller is developed to achieve the intended disturbance rejection and stabilisation of the considered system. Therein, the gain fluctuations in both controller and disturbance observer gain matrices are factored, thereby improving resiliency. Afterward, through picking mode-dependent Lyapunov-Krasovskii functional candidates, sufficient requirements are obtained in the setting of linear matrix inequalities to guarantee the asymptotic stability of the assayed system. Ultimately, the proposed control method effectiveness is exemplified through the presentation of two numerical examples.