Observer-reliant event-triggered security control design for stochastic third-order PDE systems with multiple attacks

This study accentuates the issues of state estimation and event-triggered security control design for stochastic third-order parabolic partial differential equation systems subject to nonlinearity, external disturbances, and multiple cyber attacks. Considering the unavailability of system states, a Luenberger-type state observer is implemented to acquire the approximations of actual system states for effectively addressing the problem of state unavailability. With the primary intent of utilizing network resources efficiently, we design an event-triggered controller for third-order PDE systems to effectively reduce the data transmission of the communication channel. Additionally, deception and denial-of-service attacks are assumed to occur in the communication network, which is governed by two independent sequences of Bernoulli-distributed random variables, each with its own probability. Furthermore, the dissipative performance is utilized to mitigate the effects of external disturbances. Thereafter, by constructing an appropriate Lyapunov–Krasovskii functional, a set of suitable criteria is derived within the framework of linear matrix inequalities to guarantee the mean-square exponential stability and $\{{\psi }_1,{\psi }_2,{\psi }_3\}-\rho$ dissipativity of the considered system. Further, a precise layout for the intended controller and observer gain matrices is established by employing the postulated criteria. At the end, two numerical examples are provided to demonstrate the effectiveness and relevance of the established theoretical findings.