Design of dynamic hybrid-triggered dissipative resilient control for parabolic PDE cyber–physical switched systems with attacks

The focus of this study is on investigating the design of dynamic hybrid-triggered resilient control for partial differential equation (PDE) systems even in the presence of Neumann boundary conditions. To be specific, the PDE under consideration is of the parabolic type involving cyber–physical switched systems and is subject to randomly occurring uncertainties, external disturbances and false data injection (FDI) attacks. Moreover, in an attempt to minimize the volume of data transfers, a broader dynamic hybrid-triggered (DHT) approach is executed, amalgamating both time-triggered and dynamic event-triggered techniques. Concurrently, resilient control is being considered to guarantee the required stabilization of the system, even in the presence of gain fluctuations. Within the specified context, stochastic variables that conform to the Bernoulli distribution are incorporated in the DHT resilient scheme and FDI attacks. Furthermore, the construction of a pertinent Lyapunov–Krasovskii functional leads to the establishment of required conditions for ensuring both asymptotic stability and extended dissipative performance for the closed-loop structure. Moreover, the required controller gain matrices are derived through the utilization of linear matrix inequalities. Ultimately, the suggested control design technique’s effectiveness is showcased through the presentation of two numerical examples.