Observer-based boundary control for distributed parameter system under denial-of-service attacks

This paper focuses on the problem of boundary control for a distributed parameter system (DPS) under denial-of-service (DoS) attacks. Initially, a DPS model is employed. Considering the incomplete measurement of the DPS's state, a novel boundary observer is then proposed, which only relies on the right boundary state instead of full-domain information to achieve accurate state estimation, significantly reducing the measurement cost. Subsequently, an anti-DoS observer-based boundary controller is designed, which is applied only to the spatial boundary to lower actuator deployment costs while improving robustness to intermittent DoS attacks. In addition, a Lyapunov-Krasovskii functional is introduced, and the design methods for the controller and observer are derived by solving linear matrix inequalities. Finally, the feasibility of the control strategy is verified through an example.