Safety Containment Control for Parabolic PDEs

ABSTRACT This paper investigates the output feedback containment control problem for multi‐agent systems (MASs) with multiple leaders under denial‐of‐service (DoS) attacks. In the considered system, all agents are modelled by partial differential equations. To address the issue of unmeasurable system state, a distributed observer is advanced. The distributed controller is designed based on observer state, enabling containment control of the cluster affected by DoS attacks. As a result, consensus can be achieved between leader agents and follower agents over an undirected graph. Furthermore, the tolerable frequency and duration of DoS attacks are outlined. Using Lyapunov techniques and mathematical inequalities, sufficient conditions for matrix inequalities are proven to ensure global asymptotic stability of MASs under DoS attacks. Finally, the efficacy of observer and controller is validated through illustrative examples.