  This paper focuses on the study of the finite-time consensus (FTC) and
fixed-time consensus (FXC) issues of multi-agent systems (MASs) driven by
parabolic partial differential equations (PDEs). Compared with the study in the
existing literature, the topic of FTC and FXC control is first embodied in MASs
driven by parabolic PDEs. Based on the Lyapunov theorems, the FTC and FXC
controllers are devised to ensure that the MASs converge to a stable state with
external disturbance. Furthermore, we simplify the controllers to guarantee the
FTC and FXC of MASs without external disturbance. Finally, two illustrative
examples are given to verify the feasibility of controllers.
