Predefined-Time Coordination Control for Nonlinear Multiagent Systems Governed by Diffusion PDEs Model

This paper investigates the predefined-time coordi nation control problem for multiagent systems (MASs) governed by diffusion partial differential equations (PDEs). The diffusion mechanism plays a critical role by modeling the spatially distributed state variations among agents, facilitating the continuous propagation of state information across the system and enabling distributed interactions. To address the challenges posed by spatially distributed states and the requirement for achieving consensus within a predefined time, the strongly continuous semigroup theory is utilized to establish the structured solvability of the system dynamics governed by diffusion PDEs. Building on this theoretical foundation, new predefined-time control protocols are designed for both leaderless and leader follower consensus scenarios. These protocols guarantee user specified time convergence, irrespective of initial conditions. Furthermore, the convergence principle is applied alongside a Lyapunov functional approach to derive sufficient conditions for achieving predefined-time consensus under the proposed control mechanism. Finally, numerical examples are conducted to verify the theoretical results.