Adaptive Neural Finite-Time Deployment of Heterogeneous Multi-agent Systems via a Cross-Species Bionic PDE-ODE Approach

For large-scale heterogeneous multi-agent systems (MASs) with characteristics of dense-sparse mixed distribution, this paper investigates the practical finite-time deployment problem by establishing a novel cross-species bionic analytical framework based on the partial differential equation-ordinary differential equation (PDE-ODE) approach. Specifically, by designing a specialized network communication protocol and employing the spatial continuum method for densely distributed agents, this paper models the tracking errors of densely distributed agents as a PDE equivalent to a human disease transmission model, and that of sparsely distributed agents as several ODEs equivalent to the predator population models. The coupling relationship between the PDE and ODE models is established through boundary conditions of the PDE, thereby forming a PDE-ODE-based tracking error model for the considered MASs. Furthermore, by integrating adaptive neural control scheme with the aforementioned biological models, a “Flexible Neural Network” endowed with adaptive and self-stabilized capabilities is constructed, which acts upon the considered MASs, enabling their practical finite-time deployment. Finally, effectiveness of the developed approach is illustrated through a numerical example.