PDE-Based Deployment of Heterogeneous Nonlinear Multiagents: A Single-Point Control Scheme

This article develops a methodology employing partial differential equations (PDEs) to facilitate the exponential deployment of large-scale heterogeneous nonlinear multiagent systems (MASs). The considered MASs comprise a multitude of nonlinear first-order agents (FOAs) and second-order agents (SOAs). Two heterogeneous nonlinear PDEs are established to model the considered MASs by designing appropriate network communication protocols. Unlike previous PDE-based approaches for multiagent deployment, the topological weights between neighboring agents are defined as series-dependent. An informed agent, which is able to measure the location information of other agents and transmit its location information to neighboring agents through the communication network, is placed between the final FOA and the initial SOA. This novel network-based control scheme is referred to as single-point control, which could ensure the well-posedness and exponential stability of the error system. Accordingly, pointwise and distributed measurements are employed for delay-free and time-delayed cases, respectively. Numerical examples are provided in 3-D space to substantiate the obtained theoretical results.