PDE-Based Finite-Time Deployment of Heterogeneous Multi-Agent Systems Subject to Multiple Asynchronous Semi-Markov Chains
Jingtao Man, Yin Sheng, Chongyang Chen, Zhigang Zeng
Abstract
For large-scale heterogeneous nonlinear multi-agent systems (MASs) consisting of abundant first-order and second-order agents, this paper presents a novel framework based on partial differential equations (PDEs) to facilitate their practically finite-time deployment in 2D or 3D space. First, through designing appropriate network communication protocols (NCPs), a heterogeneous nonlinear PDE model composed of a heat equation and a damped wave equation is constructed to characterize the collective dynamics of considered heterogeneous nonlinear MASs. Second, a single-point control strategy and a double-boundary control strategy are proposed, which could not only ensure the well-posedness of the closed-loop heterogeneous PDEs but also enable the finite-time deployment of multi agents. Notably, to better align with real MASs and operating environment, the network topologies and controllers are designed to be semi-Markov switched, while adhering to multiple asynchronous switching rules. Third, with the designed NCPs and control schemes, several sufficient conditions are derived to guarantee the practically finite-time stability of error systems. Finally, two numerical examples and an application example are conducted to validate effectiveness and practicability of the developed approaches.