Adaptive Neural Finite-Time Deployment of Nonlinear Heterogeneous Multi-Agent Systems With Inconsistent Semi-Markov Topologies: An ODE–PDE Approach

This article investigates the practical finite-time spatial deployment of a class of large-scale heterogeneous nonlinear multi-agent systems (MASs), for which a novel hybrid analysis methodology based on ordinary differential equations (ODEs) coupled with partial differential equations (PDEs) is proposed. The assumption is made that a portion of the agents is sparsely distributed in space, while the other portion is densely distributed. By designing appropriate network communication protocols (NCPs), the dynamics of MASs are represented by a hybrid model consisting of several ODEs and a PDE. Particularly, the network topological weights are specifically designed as semi-Markov switched to better align with real communication situations of MASs, while complying with inconsistent switching rules. Moreover, for delay-free and time-delayed cases, this article proposes two novel projection-based adaptive neural control schemes and obtains two design criteria of controller gains, such that the practical finite-time stability of the tracking error systems could be guaranteed. Finally, numerical examples are provided to illustrate the effectiveness of the developed approaches.