Unified Generic Geometric-Decompositions for Consensus or Flocking Systems of Cooperative Agents and Fast Recalculations of Decomposed Subsystems Under Topology-Adjustments
提出一种统一的几何投影方法，将耦合的协同智能体系统分解为质心子系统和多个形状子系统，并能在拓扑调整（如增删边、改权重）时仅基于旧子系统快速重算新子系统，便于分析与设计。
This paper considers a unified geometric projection approach for: 1) decomposing a general system of cooperative agents coupled via Laplacian matrices or stochastic matrices and 2) deriving a centroid-subsystem and many shape-subsystems, where each shape-subsystem has the distinct properties (e.g., preservation of formation and stability of the original system, sufficiently simple structures and explicit formation evolution of agents, and decoupling from the centroid-subsystem) which will facilitate subsequent analyses. Particularly, this paper provides an additional merit of the approach: considering adjustments of coupling topologies of agents which frequently occur in system design (e.g., to add or remove an edge, to move an edge to a new place, and to change the weight of an edge), the corresponding new shape-subsystems can be derived by a few simple computations merely from the old shape-subsystems and without referring to the original system, which will provide further convenience for analysis and flexibility of choice. Finally, such fast recalculations of new subsystems under topology adjustments are provided with examples.