抽象齐次链：多智能体系统中高阶滑模的Lyapunov框架
Abstract homogeneous chains: a Lyapunov framework for high-order sliding modes in multi-agent systems
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中文总结 AI 辅助
本文提出抽象齐次链Lyapunov框架，实现多智能体任意阶滑模算法的全局有限时间稳定，并给出递归增益优化方法及新观测器。
中文摘要 AI 辅助
本文针对多智能体系统中的一类广泛的任意阶滑模算法，开发了一个Lyapunov框架。我们引入了抽象齐次链，这是一类具有共同凸性和齐次性性质的非线性误差系统。对于这一类系统，我们建立了任意阶的全局有限时间稳定性，构造了一个齐次Lyapunov函数，并推导了一个基于递归优化的增益建议程序。该框架解决了现有动态平均共识和分布式微分结果中的几个空白：它为任意阶的EDCHO提供了基于递归数值优化的增益建议程序，将REDCHO的收敛性从局部扩展到全局，并为领导者-跟随者分布式微分提供了任意阶的数值增益建议规则，而此前仅在一阶可用。它还为多领导者仿射编队跟踪提供了一个新的任意阶观测器，具有全局有限时间收敛性。
英文摘要
This work develops a Lyapunov framework for a broad class of arbitrary-order sliding-mode algorithms in multi-agent systems. We introduce abstract homogeneous chains, a class of nonlinear error systems characterized by common convexity and homogeneity properties. For this class, we establish global finite-time stability for arbitrary order, construct a homogeneous Lyapunov function, and derive a recursive optimization-based gain-proposal procedure. The framework addresses several gaps in existing dynamic average consensus and distributed differentiation results: it provides a recursive numerical optimization-based gain-proposal procedure for EDCHO at arbitrary order, extends REDCHO convergence from local to global, and provides arbitrary-order numerical gain-proposal rules for leader-follower distributed differentiation, previously available only at first order. It also provides a new arbitrary-order observer for multi-leader affine formation tracking with global finite-time convergence.
发表机构
- Universidad de Zaragoza（萨拉戈萨大学）
机构由 AI 辅助整理，请以论文原文为准。
