[论文解读] Reaching a Consensus in Networks of High-Order Integral Agents under Switching Directed Topology

Long Cheng, Zeng‐Guang Hou+1 more|arXiv (Cornell University)|Apr 15, 2013

Distributed Control Multi-Agent Systems参考文献 21被引用 9

一句话总结

本文通过精心设计的增益向量，将高阶积分多智能体系统在切换有向拓扑下转化为等价的一阶积分系统，提出了一种分布式一致性协议。关键贡献在于证明了在目前已知最弱的连通性条件下——即一致联合准强连通拓扑——只要相对状态增益向量的特征多项式根位于开左半复平面，一致性即可实现。

ABSTRACT

Consensus problem of high-order integral multi-agent systems under switching directed topology is considered in this study. Depending on whether the agent's full state is available or not, two distributed protocols are proposed to ensure that states of all agents can be convergent to a same stationary value. In the proposed protocols, the gain vector associated with the agent's (estimated) state and the gain vector associated with the relative (estimated) states between agents are designed in a sophisticated way. By this particular design, the high-order integral multi-agent system can be transformed into a first-order integral multi-agent system. And the convergence of the transformed first-order integral agent's state indicates the convergence of the original high-order integral agent's state if and only if all roots of the polynomial, whose coefficients are the entries of the gain vector associated with the relative (estimated) states between agents, are in the open left-half complex plane. Therefore, many analysis techniques in the first-order integral multi-agent system can be directly borrowed to solve the problems in the high-order integral multi-agent system. Due to this property, it is proved that to reach a consensus, the switching directed topology of multi-agent system is only required to be "uniformly jointly quasi-strongly connected", which seems the mildest connectivity condition in the literature. In addition, the consensus problem of discrete-time high-order integral multi-agent systems is studied. The corresponding consensus protocol and performance analysis are presented. Finally, three simulation examples are provided to show the effectiveness of the proposed approach.

研究动机与目标

• 解决在切换有向拓扑下高阶积分多智能体系统缺乏一致性协议的问题。
• 克服现有方法依赖无向拓扑或频繁连通拓扑的局限性。
• 设计在智能体状态完全可测或仅部分可观测（输出反馈）时仍适用的分布式协议。
• 建立一致性所需的最小连通性条件，优于文献中已有结果。
• 将分析框架扩展至离散时间系统，并通过仿真验证方法的有效性。

提出的方法

• 提出一种状态反馈协议，通过为相对状态专门设计的增益向量，将高阶系统转化为一阶积分系统。
• 针对全状态不可测的情况，引入一种输出反馈协议，控制律中使用状态估计值。
• 通过要求由相对状态增益向量生成的特征多项式的所有根均位于开左半复平面，确保转化后的一阶系统收敛。
• 利用一阶积分多智能体系统已有的分析技术，证明在新连通性条件下的一致性。
• 采用类似李雅普诺夫的分析方法和状态转移矩阵性质，证明智能体状态的渐近收敛性。
• 通过推导相应的共识协议并利用z域分析与根位置判据，将框架扩展至离散时间系统，并分析其收敛性。

实验结果

研究问题

• RQ1 在切换有向拓扑下，高阶积分多智能体系统能否实现一致性？
• RQ2 在何种最弱的连通性条件下，切换有向拓扑仍能保证一致性？
• RQ3 当全智能体状态不可测时，如何设计分布式控制协议？
• RQ4 高阶系统能否被简化为一阶系统以利于分析？
• RQ5 离散时间高阶积分多智能体系统的一致性必要与充分条件是什么？

主要发现

• 一致性仅当由相对状态增益向量系数构成的多项式的所有根均位于开左半复平面时才可实现。
• 切换有向拓扑仅需满足一致联合准强连通性，这是文献中已知最弱的条件。
• 所提出的协议可将高阶系统转化为等价的一阶积分系统，从而可复用一阶系统的分析工具。
• 对于离散时间系统，若对应特征多项式的所有根均位于单位圆内，则可保证一致性。
• 仿真结果表明，所提协议在切换拓扑下能有效实现一致性。
• 通过反证法证明了根条件的必要性：若任一根位于开左半平面之外，则对某些初始条件，一致性将失败。