基于无源性的协同控制中的对偶性与网络理论
Duality and Network Theory in Passivity-based Cooperative Control
AI总结：
本文通过引入最大平衡独立无源性概念，建立了无源性协同控制问题与凸网络优化问题之间的显式对偶关系，揭示了系统动态变量与网络优化变量之间的对应，并统一了网络分析与最优设计框架。
摘要：
本文提出了一类与凸网络优化问题具有显式联系的无源性协同控制问题。引入了最大平衡独立无源性的新概念，并证明具有该特性的系统网络渐近逼近一对对偶网络优化问题的解，即最优势问题和最优流问题。这种联系使得系统输入输出等动态变量与网络优化框架中的散度和势等变量得以对应，并揭示了凸网络优化理论中已知的若干对偶关系直接转化为无源性协同控制问题。所提出的结果在无源性协同控制理论与网络优化理论之间建立了强而显式的联系，并为网络分析与最优设计提供了统一框架。通过一个非线性交通动力学模型验证了结果，该模型被证明是渐近聚类的。
英文摘要：
This paper presents a class of passivity-based cooperative control problems that have an explicit connection to convex network optimization problems. The new notion of maximal equilibrium independent passivity is introduced and it is shown that networks of systems possessing this property asymptotically approach the solutions of a dual pair of network optimization problems, namely an optimal potential and an optimal flow problem. This connection leads to an interpretation of the dynamic variables, such as system inputs and outputs, to variables in a network optimization framework, such as divergences and potentials, and reveals that several duality relations known in convex network optimization theory translate directly to passivity-based cooperative control problems. The presented results establish a strong and explicit connection between passivity-based cooperative control theory on the one side and network optimization theory on the other, and they provide a unifying framework for network analysis and optimal design. The results are illustrated on a nonlinear traffic dynamics model that is shown to be asymptotically clustering.
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