DynSyst_Special_Topics: Couplings, Network Dynamics, and Stability of Multi-Agent Systems

该项目的目标是开发数学工具来分析复杂工程系统分布式协调算法的稳定性。在多智能体系统中，协调算法可以看作是一组通过基本交互规则耦合在一起的动态系统。这种表面上的简单是具有欺骗性的，因为它隐藏了与丰富的互连拓扑、它们的动态性质和代理交互的空间分布特征相关的固有复杂性。本项目旨在通过分析智能体间耦合和智能体动态之间的相互影响来研究新兴网络行为。特别是，该项目旨在了解定向信息流（当信息的传输或获取在整个网络中是非对称的）和交换互连拓扑（当改变相邻关系导致网络动态演变中的不连续时）对稳定性的影响。我们创新的技术方法汇集了集值动力学、不确定性系统、非光滑分析、图论和几何优化的思想，并有可能为复杂的工程系统提供广泛适用的工具。运动协调是生物系统中一个非常重要的现象，也是移动传感器和嵌入式机器人人工网络中非常有用的工具。研究运动协调的一个重要工程原因源于最近对多智能体系统的兴趣。具有控制、通信、传感和处理能力的低成本、高度自主设备的出现，为传感器网络在各种场景中的部署铺平了道路。关于这些网络的单个组件的设计和使用，我们已经了解了很多，然而，将这些组件集成到具有可预测行为的复杂、自组织网络中的科学还处于初级阶段。我们需要工具、抽象和模型来对复杂的网络进行严格的推理，也需要技术来帮助设计真正自主和自适应的网络。该项目的成果将帮助工程师在各种情况下设计自主和自适应网络，包括灾难恢复、环境监测和海洋采样。

The goal of this project is to develop mathematical tools to analyze the stability of distributed coordination algorithms for complex engineered systems. In a multi-agent system, a coordination algorithm can be seen as a set of dynamical systems coupled through basic interaction rules. This apparent simplicity is deceptive as it hides the inherent complexity associated to the rich class of interconnection topologies, their dynamic nature, and the spatially distributed character of agent interactions. This project sets out to study emerging network behaviors by analyzing the mutual influence between the inter-agent coupling and the agent dynamics. In particular, the project seeks to understand the effects on stability of directed information flows (when the transmittal or acquisition of information is nonsymmetric across the network) and switching interconnection topologies (when changing neighboring relationships induce discontinuities in the dynamic evolution of the network). Our innovative technical approach brings together ideas from set-valued dynamics, nondeterministic systems, nonsmooth analysis, graph theory, and geometric optimization, and has the potential to provide broadly-applicable tools for complex engineered systems.Motion coordination is a remarkable phenomenon in biological systems and an extremely useful tool in man-made networks of mobile sensors and embedded robots. An important engineering reason to study motion coordination stems from the recent interest in multi-agent systems. The emergence of low-cost, highly-autonomous devices with control, communication, sensing, and processing capabilities has paved the way for the deployment of sensor networks in a wide range of scenarios. A lot is known about the design and use of the individual components of these networks, and yet the science of integrating the components into complex, self-organizing networks with predictable behavior is at a primitive stage. There is a need for tools, abstractions, and models that allow to reason rigorously about complex networks, and for techniques that help design truly autonomous and adaptive networks. The results from this project will help engineers design autonomous and adaptive networks in a variety of scenarios, including disaster recovery, environmental monitoring, and ocean sampling.