Interplay between Network Topology and Stability of Control Systems with Delays

网络拓扑与时滞目标控制系统稳定性的相互作用：时滞在控制系统中普遍存在，主要来自于感知、驱动和决策活动；拓扑图描述了哪些控制系统通过网络相互绑定，如自动驾驶汽车、远程操作、制造企业系统和车辆交通流动态的协调。在同一网络中，时延和拓扑相互影响，共同决定网络的稳定性。本程序的目的是解释网络拓扑结构之间的非平凡连接以及这些网络在存在多重延迟的情况下的稳定性机制。从文献中可以明显看出，对于具有多个延迟的控制系统不存在一般的稳定性处理，并且这种知识差距目前阻碍了明确规则的可用性，通过这些规则可以设计网络及其控制器以提高稳定性。智力优势：这个项目的智力优势是为多延迟系统的稳定性理论提供了一种新的、未被认识到的数学方法，它解开了上述知识差距，并将揭示对不同网络拓扑可以承受的延迟量的彻底理解，而不会失去稳定性。这种方法将产生新的规则，通过设计网络的拓扑、耦合强度和控制器增益，可以使网络对延迟的容忍度更高。在这个项目中获得的新工具也将在机电一体化实验中进行测试，并将阐明新知识从小型网络到大型网络的过渡。该提案的变革方面体现在采用非传统方法来实现(a)多延迟系统的稳定性分析，(b)揭示拓扑，延迟和稳定性之间交织关系的明确公式；(c)存在多重延迟的网络拓扑和控制器并行设计的新范例。更广泛的影响：项目的更广泛的影响是：(i)通过针对包括少数民族和代表性不足群体在内的受众的外展活动进行工程教育，并通过在顶点设计项目中为本科生提供建议；（ii）通过国家和国际合作加强研究基础设施；通过将开发的用于教授延迟系统分析的新辅导级网站传播结果；（iv）跨学科的新成果，包括网络控制系统、车辆交通流、运筹学和生物学。

Interplay between Network Topology and Stability of Control Systems with DelaysObjective: Delays, ubiquitous in control systems, mainly arise from sensing, actuation and decision-making activities; and the topology describes which control systems are tied with each other via a network, as seen in coordination of autonomous vehicles, tele-operation, manufacturing enterprise systems and vehicular traffic flow dynamics. Through the same network, delays and topology affect each other and combine together to determine the network stability. The objective of this program is to explain the non-trivial connections between the topologies of networks and the stability mechanisms of these networks in the presence of multiple delays. Evident from the literature, there exists no general stability treatment for control systems with multiple delays, and this knowledge gap currently prevents the availability of explicit rules by which networks and their controllers can be designed for improved stability.Intellectual merit: The intellectual merit of this project is a new and unrecognized mathematical approach for the stability theory of multiple delay systems, which unlocks the aforementioned knowledge gap and will reveal thorough understanding of the amounts of delays different network topologies can withstand without loosing stability. The approach will lead to new rules with which networks, by design of their topologies, coupling strengths and controller gains, can be rendered more tolerant against delays. The new tools attained in this project will also be tested in mechatronics experiments and will put light on the transition of the new knowledge from small size networks to large size ones. The transformative aspects of the proposal are seen in the non-traditional approaches taken to enable (a) the stability analysis of multiple delay systems, (b) the explicit formulations that reveal the intertwined relationships between topology, delays and stability; (c) new paradigms for the parallel design of network topologies and controllers in the presence of multiple delays.Broader impacts: The broader impacts of the project are: (i) engineering education via outreach activities targeted to an audience including minorities and under-represented groups, and via advising undergraduate students in capstone design projects; (ii) enhancing research infrastructures via national and international collaborations; (iii) dissemination of results via a new tutorial-level web-site that will be developed to teach the analysis of delay systems; (iv) new results across disciplines including networked control systems, vehicular traffic flow, operations research and biology.