A network-centric input-output and robustness analysis framework for distributed dynamic systems

研究计划：网络化动态系统是动态单元的集合，这些单元在运行过程中通过信息交换网络相互作用。这些系统已经在不同的领域找到了许多应用，例如多个空间，空中和陆地车辆，能源系统，生理学和医学。目前，控制和系统社区正在进行积极的研究工作，以形式化这些系统，并为它们的分析和综合奠定基础。该项目的目标是对分布式动态系统的以网络为中心的输入输出和鲁棒性分析框架进行基础研究。为此所采用的方法一方面是基于代数图论，另一方面是基于随机和随机几何图。在这个方向上，我们将解决与不确定网络上系统理论目标泛函的概率矩相关的问题，以及与相应网络系统的鲁棒性和性能测量中的时间尺度和相变相关的重要现象。将扩大华盛顿大学现有的一个计算试验台，以验证和评价拟议的方法。教育计划：分布式动态系统为控制和系统研究生提供了一个理想的场所，让他们了解系统思想的优雅和力量，不仅因为它们与工程问题有关，而且与生物学和信息科学有关。该项目的教育计划通过研究生课程提供和课程开发，研究生指导以及通过课堂研讨会和讲习班促进研究合作场所来实施。这门课程名为“以网络为中心的动态系统理论与应用”，将作为华盛顿大学控制课程的两个季度的研究生课程进行开发和提供。本课程将涵盖组合理论的各个方面，这些理论与系统理论相结合，在分析网络驱动的动态系统方面已被证明是有用的。课程的第二部分提供了系统理论和网络动态系统之间的严格桥梁，如在生物学和生理学等广泛学科中遇到的。在项目的最后一年，以网络为中心的动态系统研讨会不仅将为研究生提供一个特殊的教育渠道，而且还将作为进一步增加跨学科研究机会的工具。学术价值:提出的研究和教育计划的智力价值包括：(1)对控制理论的一个新分支学科的基础贡献，称为以网络为中心的动态系统理论(2)应用新颖的图论和系统理论技术来分析在生命和物理科学以及工程系统中遇到的网络动态系统(3)为系统和控制理论家，组合学家，华盛顿大学的生物学家和物理学家，以及(4)为系统和控制教育的研究生项目开发新课程。更广泛的影响：我们的项目将为系统和控制研究人员、图理论家和生物科学界之间的未来合作奠定肥沃的基础。通过这样做，它也将为系统和控制研究生带来一系列新的职业选择。我们对新兴网络领域的贡献将通过以下方式得到充分宣传：(1)项目第三年组织良好的研讨会，汇集来自当地计算机科学、工程和生物医学行业的跨学科研究人员；(2)通常由研究生在专业会议和研究机构中展示研究成果；(3)在非博士学位的教育机构中频繁举行研讨会。资助和/或服务弱势群体。这些更多的公开研讨会将强调跨不同学科的网络动态系统的共同复杂性，以及控制和系统理论如何为它们的分析和综合提供新的理论和算法工具。这些研讨会也将被积极用作招聘工具，特别是用于吸引来自工程领域代表性不足群体的潜在研究生。

Research Plan: A networked dynamic system is a collection of dynamical units that interact via an informationexchange network during their operation. These systems have found many applications in diverseareas such as multiple space, air, and land vehicles, energy systems, physiology, and medicine. Currently,there is an active research effort underway in the control and systems community to formalize these systemsand lay out a foundation for their analysis and synthesis. The objective of this project is to carry out foundationalstudies on a network-centric input-output and robustness analysis framework for distributed dynamicsystems. The approach adopted for this purpose is based on algebraic graph theory on one hand, and randomand random geometric graphs, on the other. In this direction, we will address problems associatedwith probabilistic moments of system-theoretic objective functionals over uncertain networks, as well asthe important phenomena associated with time-scales and phase transitions in robustness and performancemeasures of the corresponding networked systems. An existing computational testbed at the University ofWashington will be augmented for the purpose of validation and evaluation of the proposed methodologies.Education Plan: Distributed dynamic systems provide an ideal venue to engage control and systems graduatestudents in the elegance and power of system ideas, not only as they pertain to engineering problems,but also in their relation to biology and information sciences. The education program of this project isimplemented through a graduate course offering and curriculum development, graduate mentoring, and promotingresearch collaboration venues via in-class seminars and a workshop. The proposed course, NetworkcentricDynamic System Theory and Applications, will be developed and offered as a two quarters graduatelevel course in the controls curriculum of the University of Washington. The course will cover aspects ofcombinatorial theory that, in conjunction with system theory, have proved instrumental in the analysis ofnetwork-enabled dynamic systems. The second quarter of the course provides a rigorous bridge betweensystem theory and networked dynamic systems as encountered in a wide array of disciplines such as in biologyand physiology. The workshop on network-centric dynamic systems during the final year of the projectwill not only serve as an exceptional educational outlet for the graduate students, but also as a vehicle tofurther enhance opportunities for interdisciplinary research.Intellectual Merit: The intellectual merit of the proposed research and education program consists of:(1) foundational contributions to a new sub-discipline in control theory referred to as network-centric dynamicsystem theory (2) applying novel graph and system theoretic techniques for the analysis of networkeddynamic systems as encountered in life and physical sciences and engineering systems (3) providing a significantimpetus for collaborations between system and control theorists, combinatorialists, biologists, andphysicists, at the University of Washington, and (4) development of a new curriculum for graduate programin systems and control education.Broader Impact: Our project will lay a fertile ground work for future collaborations between system andcontrol researchers, graph theorists, and the biological science community. By doing so, it will also bringinto the horizon a host of new career options for system and control graduate students. Our contributions tothe emerging field of networks will be well publicized via: (1) a well-organized workshop on the third yearof the project, bringing researchers from across disciplines, from local computer science, engineering, andbiomedical industries (2) presenting research results, often by graduate students, in professional conferencesand research institutions, and (3) frequent seminars in the educational institutions that are non-Ph.D grantingand/or serve underrepresented groups. These more public seminars will highlight the common complexitiesof networked dynamic systems across various disciplines, and how control and system theory is providingnovel theoretical and algorithmic tools for their analysis and synthesis. These seminars will also be activelyused as a recruitment tool, particularly for attracting potential graduate students from underrepresentedgroups in engineering.