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

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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.