Targeted Coordination of Dynamic Populations: Fundamentals, Computational Methods, and Emerging Applications

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Complex systems that consist of populations of isolated or interacting dynamical components are prevalent in nature and human society. Notable examples of such systems include neural circuitry in the brain, metabolic chemical reaction systems in biology, and electrical power distribution, and traffic control systems in engineering. Tackling control and estimation tasks not only for one dynamical system but a whole population of a vast number of nearly identical dynamical units has thus emerged as a recurrent theme in numerous scientific and engineering areas, and the capability of precise targeted coordination and estimation of dynamic populations would open the floodgate to rapid and significant advancements in a diverse array of cutting-edge applications. The fundamental difficulty in dealing with dynamic populations is that control and observation can only be implemented at the population level, i.e., through broadcasting a single input signal to all the systems in the population, and through receiving aggregated measurements of the systems in the population, respectively, and there is a substantial lack of principled control and observation strategies for this new class of population systems. As a result, population-based technologies remain far from reaching their full potential. This research aims to establish a general and coherent theoretical and computational framework for the various emerging applications that critically rely on a targeted coordination of large populations of dynamical systems, and thereby close the current gap between theory and practice in the emerging applied problems concerned with population systems. The proposed investigation will promise new contributions to systems theory, control engineering, and biomedical and quantum technologies, and will in turn enhance the infrastructure for research and education across these disciplines. Concerted effort will be made to attract underrepresented groups and women to the research program and to engage the public and pre-college K-12 students in scientific research through the Institute for School Partnerships at Washington University.This project will systematically investigate fundamental questions of controllability with respect to a broadcast signal, as well as observability with respect to aggregated measurements of the systems in the population and develop optimal control strategies that will enable a targeted coordination of dynamical structures in populations. By bridging formal systems theory, ensemble control techniques, applied algebra and geometry with computational engineering, general and versatile frameworks for population control will be formulated. Specifically, the control analyses and designs will be carried through by leveraging highly non-obvious yet fundamentally intimate links to different domains, including polynomial approximation for controllability and mathematical tomography for observability. The exploration of these novel connections will broaden the range of the theoretical and computational efforts for understanding the mechanisms and collective behavior of complex population systems and networks. Moreover, the developed theoretical and computational methods will be applied to analyze and control dynamic behaviors in population systems, including inducing synchronization patterns, decoding spatial and temporal information in complex networks, and revealing driving mechanisms of heterogeneous responses in cancer cell signaling networks.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.