Holistic Analysis and Control of High-Dimensional Dynamical Systems via Operator-Theoretic and Data-Driven Approaches

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The rapid increase in availability of affordable ubiquitous computing power and measurement data in the age of Big Data and Internet of Things is presenting unprecedented opportunities for novel control engineering and automation solutions for a wide range of dynamic systems in nature and engineering. This project will conduct fundamental research that will contribute new knowledge on how to best utilize these recent advances in data acquisition and computing technologies to significantly enhance the performance, as well as broaden the scope of, control engineering design methodologies and principles. New formulations and frameworks pioneered in this project will allow for a more holistic understanding and treatment of increasingly complicated and high-dimensional dynamical systems that escape the scope of state-of-the-art approaches. This will also provide a solid and rigorous basis for more abstractly defined and widely encompassing high-level tasks, such as "modelling or controlling the dynamics in the brain", to be tackled in a systematic manner. The investigation in this project draws from and promises new contributions to a variety of different disciplines, such as, systems and control, data science and engineering, cell biology, brain science, and healthcare, and will in turn enhance the infrastructure for research and education across these disciplines. Concerted effort will be made to attract underrepresented groups in this multi-disciplinary research program and to engage the general public and pre-college K-12 students in scientific research through the Institute of School Partnerships at Washington University.This project will initiate a fundamental, theory-driven investigation aimed at enabling holistic analysis and control methodologies for high-dimensional nonlinear systems via merging advanced operator-theoretic and density-based approaches with differential geometric and algebraic geometric techniques. Specifically, the research team will investigate and leverage Koopman operators to establish a novel data-integrated framework for transforming nonlinear control systems defined on a on a finite-dimensional manifold to linear systems defined on a higher dimensional, possibly infinite-dimensional, vector space. The study of the dual problem using density-based system descriptions and moment-based representations will enable a data-driven framework that facilitates a more holistic control design methodology. The feasibility of the theoretical and computational advances in this project will be highlighted in diverse cutting-edge areas in science and engineering, such as in the study of brain dynamics in neuroscience and cancer treatment in cell biology.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.