Data-guided Control: Fundamental Limits in Presence of Nonlinearities, Streaming Data, and Networks

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Data-guided control is an emerging area in system sciences that aims to embrace time series data as its core construct for control of dynamic systems–replacing or complementing their models. This project addresses foundational gaps in the current state of the art in data-guided control. The approach is multi-pronged; on one hand, the current paradigm is extended by facilitating its applications in the context of nonlinear systems and trajectory funnels, as well as large-scale networked systems. On the other hand, foundational system-theoretic constructs for control with online streaming data are developed. The project also has a significant educational component. The PI will develop and re-design a number of control courses at the University of Washington, providing a complementary “data-model” perspective on dynamic systems. These courses will encourage students with interest in machine learning to appreciate the theoretical underpinnings of model-based design. In parallel, the educational goals of this project involve inspiring students with interest in systems and control theory to re-examine data-guided analysis from a perspective that is rooted in system theory, yet embraces how data, statistics, and optimization significantly complement the more traditional training in systems and control. This project contributes to making system-theoretic concepts in areas such complex networks, infrastructure systems, and health care, as relevant and useful as data analytic tools and methods. Also envisioned is reviving a deeper appreciation for systems and control in students who have gravitated towards machine learning in the past decade. This new perspective also facilitates attracting a new cohort of students to systems by broadening its scope to realms where first-principle models are neither available nor justifiable. The project will develop novel data-parameterized analysis and synthesis techniques for dynamic systems. Building on the notions of informativity and Willem’s Fundamental Lemma, the use of data-parameterized matrix inequalities is examined in the presence of disturbances and for funnel synthesis in nonlinear trajectory-following. Next, scaling laws will be examined that clarify the relation between suboptimality measures and analytic properties of design objectives on one hand, and data-snapshots required for analysis and synthesis on the other. The project will then examine new system-theoretic notions for control synthesis motivated by streaming data, as well as rigorously identify the role of data-reduction techniques for the control of networked and multi-agent systems. The overarching goal of the project is developing data-guided system-theoretic techniques that transparently capture the “duality” between models and data in online control.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.