Collaborative Research: Data-Driven Invariant Sets for Provably Safe Autonomy

This grant will support the development of novel computational tools and new knowledge that can be used to safely automate complex processes directly from data. While data-driven methods, including machine learning and AI, have advanced numerous fields in recent years, their impact has been less pronounced in the control of complex dynamical systems, especially safety-critical ones. The research funded by this grant will provide rigorous data-driven guarantees on safety and performance, progressing the science of autonomy and advancing national prosperity by increasing the safety of automated systems. However, this requires new knowledge and computational tools to overcome the inherent uncertainty of a data-driven paradigm, where we only have finite data to characterize an arbitrarily complicated, nonlinear system. This novel paradigm is attractive for non-traditional applications of automation and control without first-principle models or applications whose dynamics are too expensive or time-consuming to identify using traditional system identification. In particular, the research will be applied to data-driven automation of ultrasounds. Automating ultrasounds will free up highly trained medical professionals to engage in other areas of patient care, improving medical care in rural areas, underdeveloped nations, and military-bases, where highly trained technicians are scarce, benefiting the U.S. economy and society. This project supports research that is motivated by the question: What is the quantity and quality of data required to guarantee safety and performance in a data-driven paradigm? The research supported by this grant will address fundamental questions whose answers will enable direct data-driven synthesis of positive, control, and contractive invariant sets. The primary novelty of this research is the development of techniques for synthesizing sets that are provably invariant. The benefit of this approach is data-driven guarantees of constraint satisfaction. This research is potentially transformative since it will allow the analysis and synthesis of constraint enforcing controller directly from data. Likewise, it will enable the extension of nominal model-based designs to larger operating domains where the modeling assumptions are invalid while providing rigorous, data-driven assurances of safety, robustness, and performance. This paradigm is attractive for non-traditional applications of control without first-principle models or applications whose dynamics are too expensive or time-consuming to identify using traditional system identification. Our approach is motivated by harnessing the data revolution to provide control theoretic guarantees for data-driven 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.