Data-Driven Safety Filters: Hamilton-Jacobi Reachability, Control Barrier Functions, and Predictive Methods for Uncertain Systems
Kim P. Wabersich, Andrew J. Taylor, Jason J. Choi, Koushil Sreenath, Claire J. Tomlin, Aaron D. Ames, Melanie N. Zeilinger
Abstract
Today’s control engineering problems exhibit an unprecedented complexity, with examples including the reliable integration of renewable energy sources into power grids <xref ref-type="bibr" rid="ref1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[1]</xref> , safe collaboration between humans and robotic systems <xref ref-type="bibr" rid="ref2" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[2]</xref> , and dependable control of medical devices <xref ref-type="bibr" rid="ref3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[3]</xref> offering personalized treatment <xref ref-type="bibr" rid="ref4" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[4]</xref> . In addition to compliance with safety criteria, the corresponding control objective is often multifaceted. It ranges from relatively simple stabilization tasks to unknown objective functions, which are, for example, accessible only through demonstrations from interactions between robots and humans <xref ref-type="bibr" rid="ref5" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[5]</xref> . Classical control engineering methods are, however, often based on stability criteria with respect to set points and reference trajectories, and they can therefore be challenging to apply in such unstructured tasks with potentially conflicting safety specifications [6, Secs. 3 and 6]. While numerous efforts have started to address these challenges, missing safety certificates often still prohibit the widespread application of innovative designs outside research environments. As described in “Summary,” this article presents safety filters and advanced data-driven enhancements as a flexible framework for overcoming these limitations by ensuring that safety requirements codified as static state constraints are satisfied under all physical limitations of the system.