BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Joe Moeller (Caltech) DTSTART:20251124T160000Z DTEND:20251124T170000Z DTSTAMP:20260422T140128Z UID:BilTop/127 DESCRIPTION:Title: Hybrid dynamical systems as coalgebras\nby Joe Moeller (Caltech) as p art of Bilkent Topology Seminar\n\nLecture held in SA 141.\n\nAbstract\nLy apunov theory provides a method for certifying the stability of a dynamica l system without solving infeasible systems of differential equations. Thi s theory has practical implications in the design of control algorithms fo r many sorts of systems including robotics. We present a categorical frame work for Lyapunov stability theory. This theory is developed in the langua ge of coalgebras\, where a system is viewed as a coalgebra of an endofunct or. Examples include continuous dynamical systems as coalgebras of the tan gent bundle functor\, and discrete transition systems as coalgebras of the powerset functor. We blend these two standard examples to give a coalgebr aic encoding of hybrid dynamical systems\, which appear naturally in engin eering contexts such as robotic bipedal locomotion. This enables us to app ly the categorical Lyapunov theory to hybrid systems and find new conditio ns for certifying the stability of Zeno equilibria.\n LOCATION:https://researchseminars.org/talk/BilTop/127/ END:VEVENT END:VCALENDAR