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SUMMARY:Jared Miller Ph.D Defense/Proposal Announcement
DESCRIPTION:“Safety Analysis for Nonlinear and Time-Delay Systems using Occupation Measures” \nInternational Village 022 \nCommittee Members:\nProf. Mario Sznaier (Advisor)\nProf. Octavia Camps\nProf. Bahram Shafai\nProf. Eduardo Sontag\nProf. Didier Henrion (LAAS-CNRS) \nAbstract:\nThis research extends an occupation measure framework to analyze the behavior and safety of dynamical systems. A motivating application of trajectory analysis is in peak estimation\, which finds the extreme values of a state function along trajectories. Examples of peak estimation include finding the maximum height of a wave\, voltage on a power line\, speed of a vehicle\, and infected population in an epidemic. Peak estimation can be applied towards safety quantification\, such as by measuring the safety of a trajectory by its distance of closest approach to an unsafe set. \nA finite-dimensional but nonconvex peak estimation problem can be converted into an infinite-dimensional linear program (LP) in measures\, which is in turn bounded by a convergent sequence of semidefinite programs. The LP is posed in terms of an initial\, a terminal\, and an occupational measure\, where the occupation measure contains all possible information about the dynamical systems’ trajectories. This research applies measure-based methods towards safety quantification (e.g. distance estimation\, control effort needed to crash)\, hybrid systems\, bounded-uncertain systems (including for data-driven analysis)\, stochastic systems\, and time-delay systems. The modularity of this measure-based framework allows for multiple problem variations to be applied simultaneously (e.g. distance estimation under time-delays)\, and for optimization models to be synthesized using MATLAB. Solving these optimization problems results in certifiable guarantees on system performance and behavior.
URL:https://coe.northeastern.edu/event/jared-miller-ph-d-defense-proposal-announcement/
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