Jared Miller Ph.D Defense/Proposal Announcement

“Safety Analysis for Nonlinear and Time-Delay Systems using Occupation Measures”

International Village 022

Committee Members:
Prof. Mario Sznaier (Advisor)
Prof. Octavia Camps
Prof. Bahram Shafai
Prof. Eduardo Sontag
Prof. Didier Henrion (LAAS-CNRS)

Abstract:
This 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.

A 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.