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Cornell University

Optimally Navigating a Piecewise-deterministic World

Abstract

dc:description.abstract

We consider various problems arising in optimal control of piecewise-deterministic Markov processes (PDMPs), with an emphasis on path planning problems where a randomly switching mode impacts the dynamics and optimization objective. We introduce two application-driven modeling frameworks, each formulated as a piecewise-deterministic path planning problem. The first framework models a vehicle that may experience breakdowns of varying severity at random times as it navigates a domain. We present an efficient iterative solver to recover the mode-dependent value functions and optimal policies for this problem. The second proposes a model of optimal foraging in a continuous domain while subject to predation. We present numerical experiments to demonstrate the impact of a forager's objective on the predicted optimal behavior. We close by studying a class of "occasionally observed" PDMPs, in which the planner is not notified when a mode switch occurs, but may occasionally have access to observations of the current mode. We state sufficient assumptions under which it is possible to represent the resulting belief over the modes as an explicit function of time. We present efficient dynamic programming algorithms for computing value functions and optimal policies for a variety of horizon types and observation schemes.

Degree

thesis:*
Name thesis:degree_name
Ph. D., Applied Mathematics
Level thesis:degree_level
Doctor of Philosophy
Discipline thesis:degree_discipline
Applied Mathematics
Grantor
Cornell University
Year dc:date.issued
2024

Author and committee

dc:creator, dc:contributor.*
Author dc:creator
  • Gee, Marissa
Committee members dc:contributor.committeemember
  • Damle, Anil
  • Strogatz, Steven
  • Ellner, Stephen

Subjects

dc:subject × 4

Rights

dc:rights
Statement dc:rights
  • Attribution-NonCommercial-ShareAlike 4.0 International
Language dc:language.iso
en

Identifiers

dc:identifier.*
Dc Identifier Other
ProQuest Submission ID: 14450
ProQuest Publication ID: 31482980
OAI identifier oai:identifier
oai:ecommons.cornell.edu:1813/116454

Chain of custody

source
Harvested from
Cornell University
Base URL
ecommons.cornell.edu/server/oai/request
Last updated
2026-07-24
Source record
OAI-PMH GetRecord
citation

Gee, Marissa. Optimally Navigating a Piecewise-deterministic World. Doctor of Philosophy thesis, Cornell University, 2024. https://hdl.handle.net/1813/116454