2026-09-19T06:35:26Zhttps://ecommons.cornell.edu/server/oai/requestoai:ecommons.cornell.edu:1813/1164542026-05-15T19:43:53Zcom_1813_35col_1813_47
Gee, Marissa
Vladimirsky, Alexander
Damle, Anil
Strogatz, Steven
Ellner, Stephen
2025-01-14T19:59:22Z
2025-01-14T19:59:22Z
2024-08
ProQuest Submission ID: 14450
ProQuest Publication ID: 31482980
https://hdl.handle.net/1813/116454
https://doi.org/10.7298/68sq-ch97
16611674
155 pages
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.
en
Attribution-NonCommercial-ShareAlike 4.0 International
https://creativecommons.org/licenses/by-nc-sa/4.0/
Numerical Analysis
Optimal Control
Path Planning
Switched Systems
Optimally Navigating a Piecewise-deterministic World
dissertation or thesis
https://newcatalog.library.cornell.edu/catalog/16611674
application/pdf
Applied Mathematics
Cornell University
Doctor of Philosophy
Ph. D., Applied Mathematics
https://hdl.handle.net/1813/59810.2
Publication
Cornell Theses and Dissertations
Gee, Marissa
5893a6ea-7af3-41d7-abc6-04bcd26ab5df
open.access
open.access
<Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="0f2779cb-2353-43ab-a313-8fe3f4d6a166">
<Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type>
<Language>en</Language>
<Title>Optimally Navigating a Piecewise-deterministic World</Title>
<PublishedIn>
<Publication>
</Publication>
</PublishedIn>
<PublicationDate>2024-08</PublicationDate>
<DOI>https://doi.org/10.7298/68sq-ch97</DOI>
<Authors>
<Author>
<DisplayName>Gee, Marissa</DisplayName>
<Affiliation>
<OrgUnit>
</OrgUnit>
</Affiliation>
</Author>
</Authors>
<Editors>
</Editors>
<Publishers>
<Publisher>
<OrgUnit />
</Publisher>
</Publishers>
<License>https://creativecommons.org/licenses/by-nc-sa/4.0/</License>
<Keyword>Numerical Analysis</Keyword>
<Keyword>Optimal Control</Keyword>
<Keyword>Path Planning</Keyword>
<Keyword>Switched Systems</Keyword>
<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.</Abstract>
<Access xmlns="http://purl.org/coar/access_right"
>
</Access>
</Publication>