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Numerical Level Set Methods for High-Dimensional Dynamical Systems.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Numerical Level Set Methods for High-Dimensional Dynamical Systems./
Author:	Kirchner, Matthew R.
Description:	1 online resource (157 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 85-03, Section: B.
Contained By:	Dissertations Abstracts International85-03B.
Subject:	Electrical engineering. -
Online resource:	click for full text (PQDT)
ISBN:	9798380154444

Numerical Level Set Methods for High-Dimensional Dynamical Systems.
Kirchner, Matthew R.

Numerical Level Set Methods for High-Dimensional Dynamical Systems. - 1 online resource (157 pages)

Source: Dissertations Abstracts International, Volume: 85-03, Section: B.

Thesis (Ph.D.)--University of California, Santa Barbara, 2023.

Includes bibliographical references

Presented here is research focused on numerical advancements in Hamilton-Jacobi (HJ) theory as they provide a fundamental tool to address many problems in autonomous robotics such as optimal trajectory planning, safety critical reactive control, pursuit-evasion, and the optimal gathering of information of an unknown environment. HJ equations have had limitations in the past for computing usable solutions due to poor scaling with respect to system dimension. This was because a spatial grid had to be constructed densely in each dimension. Two general frameworks are proposed to overcome this limitation. First, methods based on trajectory optimization are presented and in particular, those based on generalizations of the Hopf formula are developed. This class of methods leverage the fact that for many real-world problems, only pointwise solutions are necessary, and this enables these optimization-based approached to be implemented on embedded hardware for real-time operation. Second, decomposition methods are developed. This class of methods leverage certain problem structures that allow smaller-dimensional subproblems to be formed. The solutions of these subproblems can then be aggregated to compute the global solution of the original HJ equation.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798380154444Subjects--Topical Terms:

596380
Electrical engineering.
Subjects--Index Terms:

Autonomous systemsIndex Terms--Genre/Form:

554714
Electronic books.

Numerical Level Set Methods for High-Dimensional Dynamical Systems.
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500 $a Advisor: Hespanha, Joao P.
502 $a Thesis (Ph.D.)--University of California, Santa Barbara, 2023.
504 $a Includes bibliographical references
520 $a Presented here is research focused on numerical advancements in Hamilton-Jacobi (HJ) theory as they provide a fundamental tool to address many problems in autonomous robotics such as optimal trajectory planning, safety critical reactive control, pursuit-evasion, and the optimal gathering of information of an unknown environment. HJ equations have had limitations in the past for computing usable solutions due to poor scaling with respect to system dimension. This was because a spatial grid had to be constructed densely in each dimension. Two general frameworks are proposed to overcome this limitation. First, methods based on trajectory optimization are presented and in particular, those based on generalizations of the Hopf formula are developed. This class of methods leverage the fact that for many real-world problems, only pointwise solutions are necessary, and this enables these optimization-based approached to be implemented on embedded hardware for real-time operation. Second, decomposition methods are developed. This class of methods leverage certain problem structures that allow smaller-dimensional subproblems to be formed. The solutions of these subproblems can then be aggregated to compute the global solution of the original HJ equation.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2024
538 $a Mode of access: World Wide Web
650 4 $a Electrical engineering. $3 596380
650 4 $a Aerospace engineering. $3 686400
650 4 $a Mechanical engineering. $3 557493
650 4 $a Robotics. $3 561941
653 $a Autonomous systems
653 $a Control theory
653 $a Level set methods
653 $a Partial Differential Equations
653 $a Pursuit-evasion
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