Advisor

J.J.P. Veerman

Date of Award

5-15-2019

Document Type

Dissertation

Degree Name

Doctor of Philosophy (Ph.D.) in Mathematical Sciences

Department

Mathematics and Statistics

Physical Description

1 online resource (vi, 78 pages)

DOI

10.15760/etd.6875

Abstract

Necessary conditions for stability of coupled autonomous vehicles in R are established in this thesis. The focus is on linear arrays with decentralized vehicles, where each vehicle interacts with only a few of its neighbors. Decentralized means that there is no central authority governing the motion. Instead, each vehicle registers only velocity and position relative to itself and bases its acceleration only on those data. Explicit expressions are obtained for necessary conditions for asymptotic stability in the cases that a system consists of a periodic arrangement of two or three different types of vehicles, i.e. configurations as follows: ...2-1-2-1 or ...3-2-1-3-2-1. Previous literature indicated that the (necessary) condition for stability in the case of a single vehicle type (...1-1-1) held that the first moment of certain coefficients of the interactions between vehicles has to be zero. Here, we show that that does not generalize. Instead, the (necessary) condition in the cases considered is that the first moment plus a nonlinear correction term must be zero.

Persistent Identifier

https://archives.pdx.edu/ds/psu/28997

Available for download on Friday, May 15, 2020

Included in

Mathematics Commons

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