Events

Pablo Baldivieso PhD Defense: Necessary Conditions for Stability of Vehicle Formations
Friday, May 3, 2019 - 8:57am

             

Ph.D. in Mathematical Sciences

Dissertation Defense

 

Pablo Baldivieso

 

Necessary Conditions for Stability of Vehicle Formations

 

 

MS, Portland State University, 2008

BS, Portland State University, 2005

 

Defense date: Friday, May 3, 2019

Time:               2:00PM

Location:        Karl Miller Center room 255

                          615 SW Harrison Street, Portland

 

 

Committee chair:                             

J.J.P. Veerman, PhD

 

Committee members:                     

Bin Jiang, PhD

Mau Nam Nguyen, PhD

Andres La Rosa, PhD

Graduate Office Representative: Bart Massey, PhD

 

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.