Control designs and stability analyses for Helly’s car-following model

Oscar A. Rosas-Jaimes, Luis A. Quezada-Téllez () and Guillermo Fernández-Anaya ()
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Oscar A. Rosas-Jaimes: Facultad de Ciencias de la Electrónica, Benemérita Universidad Autónoma de Puebla, Prol. 24 Sur S/N Ciudad Universitaria, San Manuel, 72570 Puebla, México
Luis A. Quezada-Téllez: Departamento de Matemáticas Aplicadas y Sistemas, UAM-Unidad Cuajimalpa, Av. Vasco de Quiroga 4871, Col. Santa. Fe, Cuajimalpa, C. P. 05348, Ciudad de México, México
Guillermo Fernández-Anaya: Departmento de Física y Matemáticas, Universidad Iberoamericana, Prol. Paseo de la Reforma 880, Álvaro Obregón, Lomas de Sta. Fe, Cd. de México, México

International Journal of Modern Physics C (IJMPC), 2018, vol. 29, issue 03, 1-25

Abstract: Car-following is an approach to understand traffic behavior restricted to pairs of cars, identifying a “leader” moving in front of a “follower”, which at the same time, it is assumed that it does not surpass to the first one. From the first attempts to formulate the way in which individual cars are affected in a road through these models, linear differential equations were suggested by author like Pipes or Helly. These expressions represent such phenomena quite well, even though they have been overcome by other more recent and accurate models. However, in this paper, we show that those early formulations have some properties that are not fully reported, presenting the different ways in which they can be expressed, and analyzing them in their stability behaviors. Pipes’ model can be extended to what it is known as Helly’s model, which is viewed as a more precise model to emulate this microscopic approach to traffic. Once established some convenient forms of expression, two control designs are suggested herein. These regulation schemes are also complemented with their respective stability analyses, which reflect some important properties with implications in real driving. It is significant that these linear designs can be very easy to understand and to implement, including those important features related to safety and comfort.

Keywords: Automotive applications; control system design; control system analysis; linear systems; optimal control (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1142/S0129183118500250

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