Dynamic routing problem in distributed parameter setting using semigroup theory

Pushkin Kachroo, Kaan M.A. Özbay

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

The aim of this chapter is to present the background information on semigroup theory and evolution equations and motivate their use in the design of controllers, especially feedback controllers, for the dynamic traffic routing and assignment problems. The chapter presents the highway model in the semigroup context and also provides a starting point for traffic routing control design using the semigroup theory. In order to present this framework, this chapter presents the fundamentals of the applicable functional analysis from the ground up. It reviews the topics of topological spaces, vector spaces, metric spaces, normed linear spaces, banach and Hilbert spaces, semigroups and finally how the routing problem can be viewed in this framework as an abstract differential controlled equation.

Original languageEnglish (US)
Title of host publicationAdvances in Industrial Control
PublisherSpringer International Publishing
Pages155-166
Number of pages12
Edition9783319692296
DOIs
StatePublished - 2018

Publication series

NameAdvances in Industrial Control
Number9783319692296
ISSN (Print)1430-9491
ISSN (Electronic)2193-1577

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Automotive Engineering
  • Aerospace Engineering
  • Industrial and Manufacturing Engineering

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  • Cite this

    Kachroo, P., & Özbay, K. M. A. (2018). Dynamic routing problem in distributed parameter setting using semigroup theory. In Advances in Industrial Control (9783319692296 ed., pp. 155-166). (Advances in Industrial Control; No. 9783319692296). Springer International Publishing. https://doi.org/10.1007/978-3-319-69231-9_6