Title page for ETD etd-06102007-100142


Type of Document Dissertation
Author Kachroo, Pushkin
URN etd-06102007-100142
Title Optimal and Feedback Control for Hyperbolic Conservation Laws
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Ball, Joseph A. Committee Chair
Adjerid, Slimane Committee Member
Burns, John A. Committee Member
Klaus, Martin Committee Member
Keywords
  • Optimal
  • Control
  • Entropy
  • Feedback
  • Evacuation
  • Hyperbolic PDE
Date of Defense 2007-05-10
Availability unrestricted
Abstract
This dissertation studies hyperbolic partial differential equations for Conservation Laws motivated by traffic control problems. New traffic models for multi-directional flow in two dimensions are derived and their properties studied. Control models are proposed where the control variable is a multiplicative term in the flux function. Control models are also proposed for relaxation type systems of hyperbolic PDEs. Existence of optimal control for the case of constant controls is presented. Unbounded and bounded feedback control designs are proposed. These include advective, diffusive, and advective-diffusive controls. Existence result for the bounded advective control is derived. Performance of the relaxation model using bounded advective control is analyzed. Finally simulations using Godunov scheme are performed on unbounded and bounded feedback advective controls.
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