17th International Symposium on
Mathematical Theory of Networks and Systems
Kyoto International Conference Hall, Kyoto, Japan, July 24-28, 2006

MTNS 2006 Paper Abstract

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Paper WeA06.1

Byrnes, Christopher (Washington Univ.), Dockery, Jack (Montana State Univ.), Gilliam, David (Texas Tech. Univ.)

Bifurcations and Attractors for a Controlled Burgers’ Equation

Scheduled for presentation during the Mini-Symposium "Distributed Parameter Systems-III: Control of Partial Differential Equations" (WeA06), Wednesday, July 26, 2006, 10:25−10:50, Room G

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on March 29, 2024

Keywords Control of distributed parameter systems

Abstract

In this work we consider an open loop system consisting of a viscous Burgers' equation with or without an additional forcing. Control inputs and outputs are introduced through the boundary and a closed loop system is obtained by introducing a proportional error boundary feedback law. The main point of the talk is to present several known results for this system and draw attention to some open problems. Topics discussed in the talk will include global existence and regularity of solutions, existence of local and global attractor, semiglobal and practical stabilization, and bifurcation of equilibria associated with variation of the gains in the boundary feedback law.