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Feedback Stabilization of a Thermal Fluid System with Mixed Boundary Control
Computers and Mathematics with Applications
  • John A. Burns
  • Xiaoming He, Missouri University of Science and Technology
  • Weiwei Hu
We consider the problem of local exponential stabilization of the nonlinear Boussinesq equations with control acting on portion of the boundary. In particular, given a steady state solution on an bounded and connected domain Ω Ϲ R2, we show that a finite number of controls acting on a part of the boundary through Neumann/Robin boundary conditions is sufficient to stabilize the full nonlinear equations in a neighborhood of this steady state solution. Dirichlet boundary conditions are imposed on the rest of the boundary. We prove that a stabilizing feedback control law can be obtained by solving a Linear Quadratic Regulator (LQR) problem for the linearized Boussinesq equations. Numerical result are provided for a 2D problem to illustrate the ideas.
Meeting Name
Advances in Scientific Computing and Applied Mathematics
Mathematics and Statistics
Research Center/Lab(s)
Center for High Performance Computing Research
Keywords and Phrases
  • Boundary Conditions,
  • Feedback Control,
  • Laser Diagnostics,
  • Partial Differential Equations,
  • Stabilization,
  • Dirichlet Boundary Condition,
  • Exponential Stabilization,
  • Feedback Stabilization,
  • Linear Quadratic Regulator,
  • Linearized Boussinesq Equations,
  • Nonlinear Boussinesq Equations,
  • Stabilizing Feedback Controls,
  • Thermal Fluids,
  • Nonlinear Equations
Document Type
Article - Conference proceedings
Document Version
File Type
© 2016 Elsevier Ltd, All rights reserved.
Publication Date
Citation Information
John A. Burns, Xiaoming He and Weiwei Hu. "Feedback Stabilization of a Thermal Fluid System with Mixed Boundary Control" Computers and Mathematics with Applications Vol. 71 Iss. 11 (2016) p. 2170 - 2191 ISSN: 8981221
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