Feedback stabilization of a thermal fluid system with mixed boundary control

John A. Burns, Xiaoming He, Weiwei Hu

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


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 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.

Original languageEnglish (US)
Pages (from-to)2170-2191
Number of pages22
JournalComputers and Mathematics with Applications
Issue number11
StatePublished - Jun 1 2016

Bibliographical note

Publisher Copyright:
© 2016 Elsevier Ltd.


  • Feedback control
  • Partial differential equations
  • Thermal fluid systems


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