Feedback Stabilization of a Thermal Fluid System with Mixed Boundary Control


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

International Standard Serial Number (ISSN)


Document Type

Article - Conference proceedings

Document Version


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© 2016 Elsevier Ltd, All rights reserved.

Publication Date

01 Jun 2016