Abstract
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 language | English (US) |
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Pages (from-to) | 2170-2191 |
Number of pages | 22 |
Journal | Computers and Mathematics with Applications |
Volume | 71 |
Issue number | 11 |
DOIs | |
State | Published - Jun 1 2016 |
Bibliographical note
Publisher Copyright:© 2016 Elsevier Ltd.
Keywords
- Feedback control
- Partial differential equations
- Thermal fluid systems