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.
Bibliographical noteFunding Information:
This research was supported in part by the DOE contract DE-EE0004261 under subcontract # 4345-VT-DOE-4261 from Penn State University .
- Feedback control
- Partial differential equations
- Thermal fluid systems