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.
J. A. Burns et al., "Feedback Stabilization of a Thermal Fluid System with Mixed Boundary Control," Computers and Mathematics with Applications, vol. 71, no. 11, pp. 2170-2191, Elsevier Ltd, Jun 2016.
The definitive version is available at https://doi.org/10.1016/j.camwa.2016.01.011
Advances in Scientific Computing and Applied Mathematics
Mathematics and Statistics
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)
Article - Conference proceedings
© 2016 Elsevier Ltd, All rights reserved.
01 Jun 2016