Displaying similar documents to “Feedback stabilization of the 2-D and 3-D Navier-Stokes equations based on an extended system”

Feedback stabilization of the 2-D and 3-D Navier-Stokes equations based on an extended system

Mehdi Badra (2008)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We study the local exponential stabilization of the 2D and 3D Navier-Stokes equations in a bounded domain, around a given steady-state flow, by means of a boundary control. We look for a control so that the solution to the Navier-Stokes equations be a strong solution. In the 3D case, such solutions may exist if the Dirichlet control satisfies a compatibility condition with the initial condition. In order to determine a feedback law satisfying such a compatibility condition, we consider...

Feedback stabilization of Navier–Stokes equations

Viorel Barbu (2003)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

One proves that the steady-state solutions to Navier–Stokes equations with internal controllers are locally exponentially stabilizable by linear feedback controllers provided by a L Q control problem associated with the linearized equation.

Receding horizon optimal control for infinite dimensional systems

Kazufumi Ito, Karl Kunisch (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

The receding horizon control strategy for dynamical systems posed in infinite dimensional spaces is analysed. Its stabilising property is verified provided control Lyapunov functionals are used as terminal penalty functions. For closed loop dissipative systems the terminal penalty can be chosen as quadratic functional. Applications to the Navier–Stokes equations, semilinear wave equations and reaction diffusion systems are given.

Optimal control of linearized compressible Navier–Stokes equations

Shirshendu Chowdhury, Mythily Ramaswamy (2013)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We study an optimal boundary control problem for the two dimensional unsteady linearized compressible Navier–Stokes equations in a rectangle. The control acts through the Dirichlet boundary condition. We first establish the existence and uniqueness of the solution for the two-dimensional unsteady linearized compressible Navier–Stokes equations in a rectangle with inhomogeneous Dirichlet boundary data, not necessarily smooth. Then, we prove the existence and uniqueness of the optimal...

Distributed control for multistate modified Navier-Stokes equations

Nadir Arada (2013)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

The aim of this paper is to establish necessary optimality conditions for optimal control problems governed by steady, incompressible Navier-Stokes equations with shear-dependent viscosity. The main difficulty derives from the fact that equations of this type may exhibit non-uniqueness of weak solutions, and is overcome by introducing a family of approximate control problems governed by well posed generalized Stokes systems and by passing to the limit in the corresponding optimality...

Feedback stabilization of Navier–Stokes equations

Viorel Barbu (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

One proves that the steady-state solutions to Navier–Stokes equations with internal controllers are locally exponentially stabilizable by linear feedback controllers provided by a control problem associated with the linearized equation.