Displaying similar documents to “Optimal control of linearized compressible Navier–Stokes equations”

Distributed control for multistate modified Navier-Stokes equations

Nadir Arada (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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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...

Dirichlet control of unsteady Navier–Stokes type system related to Soret convection by boundary penalty method

S. S. Ravindran (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, we study the boundary penalty method for optimal control of unsteady Navier–Stokes type system that has been proposed as an alternative for Dirichlet boundary control. Existence and uniqueness of solutions are demonstrated and existence of optimal control for a class of optimal control problems is established. The asymptotic behavior of solution, with respect to the penalty parameter , is studied. In particular, we prove convergence of solutions of penalized control problem...

Globalization of SQP-Methods in Control of the Instationary Navier-Stokes Equations

Michael Hintermüller, Michael Hinze (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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A numerically inexpensive globalization strategy of sequential quadratic programming methods (SQP-methods) for control of the instationary Navier Stokes equations is investigated. Based on the proper functional analytic setting a convergence analysis for the globalized method is given. It is argued that the formidable SQP-step can be decomposed into linear primal and linear adjoint systems, which is amenable for existing CFL-software. A report on a numerical test demonstrates the...

On exact controllability for the Navier-Stokes equations

O. Yu. Imanuvilov (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We study the local exact controllability problem for the Navier-Stokes equations that describe an incompressible fluid flow in a bounded domain with control distributed in an arbitrary fixed subdomain. The result that we obtain in this paper is as follows. Suppose that we have a given stationary point of the Navier-Stokes equations and our initial condition is sufficiently close to it. Then there exists a locally distributed control such that in a given moment of time the solution of...

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

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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...

Receding horizon optimal control for infinite dimensional systems

Kazufumi Ito, Karl Kunisch (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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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.