455 research outputs found
Stabilization of 2D Navier-Stokes equations by means of actuators with locally supported vorticity
Exponential stabilization to time-dependent trajectories for the
incompressible Navier-Stokes equations is achieved with explicit feedback
controls. The fluid is contained in two-dimensional spatial domains and the
control force is, at each time instant, a linear combination of a finite number
of given actuators. Each actuator has its vorticity supported in a small
subdomain. The velocity field is subject to Lions boundary conditions.
Simulations are presented showing the stabilizing performance of the proposed
feedback. The results also apply to a class of observer design problems.Comment: 9 figure
Stabilizability for nonautonomous linear parabolic equations with actuators as distributions
The stabilizability of a general class of abstract parabolic-like equations
is investigated, with a finite number of actuators. This class includes the
case of actuators given as delta distributions located at given points in the
spatial domain of concrete parabolic equations. A stabilizing feedback control
operator is constructed and given in explicit form. Then, an associated optimal
control is considered and the corresponding Riccati feedback is investigated.
Results of simulations are presented showing the stabilizing performance of
both explicit and Riccati feedbacks.Comment: 7 figure
Approximate Controllability for Navier–Stokes Equations in 3D Rectangles Under Lions Boundary Conditions
The 3D Navier–Stokes system, under Lions boundary conditions, is proven to be approximately controllable provided a suitable saturating set does exist. An explicit saturating set for 3D rectangles is given.acceptedVersionPeer reviewe
Stabilization to trajectories for parabolic equations
Both internal and boundary feedback exponential stabilization to trajectories for semilinear parabolic equations in a given bounded domain are addressed. The values of the controls are linear combinations of a finite number of actuators which are supported in a small region. A condition on the family of actuators is given which guarantees the local stabilizability of the control system. It is shown that a linearization-based Riccati feedback stabilizing controller can be constructed. The results of numerical simulations are presented and discussed.acceptedVersionPeer reviewe
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