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We study the stabilizability of time-periodic parabolic control systems with unbounded control operators. We give necessary and sufficient conditions for stabilizability which extend to the case of unbounded control operators, and which sharpen, ...

We study the stabilization of a fluid-structure interaction system around an unstable stationary solution. The system consists of coupling the incompressible Navier--Stokes equations, in a two-dimensional polygonal domain with mixed boundary conditions, ...

We study the boundary feedback stabilization, around an unstable stationary solution, of a two dimensional fluid flow described by the Navier--Stokes equations with mixed boundary conditions. The control is a localized Dirichlet boundary control. A ...

In this paper we consider the one-dimensional compressible Navier--Stokes system linearized about a constant steady state $(Q_0, 0)$ with $Q_0 > 0$. We study the controllability and stabilizability of this linearized system. We establish that the linearized ...

We study the robust or $H^\infty$ exponential stabilization of the linearized Navier-Stokes equations around an unstable stationary solution in a two-dimensional domain $\Omega$. The disturbance is an unknown perturbation in the boundary condition of ...

We study a system coupling the incompressible Navier-Stokes equations in a 2D rectangular-type domain with a damped Euler-Bernoulli beam equation, where the beam is a part of the upper boundary of the domain occupied by the fluid. Due to the deformation ...

We study the exact controllability of a fluid-structure model. The fluctuations of fluid velocity and pressure in a domain $\Omega$ are described by a potential $\phi$, and the structure is a membrane located in a part $\Gamma_s$ of the boundary $\Gamma=...

We obtain error estimates for the numerical approximation of a distributed control problem governed by the stationary Navier-Stokes equations, with pointwise control constraints. We show that the $L^2$-norm of the error for the control is of order $h^2$ ...

We study the numerical approximation of boundary optimal control problems governed by semilinear elliptic partial differential equations with pointwise constraints on the control. The control is the trace of the state on the boundary of the domain, ...

We study the exponential stabilization of the linearized Navier--Stokes equations around an unstable stationary solution, by means of a feedback boundary control, in dimension 2 or 3. The feedback law is determined by solving a linear-quadratic control ...

We consider optimal control problems for hyperbolic equations with controls in Neumann boundary conditions with pointwise constraints on the control and state functions. Focusing on the multidimensional wave equation with a nonlinear term, we derive new ...

\noindent We consider control problems governed by semilinear parabolic equations in the presence of pointwise mixed control-state constraints. We obtain optimality conditions with finitely additive measures as multipliers associated to the mixed ...

This paper deals with optimal control problems of semilinear parabolic equations with pointwise state constraints and coupled integral state-control constraints. We obtain necessary optimality conditions in the form of a Pontryagin's minimum principle ...

We consider systems governed by a nonlinear parabolic equation with a distributed control and a disturbance in the initial condition. We prove the existence of solutions to a corresponding minimax problem, and we obtain necessary optimality conditions ...

In this paper we study a minimax control problem for parabolic equations in the presence of pointwise state constraints. The terminology minimax here refers to a cost functional defined with a $L^{\infty}$-norm. The directional derivatives of the $L^{\...

This paper deals with optimal control problems of parabolic equations in the presence of pointwise state constraints. We consider bounded controls which act in the initial condition of the state equation. The state variable is a bounded continuous ...

This paper deals with optimal control problems governed by semilinear parabolic equations with pointwise state constraints and unbounded controls. Under some strong stability assumption, we obtain necessary optimality conditions in the form of a ...