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Your search keyword '"Takéo Takahashi"' showing total 5 results
Start Over Author "Takéo Takahashi" Publisher edp sciences
5 results on '"Takéo Takahashi"'

1. Controllability Results for Cascade Systems of m Coupled N-Dimensional Stokes and Navier-Stokes Systems by N – 1 Scalar Controls

Author

Takéo Takahashi, Luz de Teresa, and Yingying Wu-Zhang

Subjects
Computational Mathematics, Control and Optimization, Control and Systems Engineering
Abstract

In this paper we deal with the controllability properties of a system of m coupled Stokes systems or m coupled Navier-Stokes systems. We show the null-controllability of such systems in the case where the coupling is in a cascade form and when the control acts only on one of the systems. Moreover, we impose that this control has a vanishing component so that we control a m × N state (corresponding to the velocities of the fluids) by N — 1 distributed scalar controls. The proof of the controllability of the coupled Stokes systems is based on a Carleman estimate for the adjoint system. The local null-controllability of the coupled Navier-Stokes systems is then obtained by means of the source term method and a Banach fixed point.

Published
2023
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2. Optimal boundary control for steady motions of a self-propelled body in a Navier-Stokes liquid

Author

Toshiaki Hishida, Takéo Takahashi, Ana L. Silvestre, Nagoya University, Center for Computacional and Stochastic Mathematics (CEMAT), Instituto Superior Técnico, Universidade Técnica de Lisboa (IST), Departamento de Matemática [Lisbonne] (DM/IST), Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), T. Hishida is partially supported by Grant-in-Aid for Scientific Research, 18K03363, from JSPS., A. L. Silvestre acknowledges the financial support of the Portuguese FCT - Fundação para a Ciência e a Tecnologia, through the projects UIDB/04621/2020 and UIDP/04621/2020 of CEMAT/IST-ID., T. Takahashi is partially supported by the project IFSMACS ANR-15-CE40-0010, financed by the French Agence Nationale de la Recherche, and ANR-15-CE40-0010,IFSMACS,Interaction Fluide-Structure : Modélisation, analyse, contrôle et simulation(2015)

Subjects
Control and Optimization, Gâteaux derivative, 2010 Mathematics Subject Classification : 76D05, 49K21, 76D55, 49J21, Motion (geometry), Boundary (topology), 01 natural sciences, Domain (mathematical analysis), Rotating body, Mathematics - Analysis of PDEs, Drag reduction, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 3-D Navier-Stokes equations, Self-propelled motion, 0101 mathematics, Mathematics - Optimization and Control, Mathematics, Boundary control, 010102 general mathematics, Mathematical analysis, Rigid body, 010101 applied mathematics, Computational Mathematics, Control and Systems Engineering, Drag, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Unit (ring theory), Exterior domain, Reference frame
Abstract

Consider a rigid body 𝒮 ⊂ ℝ3 immersed in an infinitely extended Navier-Stokes liquid and the motion of the body-fluid interaction system described from a reference frame attached to 𝒮. We are interested in steady motions of this coupled system, where the region occupied by the fluid is the exterior domain Ω = ℝ3 \ 𝒮. This paper deals with the problem of using boundary controls v*, acting on the whole ∂Ω or just on a portion Γ of ∂Ω, to generate a self-propelled motion of 𝒮 with a target velocity V (x) := ξ + ω × x and to minimize the drag about 𝒮. Firstly, an appropriate drag functional is derived from the energy equation of the fluid and the problem is formulated as an optimal boundary control problem. Then the minimization problem is solved for localized controls, such that supp v*⊂ Γ, and for tangential controls, i.e, v*⋅ n|∂Ω = 0, where n is the outward unit normal to ∂Ω. We prove the existence of optimal solutions, justify the Gâteaux derivative of the control-to-state map, establish the well-posedness of the corresponding adjoint equations and, finally, derive the first order optimality conditions. The results are obtained under smallness restrictions on the objectives |ξ| and |ω| and on the boundary controls.

Published
2020
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3. On the Fattorini criterion for approximate controllability and stabilizability of parabolic systems

Author

Mehdi Badra, Takéo Takahashi, Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS), Robust control of infinite dimensional systems and applications (CORIDA), Institut Élie Cartan de Nancy (IECN), Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), CORIDA, Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est, and Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM)

Subjects
0209 industrial biotechnology, Control and Optimization, parabolic equation, 02 engineering and technology, Type (model theory), 01 natural sciences, Set (abstract data type), coupled, Continuation, Mathematics - Analysis of PDEs, [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM], 020901 industrial engineering & automation, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Applied mathematics, Stokes and MHD system, 0101 mathematics, Mathematics, Partial differential equation, 010102 general mathematics, Linear system, stabilizability, Approximate controllability, AMS subject classifications 93B05, 93D15, 35Q30, 76D05, 76D07, 76D55, 93B52, 93C20, Controllability, Computational Mathematics, Nonlinear system, Control and Systems Engineering, Bounded function, finite dimensional control, Analysis of PDEs (math.AP)
Abstract

International audience; In this paper, we consider the well-known Fattorini's criterion for approximate controllability of infinite dimensional linear systems of type $y'=A y+Bu$. We precise the result proved by H. O. Fattorini in \cite{Fattorini1966} for bounded input $B$, in the case where $B$ can be unbounded or in the case of finite-dimensional controls. More precisely, we prove that if Fattorini's criterion is satisfied and if the set of geometric multiplicities of $A$ is bounded then approximate controllability can be achieved with finite dimensional controls. An important consequence of this result consists in using the Fattorini's criterion to obtain the feedback stabilizability of linear and nonlinear parabolic systems with feedback controls in a finite dimensional space. In particular, for systems described by partial differential equations, such a criterion reduces to a unique continuation theorem for a stationary system. We illustrate such a method by tackling some coupled Navier-Stokes type equations (MHD system and micropolar fluid system) and we sketch a systematic procedure relying on Fattorini's criterion for checking stabilizability of such nonlinear systems. In that case, the unique continuation theorems rely on local Carleman inequalities for stationary Stokes type systems.

Published
2014
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4. Single input controllability of a simplified fluid-structure interaction model

Author

Yuning Liu, Marius Tucsnak, Takéo Takahashi, Universität Regensburg (UR), Robust control of infinite dimensional systems and applications (CORIDA), Institut Élie Cartan de Nancy (IECN), Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), CORIDA, Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Inria Nancy - Grand Est, and Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM)

Subjects
0209 industrial biotechnology, Control and Optimization, 010102 general mathematics, Mathematical analysis, Scalar (physics), Control variable, fluid-structure interaction, 35L10, 65M60, 93B05, 93B40, 93D15, 02 engineering and technology, Null-controllability, Rigid body, 01 natural sciences, Parabolic partial differential equation, Controllability, Computational Mathematics, Nonlinear system, viscous Burgers equation, 020901 industrial engineering & automation, Control and Systems Engineering, Fluid–structure interaction, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, Spectral method, Mathematics
Abstract

International audience; In this paper we study a controllability problem for a simpli ed one dimensional model for the motion of a rigid body in a viscous uid. The control variable is the velocity of the uid at one end. One of the novelties brought in with respect to the existing literature consists in the fact that we use a single scalar control. Moreover, we introduce a new methodology, which can be used for other nonlinear parabolic systems, independently of the techniques previously used for the linearized problem. This methodology is based on an abstract argument for the null controllability of parabolic equations in the presence of source terms and it avoids tackling linearized problems with time dependent coefficients.

Published
2012
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5. Towards the simulation of dense suspensions: a numerical tool

Author

Sébastien Martin, Bertrand Maury, Sylvain Faure, Takéo Takahashi, Laboratoire de Mathématiques d'Orsay (LM-Orsay), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), Robust control of infinite dimensional systems and applications (CORIDA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), CORIDA, and Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est

Subjects
Materials science, Interaction forces, Stokesian dynamics, Nanotechnology, Mechanics, Viscous liquid, 01 natural sciences, 010305 fluids & plasmas, Contact force, Physics::Fluid Dynamics, Condensed Matter::Soft Condensed Matter, Rheology, 0103 physical sciences, Lubrication, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], SPHERES, 010306 general physics, Suspension (vehicle)
Abstract

International audience; We present a numerical tool which aims at investigating the rheology of dense suspensions of entities such as spheres, red blood cells, polymer chains, or any kind of rigid or deformable bodies, in a viscous fluid. We shall pay a special attention to the short-range interactions between those entities (contact forces, lubrication forces). As for the fluid itself, our strategy consists in avoiding the direct and costly solution of the Stokes equations by integrating only the interaction forces which are likely to play a significant role in the overall behaviour of the suspension, in the spirit of Stokesian Dynamics. We present some preliminary results for suspensions of spheres, Red Blood Cells, and polymer-like chains.

Published
2009
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