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Local controllability of a 1-D tank containing a fluid modeled by the shallow water equations

Jean-Michel Coron (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a 1-D tank containing an inviscid incompressible irrotational fluid. The tank is subject to the control which consists of horizontal moves. We assume that the motion of the fluid is well-described by the Saint–Venant equations (also called the shallow water equations). We prove the local controllability of this nonlinear control system around any steady state. As a corollary we get that one can move from any steady state to any other steady state.

Local controllability of a 1-D tank containing a fluid modeled by the shallow water equations

Jean-Michel Coron (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a 1-D tank containing an inviscid incompressible irrotational fluid. The tank is subject to the control which consists of horizontal moves. We assume that the motion of the fluid is well-described by the Saint–Venant equations (also called the shallow water equations). We prove the local controllability of this nonlinear control system around any steady state. As a corollary we get that one can move from any steady state to any other steady state.

Local dependency in networks

Miloš Kudělka, Šárka Zehnalová, Zdeněk Horák, Pavel Krömer, Václav Snášel (2015)

International Journal of Applied Mathematics and Computer Science

Many real world data and processes have a network structure and can usefully be represented as graphs. Network analysis focuses on the relations among the nodes exploring the properties of each network. We introduce a method for measuring the strength of the relationship between two nodes of a network and for their ranking. This method is applicable to all kinds of networks, including directed and weighted networks. The approach extracts dependency relations among the network's nodes from the structure...

Local detection of defects from image sequences

Ewaryst Rafajłowicz, Marek Wnuk, Wojciech Rafajłowicz (2008)

International Journal of Applied Mathematics and Computer Science

Our aim is to discuss three approaches to the detection of defects in continuous production processes, which are based on local methods of processing image sequences. These approaches are motivated by and applicable to images of hot metals or other surfaces, which are uniform at a macroscopic level, when defects are not present. The first of them is based on the estimation of fractal dimensions of image cross-sections. The second and third approaches are compositions of known techniques, which are...

Local exact controllability for the 1 -d compressible Navier-Stokes equations

Sylvain Ervedoza (2011/2012)

Séminaire Laurent Schwartz — EDP et applications

In this talk, I will present a recent result obtained in [6] with O. Glass, S. Guerrero and J.-P. Puel on the local exact controllability of the 1 -d compressible Navier-Stokes equations. The goal of these notes is to give an informal presentation of this article and we refer the reader to it for extensive details.

Local exact controllability to the trajectories of the Navier-Stokes system with nonlinear Navier-slip boundary conditions

Sergio Guerrero (2006)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we deal with the local exact controllability of the Navier-Stokes system with nonlinear Navier-slip boundary conditions and distributed controls supported in small sets. In a first step, we prove a Carleman inequality for the linearized Navier-Stokes system, which leads to null controllability of this system at any time T>0. Then, fixed point arguments lead to the deduction of a local result concerning the exact controllability to the trajectories of the Navier-Stokes system.

Local null controllability of a fluid-solid interaction problem in dimension 3

Muriel Boulakia, Sergio Guerrero (2013)

Journal of the European Mathematical Society

We are interested by the three-dimensional coupling between an incompressible fluid and a rigid body. The fluid is modeled by the Navier-Stokes equations, while the solid satisfies the Newton's laws. In the main result of the paper we prove that, with the help of a distributed control, we can drive the fluid and structure velocities to zero and the solid to a reference position provided that the initial velocities are small enough and the initial position of the structure is close to the reference...

Local null controllability of a two-dimensional fluid-structure interaction problem

Muriel Boulakia, Axel Osses (2008)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we prove a controllability result for a fluid-structure interaction problem. In dimension two, a rigid structure moves into an incompressible fluid governed by Navier-Stokes equations. The control acts on a fixed subset of the fluid domain. We prove that, for small initial data, this system is null controllable, that is, for a given T > 0 , the system can be driven at rest and the structure to its reference configuration at time T . To show this result, we first consider a linearized system....

Local null controllability of a two-dimensional fluid-structure interaction problem

Muriel Boulakia, Axel Osses (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we prove a controllability result for a fluid-structure interaction problem. In dimension two, a rigid structure moves into an incompressible fluid governed by Navier-Stokes equations. The control acts on a fixed subset of the fluid domain. We prove that, for small initial data, this system is null controllable, that is, for a given T > 0, the system can be driven at rest and the structure to its reference configuration at time T. To show this result, we first consider a linearized system....

Local small time controllability and attainability of a set for nonlinear control system

Mikhail Krastanov, Marc Quincampoix (2001)

ESAIM: Control, Optimisation and Calculus of Variations

In the present paper, we study the problem of small-time local attainability (STLA) of a closed set. For doing this, we introduce a new concept of variations of the reachable set well adapted to a given closed set and prove a new attainability result for a general dynamical system. This provide our main result for nonlinear control systems. Some applications to linear and polynomial systems are discussed and STLA necessary and sufficient conditions are obtained when the considered set is a hyperplane....

Local small time controllability and attainability of a set for nonlinear control system

Mikhail Krastanov, Marc Quincampoix (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In the present paper, we study the problem of small-time local attainability (STLA) of a closed set. For doing this, we introduce a new concept of variations of the reachable set well adapted to a given closed set and prove a new attainability result for a general dynamical system. This provide our main result for nonlinear control systems. Some applications to linear and polynomial systems are discussed and STLA necessary and sufficient conditions are obtained when the considered set...

Local stability conditions for discrete-time cascade locally recurrent neural networks

Krzysztof Patan (2010)

International Journal of Applied Mathematics and Computer Science

The paper deals with a specific kind of discrete-time recurrent neural network designed with dynamic neuron models. Dynamics are reproduced within each single neuron, hence the network considered is a locally recurrent globally feedforward. A crucial problem with neural networks of the dynamic type is stability as well as stabilization in learning problems. The paper formulates local stability conditions for the analysed class of neural networks using Lyapunov's first method. Moreover, a stabilization...

Localization in wireless sensor networks: Classification and evaluation of techniques

Ewa Niewiadomska-Szynkiewicz (2012)

International Journal of Applied Mathematics and Computer Science

Recent advances in technology have enabled the development of low cost, low power and multi functional wireless sensing devices. These devices are networked through setting up a Wireless Sensor Network (WSN). Sensors that form a WSN are expected to be remotely deployed in large numbers and to self-organize to perform distributed sensing and acting tasks. WSNs are growing rapidly in both size and complexity, and it is becoming increasingly difficult to develop and investigate such large and complex...

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