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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...

Matrix quadratic equations column/row reduced factorizations and an inertia theorem for matrix polynomials

Irina Karelin, Leonid Lerer (2001)

International Journal of Applied Mathematics and Computer Science

It is shown that a certain Bezout operator provides a bijective correspondence between the solutions of the matrix quadratic equation and factorizatons of a certain matrix polynomial (which is a specification of a Popov-type function) into a product of row and column reduced polynomials. Special attention is paid to the symmetric case, i.e. to the Algebraic Riccati Equation. In particular, it is shown that extremal solutions of such equations correspond to spectral factorizations of . The proof...

Monomial subdigraphs of reachable and controllable positive discrete-time systems

Rafael Bru, Louis Caccetta, Ventsi Rumchev (2005)

International Journal of Applied Mathematics and Computer Science

A generic structure of reachable and controllable positive linear systems is given in terms of some characteristic components (monomial subdigraphs) of the digraph of a non-negative a pair. The properties of monomial subdigraphs are examined and used to derive reachability and controllability criteria in a digraph form for the general case when the system matrix may contain zero columns. The graph-theoretic nature of these criteria makes them computationally more efficient than their known equivalents....

Multiplicity of polynomials on trajectories of polynomial vector fields in C 3

Andrei Gabrielov, Frédéric Jean, Jean-Jacques Risler (1998)

Banach Center Publications

Let ξ be a polynomial vector field on n with coefficients of degree d and P be a polynomial of degree p. We are interested in bounding the multiplicity of a zero of a restriction of P to a non-singular trajectory of ξ, when P does not vanish identically on this trajectory. Bounds doubly exponential in terms of n are already known ([9,5,10]). In this paper, we prove that, when n=3, there is a bound of the form p + 2 p ( p + d - 1 ) 2 . In Control Theory, such a bound can be used to give an estimate of the degree of nonholonomy...

Neutral functional integrodifferential control systems in Banach spaces

Krishnan Balachandran, E. Radhakrishnan Anandhi (2003)

Kybernetika

Sufficient conditions for controllability of neutral functional integrodifferential systems in Banach spaces with initial condition in the phase space are established. The results are obtained by using the Schauder fixed point theorem. An example is provided to illustrate the theory.

New coprime polynomial fraction representation of transfer function matrix

Yelena M. Smagina (2001)

Kybernetika

A new form of the coprime polynomial fraction C ( s ) F ( s ) - 1 of a transfer function matrix G ( s ) is presented where the polynomial matrices C ( s ) and F ( s ) have the form of a matrix (or generalized matrix) polynomials with the structure defined directly by the controllability characteristics of a state- space model and Markov matrices H B , H A B , ...

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