356 research outputs found
La borne de Jacobi pour une diffiété définie par un système quasi régulier
Note soumise aux CRAS de ParisWe show that Jacobi's bound for the order of a system of ordinary differential equations stands in the case of a diffiety defined by a quasi-regular system. We extend the result when there are less equations than variables and characterize the case when the bound is reached
A Geometric Index Reduction Method for Implicit Systems of Differential Algebraic Equations
This paper deals with the index reduction problem for the class of
quasi-regular DAE systems. It is shown that any of these systems can be
transformed to a generically equivalent first order DAE system consisting of a
single purely algebraic (polynomial) equation plus an under-determined ODE
(that is, a semi-explicit DAE system of differentiation index 1) in as many
variables as the order of the input system. This can be done by means of a
Kronecker-type algorithm with bounded complexity
Flat singularities of chained systems, illustrated with an aircraft model
We consider flat differential control systems for which there exist flat
outputs that are part of the state variables and study them using Jacobi bound.
We introduce a notion of saddle Jacobi bound for an ordinary differential
system for equations in variables. Systems with saddle Jacobi number
generalize various notions of chained and diagonal systems and form the widest
class of systems admitting subsets of state variables as flat output, for which
flat parametrization may be computed without differentiating the initial
equations. We investigate apparent and intrinsic flat singularities of such
systems. As an illustration, we consider the case of a simplified aircraft
model, providing new flat outputs and showing that it is flat at all points
except possibly in stalling conditions. Finally, we present numerical
simulations showing that a feedback using those flat outputs is robust to
perturbations and can also compensate model errors, when using a more realistic
aerodynamic model.Comment: 36 pages, 8 figure
Representation for the radical of a finitely generated differential ideal
International audienceWe give an algorithm which represents the radical J of a finitely generated differential ideal as an intersection of radical differential ideals. The computed representation provides an algorithm for testing membership in J. This algorithm works over either an ordinary or a partial differential polynomial ring of characteristic zero. It has been programmed. We also give a method to obtain a obtain a characteristic set of J, if the ideal is prime
Nearfield Acoustic Holography using sparsity and compressive sampling principles
Regularization of the inverse problem is a complex issue when using
Near-field Acoustic Holography (NAH) techniques to identify the vibrating
sources. This paper shows that, for convex homogeneous plates with arbitrary
boundary conditions, new regularization schemes can be developed, based on the
sparsity of the normal velocity of the plate in a well-designed basis, i.e. the
possibility to approximate it as a weighted sum of few elementary basis
functions. In particular, these new techniques can handle discontinuities of
the velocity field at the boundaries, which can be problematic with standard
techniques. This comes at the cost of a higher computational complexity to
solve the associated optimization problem, though it remains easily tractable
with out-of-the-box software. Furthermore, this sparsity framework allows us to
take advantage of the concept of Compressive Sampling: under some conditions on
the sampling process (here, the design of a random array, which can be
numerically and experimentally validated), it is possible to reconstruct the
sparse signals with significantly less measurements (i.e., microphones) than
classically required. After introducing the different concepts, this paper
presents numerical and experimental results of NAH with two plate geometries,
and compares the advantages and limitations of these sparsity-based techniques
over standard Tikhonov regularization.Comment: Journal of the Acoustical Society of America (2012
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