Displaying similar documents to “Homogeneous approximations and local observer design”

Separation principle for nonlinear systems using a bilinear approximation

Mohamed Ali Hammami, Hamadi Jerbi (2001)

Kybernetika

Similarity:

In this paper, we study the local stabilization problem of a class of planar nonlinear systems by means of an estimated state feedback law. Our approach is to use a bilinear approximation to establish a separation principle.

Free algebras and noncommutative power series in the analysis of nonlinear control systems: an application to approximation problems

Grigory M. Sklyar, Svetlana Yu. Ignatovich

Similarity:

The paper contains a consistent presentation of the approach developed by the authors to analysis of nonlinear control systems, which exploits ideas and techniques of formal power series of independent noncommuting variables and the corresponding free algebras. The main part of the paper was conceived with a view of comparing our results with the results obtained by use of the differential-geometric approach. We consider control-linear systems with m controls. In a free associative algebra...

Generalizations of the Finite Element Method

Marc Schweitzer (2012)

Open Mathematics

Similarity:

This paper is concerned with the generalization of the finite element method via the use of non-polynomial enrichment functions. Several methods employ this general approach, e.g. the extended finite element method and the generalized finite element method. We review these approaches and interpret them in the more general framework of the partition of unity method. Here we focus on fundamental construction principles, approximation properties and stability of the respective numerical...

Separation principle for nonlinear systems: a bilinear approach

Mohamed Hammami, Hamadi Jerbi (2001)

International Journal of Applied Mathematics and Computer Science

Similarity:

In this paper we investigate the local stabilizability of single-input nonlinear affine systems by means of an estimated state feedback law given by a bilinear observer. The associated bilinear approximating system is assumed to be observable for any input and stabilizable by a homogeneous feedback law of degree zero. Furthermore, we discuss the case of planar systems which admit bad inputs (i.e. the ones that make bilinear systems unobservable). A separation principle for such systems...

Greedy Algorithms for Adaptive Approximation

Albert Cohen (2009)

Bollettino dell'Unione Matematica Italiana

Similarity:

We discuss the performances of greedy algorithms for two problems of numerical approximation. The first one is the best approximation of an arbitrary function by an N-terms linear combination of simple functions adaptively picked within a large dictionary. The second one is the approximation of an arbitrary function by a piecewise polynomial function on an optimally adapted triangulation of cardinality N. Performance is measured in terms of convergence rate with respect to the number...