**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.

Publication# A Class of Adaptive Nonlinear Hoo Filters with guaranteed I_2 Stability

Abstract

We pose an identification problem that involves a nonlinear output equation and proceed to suggest an approximate linear solution. The approximation is obtained in two stages. We first replace the nonlinear functional by a linear relation, thus reducing the problem to a standard linear Hoo-setting. We then suggest constructing an approximation that results in an overall feedback structure in order to meet the desired robustness and stability properties. By combining the linear Hoo solution with a widely-used small gain theorem we show, under suitable conditions, that the approximate solution still leads to a filter with guaranteed I_2 stability. An examaple in the context of pole-zero (or IIR) system identificaiton is discussed in details. The proposed structure is also shown to include, as special cases, several adaptive filters that have been employed earlier in the literature in the context of IIR modeling. In particular, two algorithms due to Feintuch and Landau, as well as the so-called pseudo-linear regression algorithm, are discussed within the framework proposed herein.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related MOOCs (25)

Related concepts (34)

Related publications (43)

Ontological neighbourhood

Algebra (part 1)

Un MOOC francophone d'algèbre linéaire accessible à tous, enseigné de manière rigoureuse et ne nécessitant aucun prérequis.

Algebra (part 1)

Un MOOC francophone d'algèbre linéaire accessible à tous, enseigné de manière rigoureuse et ne nécessitant aucun prérequis.

Algebra (part 2)

Un MOOC francophone d'algèbre linéaire accessible à tous, enseigné de manière rigoureuse et ne nécessitant aucun prérequis.

Digital filter

In signal processing, a digital filter is a system that performs mathematical operations on a sampled, discrete-time signal to reduce or enhance certain aspects of that signal. This is in contrast to the other major type of electronic filter, the analog filter, which is typically an electronic circuit operating on continuous-time analog signals. A digital filter system usually consists of an analog-to-digital converter (ADC) to sample the input signal, followed by a microprocessor and some peripheral components such as memory to store data and filter coefficients etc.

Stability theory

In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation, for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature at a later time as a result of the maximum principle. In partial differential equations one may measure the distances between functions using Lp norms or the sup norm, while in differential geometry one may measure the distance between spaces using the Gromov–Hausdorff distance.

Overdetermined system

In mathematics, a system of equations is considered overdetermined if there are more equations than unknowns. An overdetermined system is almost always inconsistent (it has no solution) when constructed with random coefficients. However, an overdetermined system will have solutions in some cases, for example if some equation occurs several times in the system, or if some equations are linear combinations of the others. The terminology can be described in terms of the concept of constraint counting.

This paper deals with the initial value problem for a semilinear wave equation on a bounded domain and solutions are required to vanish on the boundary of this domain. The essential feature of the situation considered here is that the ellipticity of the sp ...

2024Alireza Karimi, Mert Eyuboglu, Nathan Russell Powell

This paper proposes a data-driven control design method for nonlinear systems that builds upon the Koopman operator framework. In particular, the Koopman operator is used to lift the nonlinear dynamics to a higher-dimensional space where the so-called obse ...

2024The progress towards intelligent systems and digitalization relies heavily on the use of automation technology. However, the growing diversity of control objects presents significant challenges for traditional control approaches, as they are highly depende ...