Nonparametric Estimation and Adaptive Control of Functional Autoregressive Models

Portier, Bruno; Oulidi, Abderrahim

doi:10.1137/s0363012997316676

Cited by 16 publications

(9 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This result states the convergence of the estimatorf N over dilating sets. It is a particular case of a more general result of [31] who proved the convergence of the nonparametric estimatorf N in a controlled model. Complete proof with general noises is also provided in [15].…”

Section: Resultsmentioning

confidence: 94%

“…Most of the regression estimators met in the literature deal with non-controlled models and treat the case of stationary processes [6]. Duflo [7] and Senoussi [34] were the first to give convergence results for regression estimation in a controlled framework and Portier and Oulidi [31] obtained the convergence of a kernel estimator over dilating sets (see below). In a change detection context, nonparametric kernel approaches were notably used for iid observations.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Change detection for uncertain autoregressive dynamic models through nonparametric estimation

Hilgert

Verdier

Vila

2016

Statistical Methodology

View full text Add to dashboard Cite

A new statistical approach for on-line change detection in uncertain dynamic system is proposed. In change detection problem, the distribution of a sequence of observations can change at some unknown instant. The goal is to detect this change, for example a parameter change, as quickly as possible with a minimal risk of false detection. In this paper, the observations come from an uncertain system modeled by an autoregressive model containing an unknown functional component. The popular Page's CUSUM rule is not applicable anymore since it requires the full knowledge of the model. A new detection CUSUM-like scheme is proposed, which is based on the nonparametric estimation of the unknown component from a learning sample. Moreover, the estimation procedure can be updated on line which ensures a better detection, especially at the beginning of the monitoring procedure. Simulation trials were performed on a model describing a water treatment process and show the interest of this new procedure with respect to the classic CUSUM rule.

show abstract

Section: Resultsmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Change detection for uncertain autoregressive dynamic models through nonparametric estimation

Hilgert

Verdier

Vila

2016

Statistical Methodology

View full text Add to dashboard Cite

show abstract

“…In a control framework, that is, when X n is submitted to the action of an exogenous variable (also called control variable), Portier and Oulidi [21] establish the same kind of result but with a more general noise. We will now adapt these convergence results to model (1.1) and also improve them to study the prediction errors, which has never been done before.…”

Section: Strong Uniform Consistency Of F Nmentioning

confidence: 96%

Strong uniform consistency and asymptotic normality of a kernel based error density estimator in functional autoregressive models

Hilgert¹,

Portier²

2012

Stat Inference Stoch Process

Self Cite

View full text Add to dashboard Cite

Estimating the innovation probability density is an important issue in any regression analysis. This paper focuses on functional autoregressive models. A residual-based kernel estimator is proposed for the innovation density. Asymptotic properties of this estimator depend on the average prediction error of the functional autoregressive function. Sufficient conditions are studied to provide strong uniform consistency and asymptotic normality of the kernel density estimator.

show abstract

“…Adaptive control of discrete nonlinear systems using flexible nonlinear parameterization like Artificial Neural Networks (Jagannathan and Lewis, 1996;Chen and Khalil, 1995;Narendra and Parthasarathy, 1990) and nonparametric models (Murray-Smith and Sbarbaro, 2002;Portier and Oulidi, 2000;Kocijan et al, 2004) have received some attention. Most of these works have relied on the assumption that the system has stable inverse, even though in discrete systems, nonminimum phase behavior can even be brought by the sampling rate selection, as in the linear case.…”

Section: Introductionmentioning

confidence: 99%

An Adaptive Nonparametric Controller for a Class of Nonminimum Phase Non-Linear System

Sbárbaro

Murray-Smith

2005

IFAC Proceedings Volumes

View full text Add to dashboard Cite

This paper addresses the problem of controlling a class of unknown nonlinear systems with unstable inverse, by using a generalized minimum variance approach. We highlight the limitations of the classic cost function used in this context and we propose a new one based on the Generalized Feedback Linearization concept. The adaptive control algorithm uses a nonparametric model, which provides an estimate of the mean and variance of the system output. Simulation examples illustrate the main characteristics and limitation of the proposed approach.

show abstract

Nonparametric Estimation and Adaptive Control of Functional Autoregressive Models

Cited by 16 publications

References 25 publications

Change detection for uncertain autoregressive dynamic models through nonparametric estimation

Change detection for uncertain autoregressive dynamic models through nonparametric estimation

Strong uniform consistency and asymptotic normality of a kernel based error density estimator in functional autoregressive models

An Adaptive Nonparametric Controller for a Class of Nonminimum Phase Non-Linear System

Contact Info

Product

Resources

About