Similarities between non linear aspects of adaptative filtering in signal processing and in control

Abstract

When a linear filter is faced with fluctuations of the environment, adaptive filtering (AF) is a means to achieve on-line optimization . In Signal Processing it is a major technic for modeling . In the control field it is used for the general purpose of process regulation. Eventhough filtering is a linear opération in terras of input signais, it becomes nonlinear when it is made adaptive. The nonlinear nature of the AF equations is responsible for a number of difficulties such as instability, nonuniqueness of the solution, its complex dynamical behaviour .. . which are encountered both in Signal Processing and in Control. The most crucial problem is stability . Typically in Signal Processing the relevant stability is bounded input/bounded output, whereas in the Control field there is an additional requirement of asymptotic achievement, i . e., the AF trajectory reaches the true system output. Despite the differences it is shown that AF raises identical mathematical problems in both discipines.Le traiteur de signal considère le problème de stabilité au sens entrée bornée/sortie bornée, alors que l'automaticien désire des performances asymptotiques, c.a.d. la convergence de la trajectoire du filtre adaptati