An introduction to models based on Laguerre, Kautz and other related orthonormal functions – part I: linear and uncertain models

Abstract

This paper provides an overview of system identification using orthonormal basis function models, such as those based on Laguerre, Kautz, and generalised orthonormal basis functions. The paper is separated in two parts. In this first part, the mathematical foundations of these models as well as their advantages and limitations are discussed within the context of linear and robust system identification. The second part approaches the issues related with non-linear models. The discussions comprise a broad bibliographical survey of the subjects involving linear models within the orthonormal basis functions framework. Theoretical and practical issues regarding the identification of these models are presented and illustrated by means of a case study involving a polymerisation process.

Control of Constrained Linear-Time Varying Systems via Kautz Parametrization of Model Predictive Control Scheme

“…Therefore, we have to study under which conditions the Kautz network is able to capture the required optimal input signals. An infinite series of Kautz functions defines a complete set on the z-domain, and any stable transfer function ( ), can be expressed by the Kautz functions as [18]: It is shown in [19] that the necessary and sufficient condition for the completeness of the set Ω ( ) in (10), (19.a) on…”

“…Orthonormality of the Kautz network in the time domain has been proven in [18], and can be expressed as…”

An introduction to models based on Laguerre, Kautz and other related orthonormal functions – Part II: non-linear models

“…It is then possible to describe the dynamics of the set of orthonormal functions using a state-space representation. In this case, the OFB linear model can be represented as follows (Oliveira et al, 2011):…”

A Scalable Algorithm for Physically Motivated and Sparse Approximation of Room Impulse Responses With Orthonormal Basis Functions

“…Fixed-pole models based on Orthonormal Basis Functions (OBFs) [13]- [16] can be derived directly from an orthogonalization of PF models. OBF models span the same approximation space of PF models for the same set of poles, with the difference that the outputs of each secondorder all-pole filter are made orthogonal to each other by a sequence of all-pass filters (i.e.…”