An output error algorithm for piecewise affine system identification

Canty, Niel; O'Mahony, Tom; Cychowski, Marcin

doi:10.1016/j.conengprac.2011.12.005

Cited by 19 publications

(4 citation statements)

References 20 publications

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“…This dynamical system can generally be represented with two different model structures: input-output models or state-space models. The proposed methods have mostly been developed around input-output models Ferrari-Trecate et al (2003), Juloski et al (2005), Roll et al (2004), Vidal et al (2003); Ma et al (2005), Bemporad et al (2005), Canty et al (2012), Nguyen et al (2020), Jin and Huang (2012), Lu et al (2016), Wang and Xia (2019), Massucci et al (2022).…”

Section: Introductionmentioning

confidence: 99%

New Framework for Identifying Discrete-Time Switched Linear Systems

Lopes

Ishihara

Borges

2023

Preprint

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This paper addresses the problem of offline identification of a particular class of hybrid dynamical systems that are discrete-time switched linear state space models. The identification process is carried out from data previously sampled from the system. Unlike most existing methods that prioritize identifying the switching instants first, a new framework is proposed in which the local models are identified first, and the task of identifying the switching instants is performed later. The methodology involves the iterative calculation of discrete and continuous models' a posteriori probability density function using subspace identification, clustering, data classification, and hybrid stochastic filtering methods. This strategy allows grouping the data most likely to have been generated by the same submodels, thus allowing the estimation of these local models. An essential feature of the algorithm is that the matrices of the different submodels are identified with the same state-space basis allowing them to be evaluated and, if necessary, combined. The performance of the identification procedure is evaluated through numerical examples, and a comparison with a prior method described in the literature is conducted.

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Section: Introductionmentioning

confidence: 99%

New Framework for Identifying Discrete-Time Switched Linear Systems

Lopes

Ishihara

Borges

2023

Preprint

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“…A black box modelling approach for hybrid dynamical systems is included in the socalled hybrid identification toolbox (HIT). Based on measured input and output data the integrated algorithm creates an approximation of the underlying SAS structure and clusters the data to determine the domain for each submodel (Ferrari-Trecate and al, 2003;Canty et al, 2012). HIT is mainly based on regression algorithms.…”

Section: Chapter 1 Introductionmentioning

confidence: 99%

A Framework Including Artificial Neural Networks in Modelling Hybrid Dynamical Systems

Winkler¹

2020

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Ziel der Arbeit ist unterschiedliche Einsatzszenarien von neuronalen Feed-Forward Netzwerken in der hybriden Modellierung zu untersuchen. Im Speziellen konzentriert sich die Arbeit auf hybride dynamische Systeme. Dabei handelt es sich um kontinuierliche Vorgänge, welche durch diskrete Ereignisse Änderung im Verhalten aufzeigen. Dementsprechend basiert die Modellierung solcher Systeme auf einer Kombination aus diskreten und kontinuierlichen Methoden. Derzeitige Standards der hybriden Modellbildung werden überblicksmäßig zusammengefasst. In der Softwareentwicklung kommen vermehrt Machine Learning Algorithmen zur Anwendung. Ein signifikanter Anteil der dabei verwendeten Methoden sind künstliche neuronale Netze, welche vor allem im Bereich der Bild-und Datenverarbeitung eingesetzt werden. Der grundlegende Aufbau sowie unterschiedliche gängige Strukturen neuronaler Netze werden eingeführt. Aufbauend auf die Gebiete Machine Learning und hybride dynamische Systeme, wird ein Framework vorgestellt, welches es ermöglicht, einzelne Elemente hybrider Modelle durch neuronale Netzwerke zu ersetzen. Drei unterschiedliche Anwendungsszenarien werden dabei untersucht: Die Approximation des dynamischen Verhaltens, die Vorhersage der diskreten Prozesse sowie der Ersatz des gesamten hybriden Systems durch neuronale Netze. Das Framework wird eingesetzt, um die drei definierten Szenarien anhand von zwei Beispielen auf Machbarkeit zu untersuchen. Es wird sich zeigen, dass die Approximation einzelner lokaler dynamischer Prozesse mittels speziellen neuronalen Netzwerken möglich ist. Auch eine Approximation des gesamten hybriden Systems durch ein neuronales Netz kann unter speziellen Voraussetzungen zum Ziel führen. Für eine gesamte Zeitreihe des Systemzustandes werden bereits etablierte Methoden mit Hilfe des Frameworks charakterisiert. Im Bezug auf diskrete Ereignisse in hybriden Systemen kann gezeigt werden, dass sich neuronale Netze für die Klassifikation des Systemzustandes, hinsichtlich des Auftretens eines Events, nicht eignen. Abseits von Anwendungen in der Modellierung hybrider Systeme kann das Framework eingesetzt werden, um Feed-Forward Netzwerke zu charakterisieren.

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“…The identification of the PWA-OE models with known discrete mode was implemented in Rosenqvist et al 17 Juloski et al 18 developed a Bayesian approach for the identification of the PWA-OE models. Canty et al 19 developed a clusteringbased identification algorithm for the PWA-OE system. However, batch processes can be characterized by frequent repetition, which has not been fully utilized in the existing process modeling approaches.…”

Section: Introductionmentioning

confidence: 99%

“…The identification of the PWA-OE models with known discrete mode was implemented in Rosenqvist et al Juloski et al developed a Bayesian approach for the identification of the PWA-OE models. Canty et al developed a clustering-based identification algorithm for the PWA-OE system.…”

Section: Introductionmentioning

confidence: 99%

Time-Partitioned Piecewise Affine Output Error Model for Batch Processes

Huang

Zhao

et al. 2018

Ind. Eng. Chem. Res.

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In this paper, a time-partitioned piecewise affine output error (PWA-OE) model for batch processes is proposed, in which time index is used to simplify the partition of regression domain by utilizing the repetitive nature of batch processes. The identification problem involves both continuous and discrete variables, and the derivative information on discrete variables is unavailable. Thus, an identification algorithm based on separable nonlinear least-squares is developed to reduce the complexity of nonlinear minimization. Furthermore, the consistent information criterion (CIC) is used to determine model structure. Results show that the time-partitioned PWA-OE model can effectively describe batch processes.

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An output error algorithm for piecewise affine system identification

Cited by 19 publications

References 20 publications

New Framework for Identifying Discrete-Time Switched Linear Systems

New Framework for Identifying Discrete-Time Switched Linear Systems

A Framework Including Artificial Neural Networks in Modelling Hybrid Dynamical Systems

Time-Partitioned Piecewise Affine Output Error Model for Batch Processes

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