On the complexity of piecewise affine system identification

Lauer, Fabien

doi:10.1016/j.automatica.2015.09.031

Cited by 41 publications

(27 citation statements)

References 22 publications

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“…In the binary case with two categories, a linear classification is one that can be produced by a separating hyperplane dividing the space in two halfspaces. It is shown in [9] that the number of different linear classifications of N points is on the order of Ø(N d ) in Q d and that these can be constructed efficiently. Here, we use an adaptation of these results for linear classifiers, while [9] focused on affine classifiers.…”

Section: Problem 2 (Decision Form Of Switching Regression) Given a Dmentioning

confidence: 99%

On the complexity of switching linear regression

Lauer

2016

Automatica

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This technical note extends recent results on the computational complexity of globally minimizing the error of piecewise-affine models to the related problem of minimizing the error of switching linear regression models. In particular, we show that, on the one hand the problem is NP-hard, but on the other hand, it admits a polynomial-time algorithm with respect to the number of data points for any fixed data dimension and number of modes.

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Section: Problem 2 (Decision Form Of Switching Regression) Given a Dmentioning

confidence: 99%

On the complexity of switching linear regression

Lauer

2016

Automatica

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“…Furthermore, because of the equivalence between PWA and hybrid linear models [2][3][4] (such as mixed logical dynamical and linear complementarity models), well-settled tools for analysis and control of hybrid systems can be applied to systems represented in PWA form. 3,5 Learning PWA models from data is an NP-hard problem, 6 which requires to estimate both the parameters defining the local affine functions and the partition of the regressor space. Several algorithms/heuristics have been developed in the last years 7,8 for PWA regression or, in general, for data-driven modeling of hybrid systems.…”

Section: Introductionmentioning

confidence: 99%

Identification of hybrid and linear parameter‐varying models via piecewise affine regression using mixed integer programming

Mejari

Naik²,

Piga

et al. 2020

Intl J Robust & Nonlinear

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This article presents a two-stage algorithm for piecewise affine (PWA) regression. In the first stage, a moving horizon strategy is employed to simultaneously estimate the model parameters and to classify the training data by solving a small-size mixed-integer quadratic programming problem. In the second stage, linear multicategory separation methods are used to partition the regressor space. The framework of PWA regression is adapted to the identification of PWA AutoRegressive with eXogenous input (PWARX) models as well as linear parameter-varying (LPV) models. The performance of the proposed algorithm is demonstrated on an academic example and on two benchmark experimental case studies. The first experimental example concerns modeling the placement process in a pick-and-place machine, while the second one consists in the identification of an LPV model describing the input-output relationship of an electronic bandpass filter with time-varying resonant frequency.

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“…Piecewise affine system identification problem amounts to le arning from a set of training data and the parameters defining each affine sub-model (Fabien Lauer, 2011). This piecewise affine system identification problem is an NP hard problem in general, see (Fabien Lauer, 2015, 2016, for a detailed explanation on the complexity of piecewise affine system identification. For the sake of simplicity, sparse property is i mposed in piecewise affine systems (Laurent Ba ko, 2011), then the sparse optimization can greatly improve computational efficiency.…”

Section: Introductionmentioning

confidence: 99%

Zonotope Parameter Identification for Piecewise Affine System

Wang

2020

Wseas Transactions on Systems

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This paper studies the identification problem for piecewise affine system, which is a special nonlinear system. As the difficulty in identifying piecewise affine system is to determine each separated region and each unknown parameter vector simultaneously, we propose a multi class classification process to determine each separated region. This multi class classification process is similar to the classical data clustering process, and the merit of our strategy is that the first order algorithm of convex optimization can be applied to achieve this classification process. Furthermore to relax the strict probabilistic description on external noise in identifying each unknown parameter vector, zonotope parameter identification algorithm is proposed to computes a set that contains the parameter vector, consistent with the measured output and the given bound of the noise. To guarantee our derived zonotope not growing unbounded with iterations, a sufficient condition for this requirement to hold may be formulated as one linear matrix inequality. Finally a numerical example confirms our theoretical results

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On the complexity of piecewise affine system identification

Cited by 41 publications

References 22 publications

On the complexity of switching linear regression

On the complexity of switching linear regression

Identification of hybrid and linear parameter‐varying models via piecewise affine regression using mixed integer programming

Zonotope Parameter Identification for Piecewise Affine System

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