Identification of piecewise affine systems based on statistical clustering technique

Nakada, Hayato; Takaba, Kiyotsugu; Katayama, Tohru

doi:10.1016/s1474-6670(17)31464-7

Cited by 31 publications

(60 citation statements)

References 19 publications

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“…An iterative algorithm that sequentially estimates the parameters of the model and classifies the data through the use of adapted weights is described in [60]. A method based on statistical clustering of measured data via a Gaussian mixture model and support vector classifiers is presented in [56]. Several optimization problem formulations of the identification problem are proposed in [54,55].…”

Section: Paper Contributionmentioning

confidence: 99%

“…The third category contains a variety of approaches, sharing the characteristic that the parameters of the submodels and the partition of the domain are identified iteratively or in different steps, each step considering either the submodels or the regions. The algorithms proposed in [5,27,47,56,60] start by classifying the data points and estimating the linear/affine submodels simultaneously. Then, region estimation is carried out by resorting to standard linear separation techniques.…”

Section: Remark 31mentioning

confidence: 99%

“…It is stressed that most of the aforementioned approaches (e.g, [3,14,16,22,29,35,37,41,59]) assume that the system dynamics is continuous, while, e.g., [5,27,47,56,60] allow for discontinuities. Moreover, only few approaches (e.g., those in the second category, [5,56], and [26], which is an extension of [27]) estimate also the number of submodels from data.…”

Section: Remark 31mentioning

confidence: 99%

See 2 more Smart Citations

Identification of Hybrid Systems A Tutorial

Paoletti

Juloski

Ferrari-Trecate

et al. 2007

European Journal of Control

358

271

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Section: Paper Contributionmentioning

confidence: 99%

Section: Remark 31mentioning

confidence: 99%

Section: Remark 31mentioning

confidence: 99%

See 1 more Smart Citation

Identification of Hybrid Systems A Tutorial

Paoletti

Juloski

Ferrari-Trecate

et al. 2007

European Journal of Control

358

271

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“…The former approach allows us to derive a PWA model directly from input-output data of the biological network as an identification problem (e.g. Ferrari-Trecate et al 2003;Roll et al 2004;Juloski et al 2005;Nakada et al 2005;Drulhe et al 2008). Although many approaches have been developed, they in general include three steps: the inputoutput data-clustering based on k-means method or expectation maximization method, the estimation of sub-regions of the state space corresponding to each mode via support vector machine method, and the parameter identification of a linear (affine) system in each mode.…”

Section: Piecewise Affine Approximation Of Biological Networkmentioning

confidence: 99%

Piecewise affine systems approach to control of biological networks

Imura

Kashima

Kusano

et al. 2010

Phil. Trans. R. Soc. A.

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In terms of a piecewise affine system representation, which is a kind of hybrid system model, this article discusses a series of approaches to modelling, analysing and synthesizing a biological network such as a gene-regulatory network. First, the input assignment problem, the controllable state set problem (CSP) and the input trajectory generation problem are emphasized as control problems to be addressed for biological networks. Subsequently, after the modelling issue on biological networks developed in the systems and control community is briefly explained, the CSP is described in detail with reference to control of the quorum-sensing system in the pathogen Pseudomonas aeruginosa. Finally, an optimal control design method to the quorum-sensing system is proposed as a solution to the input trajectory generation problem.

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“…The first class includes the clustering-based approach, using either k-means [3] or Expectation Maximization (EM) [11], and the Bayesian approach [5]. These methods alternate between solving the classification problem for fixed model parameters and solving the estimation problem for a fixed classification.…”

Section: Introductionmentioning

confidence: 99%

A continuous optimization framework for hybrid system identification

2011

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We propose a new framework for hybrid system identification, which relies on continuous optimization. This framework is based on the minimization of a cost function that can be chosen as either the minimum or the product of loss functions. The former is inspired by traditional estimation methods, while the latter is inspired by recent algebraic and support vector regression approaches to hybrid system identification. In both cases, the identification problem is recast as a continuous optimization program involving only the real parameters of the model as variables, thus avoiding the use of discrete optimization. This program can be solved efficiently by using standard optimization methods even for very large data sets. In addition, the proposed framework easily incorporates robustness to different kinds of outliers through the choice of the loss function.

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Identification of piecewise affine systems based on statistical clustering technique

Cited by 31 publications

References 19 publications

Identification of Hybrid Systems A Tutorial

Identification of Hybrid Systems A Tutorial

Piecewise affine systems approach to control of biological networks

A continuous optimization framework for hybrid system identification

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