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Novel approaches for parameter estimation of local linear models for dynamical system identification

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Abstract

In this paper we introduce two novel techniques for local linear modeling of dynamical systems. As in the standard approach, we use vector quantization (VQ) algorithms, such as the Self-Organizing Map, to partition the joint input-output space into smaller regions. Then, to each neuron we associate a vector of parameters which must be suitably estimated. The first estimation technique uses the prototypes of the i-th neuron and its K nearest neighbors to build the corresponding local linear model. The second technique builds the i-th local linear model using the data vectors that are mapped into the regions comprised of the Voronoi cells of the i-th neuron and its K nearest neighbors. A comprehensive evaluation of the proposed techniques is carried out for the task of inverse identification of three benchmarking Single Input/Single Output (SISO) dynamical systems. Their performances are compared to those achieved by the Multilayer Perceptron and the Extreme Learning Machine networks. We also evaluate how robust are the proposed techniques with respect to the VQ algorithm used to partition the input-output space. The results show that proposed techniques consistently outperform standard approaches for all evaluated datasets.

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Notes

  1. NARX stands for Nonlinear Autoregressive model with exogenous inputs.

  2. That is, instead of using the recursive LMS rule, the D-MKSOM model uses the standard (non-recursive) least-squares method.

  3. http://www.esat.kuleuven.ac.be/sista/daisy/

  4. By the original MKSOM models, we mean the P- and D-MKSOM models that use the VQTAM method with the SOM as the VQ algorithm.

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Acknowledgments

The first author thanks CNPq for the financial support through the grant no. 309841/2012-7. The second author thanks FUNCAP and CAPES for the scholarships granted along the development of this research. Both authors thanks NUTEC (Fundação Núcleo de Tecnologia Industrial do Ceará) for providing the laboratory infrastructure for the execution of the computer experiments reported in this paper.

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  1. Department of Teleinformatics Engineering, Av. Mister Hull, S/N, Campus of Pici, Center of Technology, Federal University of Ceará, CEP 60455-970, Fortaleza, Ceará, Brazil

    Guilherme A. Barreto

  2. Department of Electrical Engineering, Av. Ministro Petrônio Portela, S/N - Campus of Ininga, Center of Technology, Federal University of Piauí, CEP 64049-550, Teresina, Piauí, Brazil

    Luís Gustavo M. Souza

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Correspondence to Guilherme A. Barreto.

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Barreto, G.A., M. Souza, L.G. Novel approaches for parameter estimation of local linear models for dynamical system identification. Appl Intell 44, 149–165 (2016). https://doi.org/10.1007/s10489-015-0699-1

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