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Comparison of Singular Perturbations Approximation Method and Meta-Heuristic-Based Techniques for Order Reduction of Linear Discrete Systems

Received: 16 August 2016     Accepted: 12 September 2016     Published: 8 December 2016
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Abstract

This paper presents a survey of Singular Perturbations Approximation (SPA) method and meta-heuristic techniques for order reduction of linear systems in discrete case. A comparison of intelligent techniques to determine the reduced order model of higher order linear systems is presented. Two approaches are considered: Particle Swarm Optimization (PSO) and Shuffled Frog Leaping Algorithm (SFLA). These methods are employed to reduce the higher order model and based on the minimization of the Mean Square Error (MSE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. Each method is illustrated through numerical examples.

Published in Applied and Computational Mathematics (Volume 6, Issue 4-1)

This article belongs to the Special Issue Some Novel Algorithms for Global Optimization and Relevant Subjects

DOI 10.11648/j.acm.s.2017060401.14
Page(s) 48-54
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Order Reduction Techniques, Singular Perturbations Approximations Method, Meta-Heuristics Methods, Particle Swarm Optimization, Shuffled Frog Leaping Algorithm

References
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  • APA Style

    Anouar Bouazza. (2016). Comparison of Singular Perturbations Approximation Method and Meta-Heuristic-Based Techniques for Order Reduction of Linear Discrete Systems. Applied and Computational Mathematics, 6(4-1), 48-54. https://doi.org/10.11648/j.acm.s.2017060401.14

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    ACS Style

    Anouar Bouazza. Comparison of Singular Perturbations Approximation Method and Meta-Heuristic-Based Techniques for Order Reduction of Linear Discrete Systems. Appl. Comput. Math. 2016, 6(4-1), 48-54. doi: 10.11648/j.acm.s.2017060401.14

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    AMA Style

    Anouar Bouazza. Comparison of Singular Perturbations Approximation Method and Meta-Heuristic-Based Techniques for Order Reduction of Linear Discrete Systems. Appl Comput Math. 2016;6(4-1):48-54. doi: 10.11648/j.acm.s.2017060401.14

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  • @article{10.11648/j.acm.s.2017060401.14,
      author = {Anouar Bouazza},
      title = {Comparison of Singular Perturbations Approximation Method and Meta-Heuristic-Based Techniques for Order Reduction of Linear Discrete Systems},
      journal = {Applied and Computational Mathematics},
      volume = {6},
      number = {4-1},
      pages = {48-54},
      doi = {10.11648/j.acm.s.2017060401.14},
      url = {https://doi.org/10.11648/j.acm.s.2017060401.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.s.2017060401.14},
      abstract = {This paper presents a survey of Singular Perturbations Approximation (SPA) method and meta-heuristic techniques for order reduction of linear systems in discrete case. A comparison of intelligent techniques to determine the reduced order model of higher order linear systems is presented. Two approaches are considered: Particle Swarm Optimization (PSO) and Shuffled Frog Leaping Algorithm (SFLA). These methods are employed to reduce the higher order model and based on the minimization of the Mean Square Error (MSE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. Each method is illustrated through numerical examples.},
     year = {2016}
    }
    

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Author Information
  • Department of Electrical Engineering, National Engineering School of Monastir, Sousse, Tunisia

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