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New Method for Nonlinear Fuzzy Correction Modelling of Dynamic Objects

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Artificial Intelligence and Soft Computing (ICAISC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8467))

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Abstract

In the paper a method to use the equivalent linearization technique of the nonlinear state equation with the coefficients generated by the fuzzy rules for current operating point is proposed. On the basis of the evolutionary strategy and properly defined identification procedure, the fuzzy rules are automatically designed to maximize the accuracy of the resulting linear model.

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References

  1. Caughey, T.K.: Equivalent Linearization Techniques. The Journal of the Acoustical Society of America 35(11), 1706–1711 (1963)

    Article  MathSciNet  Google Scholar 

  2. Barland, M., et al.: Commende optimal d’un systeme generateur photovoltaique converisseur statique - receptur. Revue Phys. Appl. 19, 905–915 (1984)

    Article  Google Scholar 

  3. Bartczuk, Ł., Przybył, A., Dziwiński, P.: Hybrid State Variables - Fuzzy Logic Modelling of Nonlinear Objects. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part I. LNCS (LNAI), vol. 7894, pp. 227–234. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  4. Bilski, J., Litwiński, S., Smoląg, J.: Parallel Realisation of QR Algorithm for Neural Networks Learning. In: Rutkowski, L., Siekmann, J.H., Tadeusiewicz, R., Zadeh, L.A. (eds.) ICAISC 2004. LNCS (LNAI), vol. 3070, pp. 158–165. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  5. Bilski, J., Rutkowski, L.: Numerically Robust Learning Algorithms for Feed Forward Neural Networks. In: Neural Networks and Soft Computing. Advances in Soft Computing, pp. 149–154. Physica-Verlag, A Springer-Verlag Company (2003)

    Google Scholar 

  6. Bilski, J., Smoląg, J.: Parallel Approach to Learning of the Recurrent Jordan Neural Network. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part I. LNCS (LNAI), vol. 7894, pp. 32–40. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  7. Bilski, J., Smoląg, J.: Parallel Realisation of the Recurrent Elman Neural Network Learning. In: Rutkowski, L., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2010, Part II. LNCS (LNAI), vol. 6114, pp. 19–25. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  8. Bilski, J., Smoląg, J.: Parallel Realisation of the Recurrent Multi Layer Perceptron Learning. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2012, Part I. LNCS (LNAI), vol. 7267, pp. 12–20. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  9. Bilski, J., Smoląg, J.: Parallel Realisation of the Recurrent RTRN Neural Network Learning. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2008. LNCS (LNAI), vol. 5097, pp. 11–16. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  10. Chang, W.-J., Chang, W., Liu, H.-H.: Model-based fuzzy modeling and control for autonomous underwater vehicles in the horizontal plane. Journal of Marine Science and Technology 11(3), 155–163 (2003)

    MathSciNet  Google Scholar 

  11. Cordon, O., Herrera, F., Hoffmann, F., Magdalena, L.: Genetic Fuzzy Systems: Evolutionary tuning and learning of fuzzy knowledge bases. World Scientific (2001)

    Google Scholar 

  12. Cpalka, K.: A Method for Designing Flexible Neuro-fuzzy Systems. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Żurada, J.M. (eds.) ICAISC 2006. LNCS (LNAI), vol. 4029, pp. 212–219. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  13. Cpałka, K.: On evolutionary designing and learning of flexible neuro-fuzzy structures for nonlinear classification. In: Nonlinear Analysis Series A: Theory, Methods and Applications, vol. 71, pp. 1659–1672. Elsevier (2009)

    Google Scholar 

  14. Cpałka, K., Rutkowski, L.: A New Method for Designing and Reduction of Neuro-fuzzy Systems. In: Proceedings of the 2006 IEEE International Conference on Fuzzy Systems (IEEE World Congress on Computational Intelligence, WCCI 2006), Vancouver, BC, Canada, pp. 8510–8516 (2006)

    Google Scholar 

  15. Cpałka, K., Rutkowski, L.: Flexible Takagi-Sugeno Fuzzy Systems. In: Proceedings of the International Joint Conference on Neural Networks 2005, Montreal, pp. 1764–1769 (2005)

    Google Scholar 

  16. Cpałka, K., Rutkowski, L.: Flexible Takagi Sugeno Neuro-fuzzy Structures for Nonlinear Approximation. WSEAS Transactions on Systems 4(9), 1450–1458 (2005)

    Google Scholar 

  17. Cpałka, K., Łapa, K., Przybył, A., Zalasiński, M.: A new method for designing neuro-fuzzy systems for nonlinear modelling with interpretability aspects. Neurocomputing (in print, 2014), http://dx.doi.org/10.1016/j.neucom.2013.12.031

  18. Dziwiński, P., Bartczuk, Ł., Starczewski, J.T.: Fully controllable ant colony system for text data clustering. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) SIDE 2012 and EC 2012. LNCS, vol. 7269, pp. 199–205. Springer, Heidelberg (2012)

    Google Scholar 

  19. Dziwiński, P., Rutkowska, D.: Algorithm for generating fuzzy rules for WWW document classification. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Żurada, J.M. (eds.) ICAISC 2006. LNCS (LNAI), vol. 4029, pp. 1111–1119. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  20. Dziwiński, P., Rutkowska, D.: Ant focused crawling algorithm. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2008. LNCS (LNAI), vol. 5097, pp. 1018–1028. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  21. Dziwiński, P., Starczewski, J.T., Bartczuk, Ł.: New linguistic hedges in construction of interval type-2 FLS. In: Rutkowski, L., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2010, Part II. LNCS, vol. 6114, pp. 445–450. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  22. El-Abd, M.: On the hybridization on the artificial bee colony and particle swarm optimization algorithms. Journal of Artificial Intelligence and Soft Computing Research 2(2), 147–155 (2012)

    MathSciNet  Google Scholar 

  23. Gabryel, M., Cpałka, K., Rutkowski, L.: Evolutionary strategies for learning of neuro-fuzzy systems. In: Proceedings of the I Workshop on Genetic Fuzzy Systems, Granada, pp. 119–123 (2005)

    Google Scholar 

  24. Gabryel, M., Korytkowski, M., Scherer, R., Rutkowski, L.: Object Detection by Simple Fuzzy Classifiers Generated by Boosting. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part I. LNCS, vol. 7894, pp. 540–547. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  25. Gabryel, M., Woźniak, M., Nowicki, R.K.: Creating Learning Sets for Control Systems Using an Evolutionary Method. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) SIDE 2012 and EC 2012. LNCS, vol. 7269, pp. 206–213. Springer, Heidelberg (2012)

    Google Scholar 

  26. Gacto, M.J., Alcala, R., Herrera, F.: Interpretability of linguistic fuzzy rule-based systems: An overview of interpretability measures. Information Sciences 181, 4340–4360 (2011)

    Article  Google Scholar 

  27. Greenfield, S., Chiclana, F.: Type-reduction of the discretized interval type-2 fuzzy set: approaching the continuous case through progressively finer discretization. Journal of Artificial Intelligence and Soft Computing Research 1(3), 183–193 (2011)

    Google Scholar 

  28. Johansen, T.A., Shorten, R., Murray-Smith, R.: On the Interpretation and Identification of Dynamic Takagi–Sugeno Fuzzy Models. IEEE Transactions on Fuzzy Systems 8(3) (2000)

    Google Scholar 

  29. Jordan, A.J.: Linearization of non-linear state equation. Bulletin of the Polish Academy of Science. Technical Science 54(1), 63–73 (2006)

    Article  MATH  Google Scholar 

  30. Kaczorek, T., Dzieliński, A., Dąbrowski, L., Łopatka, R.: The Basis of Control Theory. WNT, Warsaw (2006) (in Polish)

    Google Scholar 

  31. Kamyar, M.: Takagi-Sugeno Fuzzy Modeling for Process Control. In: Industrial Automation, Robotics and Artificial Intelligence (EEE8005), School of Electrical, Electronic and Computer Engineering, vol. 8 (2008)

    Google Scholar 

  32. Koprinkova-Hristova, P.: Backpropagation through time training of a neuro-fuzzy controller. International Journal of Neural Systems 20(5), 421–428 (2010)

    Article  Google Scholar 

  33. Korytkowski, M., Nowicki, R., Rutkowski, L., Scherer, R.: AdaBoost Ensemble of DCOG Rough–Neuro–Fuzzy Systems. In: Jędrzejowicz, P., Nguyen, N.T., Hoang, K. (eds.) ICCCI 2011, Part I. LNCS, vol. 6922, pp. 62–71. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  34. Korytkowski, M., Rutkowski, L., Scherer, R.: On combining backpropagation with boosting. In: Proceedings of the IEEE International Joint Conference on Neural Network (IJCNN), vols. 1-10, pp. 1274–1277 (2006)

    Google Scholar 

  35. Korytkowski, M., Rutkowski, L., Scherer, R.: From Ensemble of Fuzzy Classifiers to Single Fuzzy Rule Base Classifier. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2008. LNCS (LNAI), vol. 5097, pp. 265–272. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  36. Kroll, A.: On choosing the fuzziness parameter for identifying TS models with multidimensional membership functions. Journal of Artificial Intelligence and Soft Computing Research 1(4), 283–300 (2011)

    Google Scholar 

  37. Laskowski, L.: A Novel Continuous Dual Mode Neural Network in Stereo-Matching Process. In: Diamantaras, K., Duch, W., Iliadis, L.S. (eds.) ICANN 2010, Part III. LNCS, vol. 6354, pp. 294–297. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  38. Laskowski, Ł.: Hybrid-Maximum Neural Network for Depth Analysis from Stereo-Image. In: Rutkowski, L., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2010, Part II. LNCS, vol. 6114, pp. 47–55. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  39. Li, X., Er, M.J., Lim, B.S., Zhou, J.H., Gan, O.P., Rutkowski, L.: Fuzzy Regression Modeling for Tool Performance Prediction and Degradation Detection. International Journal of Neural Systems 20(5), 405–419 (2010)

    Article  Google Scholar 

  40. Lobato, F.S., Steffen Jr., V.: A new multi-objective optimization algorithm based on differential evolution and neighborhood exploring evolution strategy. Journal of Artificial Intelligence and Soft Computing Research 1(4), 259–267 (2011)

    Google Scholar 

  41. Lobato, F.S., Steffen Jr., V., Silva Neto, A.J.: Solution of singular optimal control problems using the improved differential evolution algorithm. Journal of Artificial Intelligence and Soft Computing Research 1(3), 195–206 (2011)

    Google Scholar 

  42. Łapa, K., Przybył, A., Cpałka, K.: A new approach to designing interpretable models of dynamic systems. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part II. LNCS (LNAI), vol. 7895, pp. 523–534. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  43. Łapa, K., Zalasiński, M., Cpałka, K.: A new method for designing and complexity reduction of neuro-fuzzy systems for nonlinear modelling. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part I. LNCS (LNAI), vol. 7894, pp. 329–344. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  44. Patan, K., Patan, M.: Optimal Training strategies for locally recurrent neural networks. Journal of Artificial Intelligence and Soft Computing Research 1(2), 103–114 (2011)

    Google Scholar 

  45. Peteiro-Barral, D., Bardinas, B.G., Perez-Sanchez, B.: Learning from heterogeneously distributed data sets using artificial neural networks and genetic algorithms. Journal of Artificial Intelligence and Soft Computing Research 2(1), 5–20 (2012)

    Google Scholar 

  46. Prampero, P.S., Attux, R.: Magnetic particle swarm optimization. Journal of Artificial Intelligence and Soft Computing Research 2(1), 59–72 (2012)

    Google Scholar 

  47. Przybył, A., Cpałka, K.: A new method to construct of interpretable models of dynamic systems. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2012, Part II. LNCS (LNAI), vol. 7268, pp. 697–705. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  48. Rutkowski, L.: Computational Intelligence: Methods and Techniques. Springer (2008)

    Google Scholar 

  49. Rutkowski, L., Cpałka, K.: Compromise approach to neuro-fuzzy systems. In: Sincak, P., Vascak, J., Kvasnicka, V., Pospichal, J. (eds.) Intelligent Technologies - Theory and Applications, vol. 76, pp. 85–90. IOS Press (2002)

    Google Scholar 

  50. Rutkowski, L., Cpałka, K.: Flexible weighted neuro-fuzzy systems. In: Proceedings of the 9th International Conference on Neural Information Processing (ICONIP 2002), Orchid Country Club, Singapore, CD, November 18-22 (2002)

    Google Scholar 

  51. Rutkowski, L., Cpałka, K.: Neuro-fuzzy systems derived from quasi-triangular norms. In: Proceedings of the IEEE International Conference on Fuzzy Systems, Budapest, July 26-29, vol. 2, pp. 1031–1036 (2004)

    Google Scholar 

  52. Rutkowski, L., Przybył, A., Cpałka, K.: Novel on-line speed profile generation for industrial machine tool based on flexible neuro-fuzzy approximation. IEEE Transactions on Industrial Electronics 59, 1238–1247 (2012)

    Article  Google Scholar 

  53. Rutkowski, L., Przybył, A., Cpałka, K., Er, M.J.: Online Speed Profile Generation for Industrial Machine Tool Based on Neuro-fuzzy Approach. In: Rutkowski, L., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2010, Part II. LNCS (LNAI), vol. 6114, pp. 645–650. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  54. Starczewski, J., Rutkowski, L.: Connectionist Structures of Type 2 Fuzzy Inference Systems. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds.) PPAM 2001. LNCS, vol. 2328, pp. 634–642. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  55. Starczewski, J., Scherer, R., Korytkowski, M., Nowicki, R.: Modular Type-2 Neuro-fuzzy Systems. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Wasniewski, J. (eds.) PPAM 2007. LNCS, vol. 4967, pp. 570–578. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  56. Theodoridis, D.C., Boutalis, Y.S., Christodoulou, M.A.: Robustifying analysis of the direct adaptive control of unknown multivariable nonlinear systems based on a new neuro-fuzzy method. Journal of Artificial Intelligence and Soft Computing Research 1(1), 59–79 (2011)

    Google Scholar 

  57. Tran, V.N., Brdys, M.A.: Optimizing control by robustly feasible model predictive control and application to drinking water distribution systems. Journal of Artificial Intelligence and Soft Computing Research 1(1), 43–57 (2011)

    Google Scholar 

  58. Zalasiński, M., Cpałka, K.: A new method of on-line signature verification using a flexible fuzzy one-class classifier, pp. 38–53. Academic Publishing House EXIT (2011)

    Google Scholar 

  59. Zalasiński, M., Cpałka, K.: New Approach for the On-Line Signature Verification Based on Method of Horizontal Partitioning. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part II. LNCS, vol. 7895, pp. 342–350. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  60. Zalasiński, M., Cpałka, K.: Novel algorithm for the on-line signature verification. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2012, Part II. LNCS, vol. 7268, pp. 362–367. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  61. Zalasiński, M., Cpałka, K.: Novel Algorithm for the On-Line Signature Verification Using Selected Discretization Points Groups. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part I. LNCS (LNAI), vol. 7894, pp. 493–502. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  62. Zalasiński, M., Łapa, K., Cpałka, K.: New Algorithm for Evolutionary Selection of the Dynamic Signature Global Features. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part II. LNCS (LNAI), vol. 7895, pp. 113–121. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

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Authors and Affiliations

  1. Institute of Computational Intelligence, Czȩstochowa University of Technology, Poland

    Łukasz Bartczuk & Andrzej Przybył

  2. Institute of Control and System Research, Bulgarian Academy of Sciences, Bulgaria

    Petia Koprinkova-Hristova

Authors
  1. Łukasz Bartczuk
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  2. Andrzej Przybył
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  3. Petia Koprinkova-Hristova
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Editor information

Editors and Affiliations

  1. Częstochowa University of Technology, Armii Krajowej 36, 42-200, Częstochowa, Poland

    Leszek Rutkowski , Marcin Korytkowski  & Rafał Scherer ,  & 

  2. AGH University of Science and Technology, Mickiewicza 30, 30-059, Kraków, Poland

    Ryszard Tadeusiewicz

  3. Computer Science Division, Department of Electrical Engineering and Computer Sciences, University of California Berkeley, 94720-1776, Berkeley, CA, USA

    Lotfi A. Zadeh

  4. Computational Intelligence Laboratory, Electrical and Computer Engineering, University of Louisville, 405 Lutz Hall, 40292, Louisville, KY, USA

    Jacek M. Zurada

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Bartczuk, Ł., Przybył, A., Koprinkova-Hristova, P. (2014). New Method for Nonlinear Fuzzy Correction Modelling of Dynamic Objects. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing. ICAISC 2014. Lecture Notes in Computer Science(), vol 8467. Springer, Cham. https://doi.org/10.1007/978-3-319-07173-2_16

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