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New Method for Non-linear Correction Modelling of Dynamic Objects with Genetic Programming

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9120))

Abstract

In the paper a method to adapt the equivalent linearization technique of the non-linear state equation is proposed. This algorithm uses correction matrices. It also uses arrays amendments which elements are determined for each new point. These elements are generated by a formula created automatically using genetic programming.

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References

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

    Article  Google Scholar 

  2. Bartczuk, Ł., Dziwiński, P., Starczewski, J.T.: New Method for Generation Type-2 Fuzzy Partition for FDT. In: Rutkowski, L., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2010, Part I. LNCS, vol. 6113, pp. 275–280. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  3. Bartczuk, Ł., Przybył, A., Koprinkova-Hristova, P.: 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.) ICAISC 2014, Part I. LNCS (LNAI), vol. 8467, pp. 169–180. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  4. 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 

  5. Bartczuk, Ł., Dziwiński, P., Starczewski, J.T.: A new method for dealing with unbalanced linguistic term set. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2012, Part I. LNCS, vol. 7267, pp. 207–212. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  6. Bilski, J.: Momentum modification of the RLS algorithms. In: Rutkowski, L., Siekmann, J.H., Tadeusiewicz, R., Zadeh, L.A. (eds.) ICAISC 2004. LNCS (LNAI), vol. 3070, pp. 151–157. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  7. Bilski, J., Rutkowski, L.: Numerically robust learning algorithms for feed forward neural networks. Advances in Soft Computing, pp. 149–154 (2003)

    Google Scholar 

  8. 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 

  9. 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 

  10. 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, vol. 7267, pp. 12–20. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  11. 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 

  12. Bilski, J., Smoląg, J.: Parallel architectures for learning the RTRN and Elman dynamic neural networks. IEEE Trans. Parallel and Distributed Systems PP(99) (2014)

    Google Scholar 

  13. Bilski, J., Smoląg, J., Galushkin, A.I.: The Parallel Approach to the Conjugate Gradient Learning Algorithm for the Feedforward Neural Networks. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2014, Part I. LNCS, vol. 8467, pp. 12–21. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  14. 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 

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

    Article  MathSciNet  Google Scholar 

  16. Chaibakhsh, A., Chaibakhsh, N., Abbasi, M., Norouzi, A.: Orthonormal Basis Function Fuzzy Systems for Biological Wastewater Treatment Processes Modeling. Journal of Artificial Intelligence and Soft Computing Research 2(4), 343–356

    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 135, 203–217 (2014)

    Article  Google Scholar 

  18. Cpałka, K., Łapa, K., Przybył, A., Zalasiński, M., Rutkowski, L.: A new method for designing neuro-fuzzy systems for nonlinear modelling with interpretability aspects. Neurocomputing 135, 203–217 (2014)

    Article  Google Scholar 

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

    Article  Google Scholar 

  20. 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 

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

    Google Scholar 

  22. Cpałka, K., Zalasiński, M.: Online signature verification using vertical signature partitioning. Expert Systems with Applications 41, 4170–4180 (2014)

    Article  Google Scholar 

  23. Cpałka, K., Zalasiński, M., Rutkowski, L.: New method for the on-line signature verification based on horizontal partitioning. Pattern Recognition 47, 2652–2661 (2014)

    Article  Google Scholar 

  24. 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.) EC 2012 and SIDE 2012. LNCS, vol. 7269, pp. 199–205. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  25. 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 (LNAI), vol. 6114, pp. 445–450. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  26. Dziwiński, P., Bartczuk, Ł., Przybył, A., Avedyan, E.D.: A New Algorithm for Identification of Significant Operating Points Using Swarm Intelligence. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2014, Part II. LNCS, vol. 8468, pp. 349–362. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  27. Ferreira, C.: Gene expression programming: a new algorithm for solving problems. Complex Systems 13(2), 87–129 (2001)

    MathSciNet  MATH  Google Scholar 

  28. Ferreira, C.: Gene expression programming in problem solving. In: Soft Computing and Industry, pp. 635–653. Springer London (2002)

    Google Scholar 

  29. Ferreira, C.: Gene Expression Programming: Mathematical Modeling by an Artificial Intelligence, 2nd edn. Springer, Germany (2006)

    Google Scholar 

  30. Folly, K.: Parallel Pbil Applied to Power System Controller Design. Journal of Artificial Intelligence and Soft Computing Research, 3(3), 215–223 (2013)

    Article  Google Scholar 

  31. Ismail, S., Pashilkar, A.A., Ayyagari, R., Sundararajan, N.: Neural-Sliding Mode Augmented Robust Controller for Autolanding of Fixed Wing Aircraft. Journal of Artificial Intelligence and Soft Computing Research 2(4), 317–330 (2012)

    Google Scholar 

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

    MATH  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  35. 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 

  36. 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)

    MATH  Google Scholar 

  37. 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 

  38. 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 

  39. 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 

  40. 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 

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

    Google Scholar 

  42. 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, vol. 7268, pp. 697–705. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  43. Rutkowski, L.: On Bayes risk consistent pattern-recognition procedures in a quasi-stationary environment. IEEE Trans. Pattern Analysis and Machine Intelligence 4(1), 84–87 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  44. Rutkowski, L.: Online Identification Of Time-Varying Systems by Nonparametric Techniques. IEEE Trans. Automatic Control 27(1), 228–230 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  45. Rutkowski, L.: On nonparametric identification with prediction of time-varying systems. IEEE Trans. Automatic Control 29(1), 58–60 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  46. Rutkowski, L.: Multiple Fourier-series procedures for extraction of nonlinear regressions from noisy data. IEEE Trans. Signal Processing 41(10), 3062–3065 (1993)

    Article  MATH  Google Scholar 

  47. Rutkowski, L., Cpałka, K.: A neuro-fuzzy controller with a compromise fuzzy reasoning. Control and Cybernetics 31(2), 297–308 (2002)

    Google Scholar 

  48. 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 

  49. 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 

  50. Rutkowski, L., Jaworski, M., Pietruczuk, L., Duda, P.: Decision Trees for Mining Data Streams Based on the Gaussian Approximation. IEEE Transactions on Knowledge and Data Engineering 26, 108–119 (2014)

    Article  Google Scholar 

  51. Rutkowski, L., Jaworski, M., Pietruczuk, L., Duda, P.: The CART decision tree for mining data streams. Information Sciences 266, 1–15 (2014)

    Article  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. 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 

  55. 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 

  56. 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 

  57. 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 

  58. 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 (LNAI), vol. 7895, pp. 342–350. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  59. Zalasiński, M., Cpałka, K., Er, M.J.: New Method for Dynamic Signature Verification Using Hybrid Partitioning. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2014, Part II. LNCS (LNAI), vol. 8468, pp. 216–230. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  60. Zalasiński, M., Cpałka, K., Hayashi, Y.: New Method for Dynamic Signature Verification Based on Global Features. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2014, Part II. LNCS (LNAI), vol. 8468, pp. 231–245. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  61. 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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Bartczuk, Ł., Przybył, A., Koprinkova-Hristova, P. (2015). New Method for Non-linear Correction Modelling of Dynamic Objects with Genetic Programming. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L., Zurada, J. (eds) Artificial Intelligence and Soft Computing. ICAISC 2015. Lecture Notes in Computer Science(), vol 9120. Springer, Cham. https://doi.org/10.1007/978-3-319-19369-4_29

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