Adaptive control over non­linear objects using the robust neural network FCMAC

Authors

DOI:

https://doi.org/10.15587/1729-4061.2018.128270

Keywords:

artificial neural network, fuzzy-СМАС, identification, modeling, indirect adaptive control, hashing

Abstract

The paper explores issues related to the application of artificial neural networks (ANN) when solving the problems on identification and control of nonlinear dynamic systems. We have investigated characteristics of the network, which is a result of the application of the apparatus of fuzzy logic in a classical СМАС neural network, which is titled FCMAC ‒ Fuzzy Cerebral Model Arithmetic Computer. We studied influence of the form of receptive fields of associative neurons on the accuracy of identification and control; various information hashing algorithms that make it possible to reduce the amount of memory required for the implementation of a network; robust learning algorithms are proposed allowing the use of a network in systems with strong perturbations. It is shown that the FСМАС network, when selecting appropriate membership functions, can be applied in order to synthesize indirect control systems with and without a reference model; it is more efficient to use it in control systems with the reference model. This sharply reduces the quantity of training pairs and simplifies the coding due to the narrower range of the applied values of input signals. The results obtained are confirmed by simulation modeling of the processes of identification of and control over nonlinear dynamical systems

Author Biographies

Oleg Rudenko, Simon Kuznets Kharkiv National University of Economics Nauky ave., 9-A, Kharkiv, Ukraine, 61166

Doctor of Technical Sciences, Professor, Head of Department

Department of information systems

Oleksandr Bezsonov, Simon Kuznets Kharkiv National University of Economics Nauky ave., 9-A, Kharkiv, Ukraine, 61166

Doctor of Technical Sciences, Professor

Department of information systems

Oleh Lebediev, Kharkiv National University of Radio Electronics Nauka аve., 14, Kharkiv, Ukraine, 61166

PhD, Associate Professor

Department of electronic computers

References

  1. Marr, D. (1969). A theory of cerebellar cortex. The Journal of Physiology, 202 (2), 437–470. doi: 10.1113/jphysiol.1969.sp008820
  2. Albus, J. S. (1975). A New Approach to Manipulator Control: The Cerebellar Model Articulation Controller (CMAC). Journal of Dynamic Systems, Measurement, and Control, 97 (3), 220. doi: 10.1115/1.3426922
  3. Albus, J. S. (1975). Data Storage in the Cerebellar Model Articulation Controller (CMAC). Journal of Dynamic Systems, Measurement, and Control, 97 (3), 228. doi: 10.1115/1.3426923
  4. Wang, L.-X. (1992). Fuzzy systems are universal approximators. Proc. IEEE Int. Conf. On Fuzzy Systems. San Diego, 1163–1170. doi: 10.1109/fuzzy.1992.258721
  5. Li, H.-Y., Yeh, R.-G., Lin, Y.-C., Lin, L.-Y., Zhao, J., Lin, C.-M., Rudas, I. J. (2016). Medical sample classifier design using fuzzy cerebellar model neural networks. Acta polytechnica Hungarica, 13 (6), 7–24. doi: 10.12700/aph.13.6.2016.6.1
  6. Lee, C.-H., Chang, F.-Y., Lin, C.-M. (2014). An Efficient Interval Type-2 Fuzzy CMAC for Chaos Time-Series Prediction and Synchronization. IEEE Transactions on Cybernetics, 44 (3), 329–341. doi: 10.1109/tcyb.2013.2254113
  7. Chung, C.-C., Lin, C.-C. (2015). Fuzzy Brain Emotional Cerebellar Model Articulation Control System Design for Multi-Input Multi-Output Nonlinear. Acta Polytechnica Hungarica, 12 (4), 39–58. doi: 10.12700/aph.12.4.2015.4.3
  8. Xu, S., Jing, Y. (2013). Research and Application of the Pellet Grate Thickness Control System Base on Improved CMAC Neural Network Algorithm. Journal of Residuals Science & Technology, 13 (6), 150.1–150.9.
  9. Cheng, H. (2013). The Fuzzy CMAC Based on RLS Algorithm. Applied Mechanics and Materials, 432, 478–482. doi: 10.4028/www.scientific.net/amm.432.478
  10. Huber, P. J., Ronchetti, E. M. (2009). Robust Statistics. Wiley, 380.
  11. Jou, C.-C. (1992). A fuzzy cerebellar model articulation controller. [1992 Proceedings] IEEE International Conference on Fuzzy Systems. doi: 10.1109/fuzzy.1992.258722
  12. Nie, J., Linkens, D. A. (1994). FCMAC: A fuzzified cerebellar model articulation controller with self-organizing capacity. Automatica, 30 (4), 655–664. doi: 10.1016/0005-1098(94)90154-6
  13. Knuth, D. (1973). Sorting and Searching. The Art of Computer Programming. Vol. 3. Menlo Park, Calif.: Addison Wesley, 506.
  14. Wang, Z.-Q., Schiano, J. L., Ginsberg, M. (1996). Hash-coding in CMAC neural networks. Proceedings of International Conference on Neural Networks (ICNN'96). doi: 10.1109/icnn.1996.549156
  15. Rudenko, O. G., Bessonov, A. A. (2004). Heshirovanie informacii v neyronnoy seti SMAS. Upravlyayushchie sistemy i mashiny, 5, 67–73.
  16. Ching-Tsan, C., Chun-Shin, L. (1996). CMAC with General Basis Functions. Neural Networks, 9 (7), 1199–1211. doi: 10.1016/0893-6080(96)00132-3
  17. Lane, S. H., Handelman, D. A., Gelfand, J. J. (1992). Theory and development of higher-order CMAC neural networks. IEEE Control Systems, 12 (2), 23–30. doi: 10.1109/37.126849
  18. Wang, S., Lu, H. (2003). Fuzzy system and CMAC network with B-spline membership/basis functions are smooth approximators. Soft Computing – A Fusion of Foundations, Methodologies and Applications, 7 (8), 566–573. doi: 10.1007/s00500-002-0242-2
  19. Rudenko, O. G., Bessonov, A. A. (2012). M-obuchenie radial'no-bazisnyh setey s ispol'zovaniem asimmetrichnyh funkciy vliyaniya. Problemy upravleniya i informatiki, 1, 79–93.
  20. Rudenko, O. G., Bessonov, A. A. (2011). Robastnoe obuchenie radial'no-bazisnyh setey. Kibernetika i sistemnyy analiz, 6, 38–46.
  21. Rudenko, O. G., Bezsonov, A. A. (2010). Robust Learning Wavelet Neural Networks. Journal of Automation and Information Sciences, 42 (10), 1–15. doi: 10.1615/jautomatinfscien.v42.i10.10
  22. Vazan, M. (1972). Stohasticheskaya approksimaciya. Moscow: Mir, 289.
  23. Cypkin, Ya. Z. (1984). Osnovy informacionnoy teorii identifikacii. Moscow: Nauka, 320.
  24. Cypkin, Ya. Z., Polyak, B. T. (1977). Ogrublennyy metod maksimal'nogo pravdopodobiya. Dinamika sistem, 12, 22–46.
  25. Narendra, K. S., Parthasarathy, K. (1990). Identification and control of dynamical systems using neural networks. IEEE Transactions on Neural Networks, 1 (1), 4–27. doi: 10.1109/72.80202
  26. Rudenko, O. G., Bessonov, A. A. (2005). Neyronnaya set' SMAS i ee primenenie v zadachah identifikacii i upravleniya nelineynymi dinamicheskimi ob'ektami. Kibernetika i sistemniy analiz, 5, 16–28.
  27. Liao, Y.-L., Peng, Y.-F. (2011). Applications of Prediction and Identification Using Adaptive DCMAC Neural Networks. International Journal of Computer and Information Engineering, 5 (6), 677–682.
  28. Zhao, J., Lin, L.-Y., Lin, C.-M. (2016). A General Fuzzy Cerebellar Model Neural Network Multidimensional Classifier Using Intuitionistic Fuzzy Sets for Medical Identification. Computational Intelligence and Neuroscience, 2016, 1–9. doi: 10.1155/2016/8073279
  29. Commuri, S., Lewis, F. L. (1995). CMAC neural networks for control of nonlinear dynamical systems, structure, stability, and passivity. Proc. IEEE Int. Symp. Intell. Control. San Francisco, 123–129.
  30. Commuri, S., Lewis, F. L., Jagannathan, S. (1995). Discrete-time CMAC neural networks for control applications. Proceedings of 1995 34th IEEE Conference on Decision and Control. New Orleans. doi: 10.1109/cdc.1995.478453
  31. Jagannathan, S. (1999). Discrete-time CMAC NN control of feedback linearizable nonlinear systems under a persistence of excitation. IEEE Transactions on Neural Networks, 10 (1), 128–137. doi: 10.1109/72.737499
  32. Lin, C.-M., Peng, Y.-F. (2004). Adaptive CMAC-Based Supervisory Control for Uncertain Nonlinear Systems. IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics), 34 (2), 1248–1260. doi: 10.1109/tsmcb.2003.822281
  33. Lee, C.-H., Wang, B.-H., Chang, H.-H., Pang, Y.-H. (2006). A Novel Wavelet-based-CMAC Neural Network Controller for Nonlinear Systems. The 2006 IEEE International Joint Conference on Neural Network Proceedings. Vancouver, BC, Canada, 2593–2599. doi: 10.1109/ijcnn.2006.247136
  34. Aved'yan, E. D., Hormel', M. (1991). Povyshenie skorosti skhodimosti processa obucheniya v special'noy sisteme associativnoy pamyati. Avtomatika i telemekhanika, 12, 100–109.
  35. Mohajeri, K., Zakizadeh, M., Moaveni, B., Teshnehlab, M. (2009). Fuzzy CMAC structures. 2009 IEEE International Conference on Fuzzy Systems. doi: 10.1109/fuzzy.2009.5277185

Downloads

Published

2018-04-10

How to Cite

Rudenko, O., Bezsonov, O., & Lebediev, O. (2018). Adaptive control over non­linear objects using the robust neural network FCMAC. Eastern-European Journal of Enterprise Technologies, 2(4 (92), 4–14. https://doi.org/10.15587/1729-4061.2018.128270

Issue

Section

Mathematics and Cybernetics - applied aspects