Adaptive control over non­linear objects using the robust neural network FCMAC

Oleg Rudenko, Oleksandr Bezsonov, Oleh Lebediev

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

Keywords


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

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References


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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

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Cypkin, Ya. Z., Polyak, B. T. (1977). Ogrublennyy metod maksimal'nogo pravdopodobiya. Dinamika sistem, 12, 22–46.

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

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.

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.

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

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.

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

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

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

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

Aved'yan, E. D., Hormel', M. (1991). Povyshenie skorosti skhodimosti processa obucheniya v special'noy sisteme associativnoy pamyati. Avtomatika i telemekhanika, 12, 100–109.

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


GOST Style Citations


Marr D. A theory of cerebellar cortex // The Journal of Physiology. 1969. Vol. 2002, Issue 2. P. 437–470. doi: 10.1113/jphysiol.1969.sp008820 

Albus J. S. A New Approach to Manipulator Control: The Cerebellar Model Articulation Controller (CMAC) // Journal of Dynamic Systems, Measurement, and Control. 1975. Vol. 97, Issue 3. P. 220. doi: 10.1115/1.3426922 

Albus J. S. Data Storage in the Cerebellar Model Articulation Controller (CMAC) // Journal of Dynamic Systems, Measurement, and Control. 1975. Vol. 97, Issue 3. P. 228. doi: 10.1115/1.3426923 

Wang L.-X. Fuzzy systems are universal approximators // Proc. IEEE Int. Conf. On Fuzzy Systems. San Diego, 1992. P. 1163–1170. doi: 10.1109/fuzzy.1992.258721 

Medical sample classifier design using fuzzy cerebellar model neural networks / Li H.-Y., Yeh R.-G., Lin Y.-C., Lin L.-Y., Zhao J., Lin C.-M., Rudas I. J. // Acta polytechnica Hungarica. 2016. Vol. 13, Issue 6. P. 7–24. doi: 10.12700/aph.13.6.2016.6.1 

Lee C.-H., Chang F.-Y., Lin C.-M. An Efficient Interval Type-2 Fuzzy CMAC for Chaos Time-Series Prediction and Synchronization // IEEE Transactions on Cybernetics. 2014. Vol. 44, Issue 3. P. 329–341. doi: 10.1109/tcyb.2013.2254113 

Chung C.-C., Lin C.-C. Fuzzy Brain Emotional Cerebellar Model Articulation Control System Design for Multi-Input Multi-Output Nonlinear // Acta Polytechnica Hungarica. 2015. Vol. 12, Issue 4. P. 39–58. doi: 10.12700/aph.12.4.2015.4.3 

Xu S., Jing Y. Research and Application of the Pellet Grate Thickness Control System Base on Improved CMAC Neural Network Algorithm // Journal of Residuals Science & Technology. 2016. Vol. 13, Issue 6. P. 150.1–150.9.

Cheng H. The Fuzzy CMAC Based on RLS Algorithm // Applied Mechanics and Materials. 2013. Vol. 432. P. 478–782. doi: 10.4028/www.scientific.net/amm.432.478 

Huber P. J., Ronchetti E. M. Robust Statistics. 2nd ed. Wiley, 2009. 380 p.

Jou C.-C. A fuzzy cerebellar model articulation controller // [1992 Proceedings] IEEE International Conference on Fuzzy Systems. 1992. doi: 10.1109/fuzzy.1992.258722 

Nie J., Linkens D. A. FCMAC: A fuzzified cerebellar model articulation controller with self-organizing capacity // Automatica. 1994. Vol. 30, Issue 4. P. 655–664. doi: 10.1016/0005-1098(94)90154-6 

Knuth D. Sorting and Searching. The Art of Computer Programming. Vol. 3. Menlo Park, Calif.: Addison Wesley, 1973. 506 p.

Wang Z.-Q., Schiano J. L., Ginsberg M. Hash-coding in CMAC neural networks // Proceedings of International Conference on Neural Networks (ICNN'96). 1996. doi: 10.1109/icnn.1996.549156 

Rudenko O. G., Bessonov A. A. Heshirovanie informacii v neyronnoy seti SMAS // Upravlyayushchie sistemy i mashiny. 2004. Issue 5. P. 67–73.

Ching-Tsan C., Chun-Shin L. CMAC with General Basis Functions // Neural Networks. 1996. Vol. 9, Issue 7. P. 1199–1211. doi: 10.1016/0893-6080(96)00132-3 

Lane S. H., Handelman D. A., Gelfand J. J. Theory and development of higher-order CMAC neural networks // IEEE Control Systems. 1992. Vol. 12, Issue 2. P. 23–30. doi: 10.1109/37.126849 

Wang S., Lu H. Fuzzy system and CMAC network with B-spline membership/basis functions are smooth approximators // Soft Computing – A Fusion of Foundations, Methodologies and Applications. 2003. Vol. 7, Issue 8. P. 566–573. doi: 10.1007/s00500-002-0242-2 

Rudenko O. G., Bessonov A. A. M-obuchenie radial'no-bazisnyh setey s ispol'zovaniem asimmetrichnyh funkciy vliyaniya // Problemy upravleniya i informatiki. 2012. Issue 1. P. 79–93.

Rudenko O. G., Bessonov A. A. Robastnoe obuchenie radial'no-bazisnyh setey // Kibernetika i sistemnyy analiz. 2011. Issue 6. P. 38–46.

Rudenko O. G., Bezsonov A. A. Robust Learning Wavelet Neural Networks // Journal of Automation and Information Sciences. 2010. Vol. 42, Issue 10. P. 1–15. doi: 10.1615/jautomatinfscien.v42.i10.10 

Vazan M. Stohasticheskaya approksimaciya. Moscow: Mir, 1972. 289 p.

Cypkin Ya. Z. Osnovy informacionnoy teorii identifikacii. Moscow: Nauka, 1984. 320 p.

Cypkin Ya. Z., Polyak B. T. Ogrublennyy metod maksimal'nogo pravdopodobiya // Dinamika sistem. 1977. Issue 12. P. 22–46.

Narendra K. S., Parthasarathy K. Identification and control of dynamical systems using neural networks // IEEE Transactions on Neural Networks. 1990.Vol. 1, Issue 1. P. 4–27. doi: 10.1109/72.80202 

Rudenko O. G., Bessonov A. A. Neyronnaya set' SMAS i ee primenenie v zadachah identifikacii i upravleniya nelineynymi dinamicheskimi ob'ektami // Kibernetika i sistemniy analiz. 2005. Issue 5. P. 16–28.

Liao Y.-L., Peng Y.-F. Applications of Prediction and Identification Using Adaptive DCMAC Neural Networks // International Journal of Computer and Information Engineering. 2011. Vol. 5, Issue 6. P. 677–682.

Zhao J., Lin L.-Y., Lin C.-M. A General Fuzzy Cerebellar Model Neural Network Multidimensional Classifier Using Intuitionistic Fuzzy Sets for Medical Identification // Computational Intelligence and Neuroscience. 2016. Vol. 2016. P. 1–9. doi: 10.1155/2016/8073279 

Commuri S., Lewis F. L. CMAC neural networks for control of nonlinear dynamical systems, structure, stability, and passivity // Proc. IEEE Int. Symp. Intell. Control. San Francisco, 1995. P. 123–129.

Commuri S., Lewis F. L., Jagannathan S. Discrete-time CMAC neural networks for control applications // Proceedings of 1995 34th IEEE Conference on Decision and Control. New Orleans, 1995. doi: 10.1109/cdc.1995.478453 

Jagannathan S. Discrete-time CMAC NN control of feedback linearizable nonlinear systems under a persistence of excitation // IEEE Transactions on Neural Networks. 1999. Vol. 10, Issue 1. P. 128–137. doi: 10.1109/72.737499 

Lin C.-M., Peng Y.-F. Adaptive CMAC-Based Supervisory Control for Uncertain Nonlinear Systems // IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics). 2004. Vol. 34, Issue 1. P. 1248–1260. doi: 10.1109/tsmcb.2003.822281 

A Novel Wavelet-based-CMAC Neural Network Controller for Nonlinear Systems / Lee C.-H., Wang B.-H., Chang H.-H., Pang Y.-H. // The 2006 IEEE International Joint Conference on Neural Network Proceedings. Vancouver, BC, Canada, 2006. P. 2593–2599. doi: 10.1109/ijcnn.2006.247136 

Aved'yan E. D., Hormel' M. Povyshenie skorosti skhodimosti processa obucheniya v special'noy sisteme associativnoy pamyati // Avtomatika i telemekhanika. 1991. Issue 12. P. 100–109.

Fuzzy CMAC structures / Mohajeri K., Zakizadeh M., Moaveni B., Teshnehlab M. // 2009 IEEE International Conference on Fuzzy Systems. 2009. doi: 10.1109/fuzzy.2009.5277185 



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

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Copyright (c) 2018 Oleg Rudenko, Oleksandr Bezsonov, Oleh Lebediev

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ISSN (print) 1729-3774, ISSN (on-line) 1729-4061