222
Views
7
CrossRef citations to date
0
Altmetric
Original Articles

Application of neural networks with orthogonal activation functions in control of dynamical systems

, , , , &
Pages 667-685 | Received 22 Aug 2014, Accepted 07 Mar 2015, Published online: 27 Apr 2015

References

  • Antić, D., Danković, B., Nikolić, S., Milojković, M., & Jovanović, Z. (2012). Approximation based on orthogonal and almost orthogonal functions. Journal of the Franklin Institute, 349(1), 323–336. doi:10.1016/j.jfranklin.2011.11.006
  • Antić, D., Milovanović, M., Nikolić, S., Milojković, M., & Perić, S. (2013). Simulation model of magnetic levitation based on NARX neural networks. International Journal of Intelligent Systems and Applications, 5(5), 25–32. doi:10.5815/ijisa
  • Antić, D., Nikolić, S., Milojković, M., Danković, N., Jovanović, Z., & Perić, S. (2011). Sensitivity analysis of imperfect systems using almost orthogonal filters. Acta Polytechnica Hungarica, 8(6), 79–94.
  • Becerra, V. M., Garces, F. R., Nasuto, S. J., & Holderbaum, W. (2005). An efficient parameterization of dynamic neural networks for nonlinear system identification. IEEE Transactions on Neural Networks, 16(4), 983–988. doi:10.1109/TNN.2005.849844
  • Bilgili, E., Göknar, İ. C., & Ucan, O. N. (2005). Cellular neural network with trapezoidal activation function. International Journal of Circuit Theory and Applications, 33(5), 393–417. doi:10.1002/(ISSN)1097-007X
  • Brezinski, C., Driver, K. A., & Redivo-Zaglia, M. (2004). Quasi-orthogonality with applications to some families of classical orthogonal polynomials. Applied Numerical Mathematics, 48(2), 157–168. doi:10.1016/j.apnum.2003.10.001
  • Danković, B., Nikolić, S., Milojković, M., & Jovanović, Z. (2009). A class of almost orthogonal filters. Journal of Circuits, Systems and Computers, 18(5), 923–931. doi:10.1142/S0218126609005447
  • David, R.-C., Dragos, C.-A., Bulzan, R.-G., Precup, R.-E., Petriu, E. M., & Radac, M.-B. (2012). An approach to fuzzy modeling of magnetic levitation systems. International Journal of Artificial Intelligence, 9(A12), 1–18.
  • Godarzi, A. A., Amiri, R. M., Talaei, A., & Jamasb, T. (2014). Predicting oil price movements: A dynamic artificial neural network approach. Energy Policy, 68, 371–382. doi:10.1016/j.enpol.2013.12.049
  • Heuberger, P., Hof, P. V., & Wahlberg, B. (2005). Modelling and identification with rational orthogonal basis functions. London: Springer-Verlag.
  • Inteco. (2011). The magnetic levitation system (MLS)-user’s manual. Retrieved from www.inteco.com.pl
  • Jalab, H. A., & Ibrahim, R. W. (2011). New activation functions for complex-valued neural network. International Journal of the Physical Sciences, 6(7), 1766–1772.
  • Li, Z., Sun, H., Wu, X., & Liu, Q. (2012). Modeling and levitation control of a novel M-DOF actuator based on neural network. International Journal of Applied Electromagnetics and Mechanics, 38(4), 217–230.
  • Lin, F.-J., Teng, L.-T., & Shieh, P. H. (2007). Adaptive backstepping control system for magnetic levitation apparatus using recurrent neural network. In Proceedings of the 33rd annual conference of the IEEE, IECON 2007 (pp. 671–676). Taipei: IEEE.
  • Lin, T., Horne, B. G., Tino, P., & Giles, C. L. (1995). Learning long-term dependencies is not as difficult with NARX networks. In Proceedings of the advances in neural information processing systems 8 (pp. 577–583). Cambridge, MA: MIT Press.
  • Lin, T., Horne, B. G., Tino, P., & Giles, C. L. (1996). Learning long-term dependencies in NARX recurrent neural networks. IEEE Transactions on Neural Networks, 7(6), 1329–1338. doi:10.1109/72.548162
  • Milojković, M., Nikolić, S., Danković, B., Antić, D., & Jovanović, Z. (2010). Modelling of dynamical systems based on almost orthogonal polynomials. Mathematical and Computer Modelling of Dynamical Systems, 16(2), 133–144. doi:10.1080/13873951003740082
  • Milojković, M. T., Antić, D. S., Nikolić, S. S., Jovanović, Z. D., & Perić, S. L. (2013). On a new class of quasi-orthogonal filters. International Journal of Electronics, 100(10), 1361–1372. doi:10.1080/00207217.2012.743087
  • Nelles, O. (2001). Nonlinear system identification: From classical approaches to neural networks and fuzzy models. Berlin: Springer-Verlag.
  • Nikolić, S., Antić, D., Danković, B., Milojković, M., Jovanović, Z., & Perić, S. (2010). Orthogonal functions applied in antenna positioning. Advances in Electrical and Computer Engineering, 10(4), 35–42. doi:10.4316/aece.2010.04006
  • Nikolić, S. S. (2014). Application of generalized classical filters in intelligent control systems (PhD dissertation). University of Niš, Faculty of Electronic Engineering, Department of Control Systems, Republic of Serbia.
  • Nikolić, S. S., Antić, D. S., Perić, S. L., Danković, N. B., & Milojković, M. T. (2015). Design of generalized orthogonal filters: Application to the modelling of dynamical systems. International Journal of Electronics. Advance online publication. doi:10.1080/00207217.2015.1036367
  • Özdemir, N., İskender, B., & Özgür, N. Y. (2011). Complex valued neural network with Möbius activation function. Communications in Nonlinear Science and Numerical Simulation, 16(12), 4698–4703. doi:10.1016/j.cnsns.2011.03.005
  • Plett, G. L. (2003). Adaptive inverse control of linear and nonlinear systems using dynamic neural networks. IEEE Transactions on Neural Networks, 14(2), 360–376. doi:10.1109/TNN.2003.809412
  • Sathasivam, S. (2011). Boltzmann machine and new activation function comparison. Applied Mathematical Sciences, 5(78), 3853–3860.
  • Sibi, P., Jones, S. A., & Siddarth, P. (2013). Analysis of different activation functions using back propagation neural networks. Journal of Theoretical and Applied Information Technology, 47(3), 1264–1268.
  • Widrow, B., Plett, G., Ferreira, E., & Lamego, M. (1998). Adaptive inverse control based on nonlinear adaptive filtering. In Proceedings of the 5th IFAC workshop on algorithms and architectures for real-time control (pp. 247–252). Cancun: Oxford.
  • Yang, S., & Tseng, C. (1996). An orthogonal neural network for function approximation. IEEE Transactions on Systems, Manual and Cybernetics, Particle B (Cybernetics), 26(5), 779–785. doi:10.1109/3477.537319
  • Zuo, W., Zhu, Y., & Cai, L. (2009). Fourier-neural-network-based learning control for a class of nonlinear systems with flexible components. IEEE Transactions on Neural Networks, 20(1), 139–151. doi:10.1109/TNN.2008.2006496

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.