1,765
Views
2
CrossRef citations to date
0
Altmetric
Research Article

Input-to-state stability for system identification with continuous-time Runge–Kutta neural networks

ORCID Icon, &
Pages 24-40 | Received 04 Jan 2021, Accepted 05 Sep 2021, Published online: 08 Nov 2021

References

  • Ahmed, N. K., Atiya, A. F., Gayar, N. E., & El-Shishiny, H. (2010). An empirical comparison of machine learning models for time series forecasting. Econometric Reviews, 29(5–6), 594–621. https://doi.org/10.1080/07474938.2010.481556
  • Aljamaan, I. A., Al-Dhaifallah, M. M., & Westwick, D. T. (2021). Hammerstein box-Jenkins system identification of the cascaded tanks benchmark system. Mathematical Problems in Engineering, 2021(6), 1–8. https://doi.org/10.1155/2021/6613425
  • Barabanov, N. E., & Prokhorov, D. V. (2002). Stability analysis of discrete-time recurrent neural networks. IEEE Transactions on Neural Networks, 13(2), 292–303. https://doi.org/10.1109/72.991416
  • Belz, J., Münker, T., Heinz, T. O., Kampmann, G., & Nelles, O. (2017). Automatic modeling with local model networks for benchmark processes. IFAC-PapersOnLine, 50(1), 470–475. https://doi.org/10.1016/j.ifacol.2017.08.089
  • Birpoutsoukis, G., P. Z. Csurcsia, & Schoukens, J. (2018). Efficient multidimensional regularization for Volterra series estimation. Mechanical Systems and Signal Processing, 104(11), 896–914. https://doi.org/10.1016/j.ymssp.2017.10.007
  • Butcher, J. C. (2016). Numerical methods for ordinary differential equations (3rd ed.). Wiley. https://doi.org/10.1002/9781119121534
  • Byrd, R. H., Hribar, M. E., & Nocedal, J. (1999). An interior point algorithm for large-scale nonlinear programming. SIAM Journal on Optimization, 9(4), 877–900. https://doi.org/10.1137/S1052623497325107
  • Chaves Ferreira Pinto, W., & Hultmann Ayala, H. V. (2020). Ensemble grey and black-box nonlinear system identification of a positioning system. Anais da Sociedade Brasileira de Automatica, 2(1), CBA2020. https://doi.org/10.48011/asba.v2i1.1570
  • Chen, S., Billings, S. A., & Grant, P. M. (1990). Non-linear system identification using neural networks. International Journal of Control, 51(6), 1191–1214. https://doi.org/10.1080/00207179008934126
  • Cooper, G. J. (1984). A generalization of algebraic stability for Runge–Kutta methods. IMA Journal of Numerical Analysis, 4(4), 427–440. https://doi.org/10.1093/imanum/4.4.427
  • Deflorian, M. (2010). On Runge-Kutta neural networks: Training in series-parallel and parallel configuration. 49th IEEE Conference on Decision and Control (CDC) (pp. 4480–4485). https://doi.org/10.1109/CDC.2010.5717492
  • Deflorian, M. (2011). Versuchsplanung und Methoden zur Identifikation zeitkontinuierlicher Zustandsraummodelle am Beispiel des Verbrennungsmotors [Dissertation]. Technische Universität München.
  • Deflorian, M., Klöpper, F., & Rückert, J. (2010). Online dynamic black box modelling and adaptive experiment design in combustion engine calibration. IFAC Proceedings Volumes, 43(7), 703–708. https://doi.org/10.3182/20100712-3-DE-2013.00068
  • Deflorian, M., & Rungger, M. (2014). Generalization of an input-to-state stability preserving Runge–Kutta method for nonlinear control systems. Journal of Computational and Applied Mathematics, 255(1), 346–352. https://doi.org/10.1016/j.cam.2013.05.017
  • Efe, M. O., & Kaynak, O. (2000). A comparative study of soft-computing methodologies in identification of robotic manipulators. Robotics and Autonomous Systems, 30(3), 221–230. https://doi.org/10.1016/S0921-8890(99)00087-1
  • Forgione, M., & Piga, D. (2021a). Continuous-time system identification with neural networks: Model structures and fitting criteria. European Journal of Control, 59(5), 69–81. https://doi.org/10.1016/j.ejcon.2021.01.008
  • Forgione, M., & Piga, D. (2021b). dynoNet: a neural network architecture for learning dynamical systems. International Journal of Adaptive Control and Signal Processing, 35(4), 612–626. https://doi.org/10.1002/acs.v35.4
  • Giorgio, G. (2017). Various proofs of the sylvester criterion for quadratic forms. Journal of Mathematics Research, 9(6), 55. https://doi.org/10.5539/jmr.v9n6p55
  • Haykin, S. (1990). Neural networks – A comprehensive foundation. Prentice Hall.
  • Horn, R. A., & Johnson, C. R. (2012). Matrix analysis (2nd ed.). Cambridge University Press.
  • Hostettler, R., Tronarp, F., & Särkkä, S. (2018). Modeling the drift function in stochastic differential equations using reduced rank Gaussian processes. IFAC-PapersOnLine, 51(15), 778–783. https://doi.org/10.1016/j.ifacol.2018.09.137
  • Hu, S., & Wang, J. (2002a). Global stability of a class of continuous-time recurrent neural networks. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 49(9), 1334–1347. https://doi.org/10.1109/TCSI.2002.802360
  • Hu, S., & Wang, J. (2002b). Global stability of a class of discrete-time recurrent neural networks. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 49(8), 1104–1117. https://doi.org/10.1109/TCSI.2002.801284
  • Janot, A., Gautier, M., & Brunot, M. (2019). Data Set and Reference Models of EMPS. 2019 Workshop on Nonlinear System Identification Benchmarks, Eindhoven, The Netherlands.
  • Janot, A., Young, P. C., & Gautier, M. (2017). Identification and control of electro-mechanical systems using state-dependent parameter estimation. International Journal of Control, 90(4), 643–660. https://doi.org/10.1080/00207179.2016.1209565
  • Jiang, Z. P.., & Wang, Y. (2001). Input-to-state stability for discrete-time nonlinear systems. Automatica, 37(6), 857–869. https://doi.org/10.1016/S0005-1098(01)00028-0
  • Khalil, H. K. (2002). Nonlinear systems (3rd ed.). Prentice Hall.
  • Mavkov, B., Forgione, M., & Piga, D. (2020). Integrated neural networks for nonlinear continuous-time system identification. IEEE Control Systems Letters, 4(4), 851–856. https://doi.org/10.1109/LCSYS.2020.2994806
  • Narendra, K., & Parthasarathy, K. (1990). Identification and control of dynamical systems using neural networks. IEEE Transactions on Neural Networks, 1(1), 4–27. https://doi.org/10.1109/72.80202
  • Nelles, O. (2001). Nonlinear system identification. Springer Verlag.
  • Relan, R., Tiels, K., Marconato, A., & Schoukens, J. (2017). An unstructured flexible nonlinear model for the cascaded water-tanks benchmark. IFAC-PapersOnLine, 50(1), 452–457. https://doi.org/10.1016/j.ifacol.2017.08.074
  • Sanchez, E. N., & Perez, J. P. (1999). Input-to-state stability (ISS) analysis for dynamic neural networks. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 46(11), 1395–1398. https://doi.org/10.1109/81.802844
  • Schoukens, M., Mattsson, P., Wigren, T., & Noel, J. P. (2016). Cascaded tanks benchmark combining soft and hard nonlinearities. Workshop on Nonlinear System Identification Benchmarks, Brussels, Belgium.
  • Sjoberg, J., Zhang, Q., Ljung, L., Benveniste, A., Deylon, B., Glorennec, P. Y.., & Juditsky, A. (1995). Nonlinear black-box modeling in system identification: a unified overview. Automatica, 31(12), 1691–1724. https://doi.org/10.1016/0005-1098(95)00120-8
  • Sontag, E. D. (2008). Input to state stability: basic concepts and results. In P. Nistri & G. Stefani (Eds.), Nonlinear and optimal control theory (pp. 163–220). Lecture notes in mathematics (Vol. 1932). Springer. https://doi.org/10.1007/978-3-540-77653-6_3.
  • Svensson, A., & Schön, T. B. (2017). A flexible state–space model for learning nonlinear dynamical systems. Automatica, 80(11), 189–199. https://doi.org/10.1016/j.automatica.2017.02.030
  • Uçak, K. (2020). A novel model predictive Runge–Kutta neural network controller for nonlinear MIMO systems. Neural Processing Letters, 51(2), 1789–1833. https://doi.org/10.1007/s11063-019-10167-w
  • Wang, L., & Xu, Z. (2006). Sufficient and necessary conditions for global exponential stability of discrete-time recurrent neural networks. IEEE Transactions on Circuits and Systems I: Regular Papers, 53(6), 1373–1380. https://doi.org/10.1109/TCSI.2006.874179
  • Wang, Y. J., & Lin, C. T. (1998). Runge–Kutta neural network for identification of dynamical systems in high accuracy. IEEE Transactions on Neural Networks, 9(2), 294–307. https://doi.org/10.1109/72.661124
  • Weigand, J., Volkmann, M., & Ruskowski, M. (2020). Neural Adaptive Control of a Robot Joint Using Secondary Encoders. In K. Berns and D. Görges (Eds), Advances in service and industrial robotics (Vol. 980, pp. 153–161). Cham: Springer International Publishing. https://doi.org/10.1007/978-3-030-19648-6_18
  • Williams, R. J., & Zipser, D. (1989). A learning algorithm for continually running fully recurrent neural networks. Neural Computation, 1(2), 270–280. https://doi.org/10.1162/neco.1989.1.2.270
  • Worden, K., Barthorpe, R. J., Cross, E. J., Dervilis, N., Holmes, G. R., Manson, G., & Rogers, T. J. (2018). On evolutionary system identification with applications to nonlinear benchmarks. Mechanical Systems and Signal Processing, 112, 194–232. https://doi.org/10.1016/j.ymssp.2018.04.001
  • Yu, W. (2004). Nonlinear system identification using discrete-time recurrent neural networks with stable learning algorithms. Information Sciences, 158, 131–147. https://doi.org/10.1016/j.ins.2003.08.002