“A NARMAX model representation for adaptive control based on local models”
Authors: Tor A. Johansen and Bjarne A. Foss,Affiliation: NTNU, Department of Engineering Cybernetics
Reference: 1992, Vol 13, No 1, pp. 25-39.
Keywords: Nonlinear systems, adaptive control, model representation, system identification, NARMAX models
Abstract: Here we address the problem of representing NARMAX (nonlinear ARMAX) models with application to adaptive control. We propose a nonlinear model representation where a number of simple local models are combined. The local models are valid in specific operation regimes of the process. Explicitly defined model validity functions make it possible to combine the local models by interpolation. During online identification, only the local models corresponding to the current process operation regime are updated. It is therefore not necessary to relearn the model each time there is a change in the operation regime of the process. The concept is illustrated by a simulation example of a nonlinear pH-neutralization process.
PDF (1534 Kb)
DOI: 10.4173/mic.1992.1.3DOI forward links to this article:
| [1] J. Kalkkuhl, K.J. Hunt and H. Fritz (1999), doi:10.1109/72.774241 |
| [2] Yun Li and Kay Chen Tan (2000), doi:10.1007/BF02703752 |
| [3] F. Azimzadeh, O. Galán and J.A. Romagnoli (2001), doi:10.1016/S0098-1354(00)00629-3 |
| [4] S. Pettersson and B. Lennartson (2002), doi:10.1080/0020717021000023762 |
| [5] K.J. Hunt, J.C. Kalkkuhl, H. Fritz and T.A. Johansen (1996), doi:10.1016/0967-0661(95)00223-5 |
| [6] N. de N. Donaldson, H. Gollee, K.J. Hunt, J.C. Jarvis and M.K.N. Kwende (1995), doi:10.1016/1350-4533(94)00013-Y |
| [7] K. Srinivasan and K. Anbarasan (2013), doi:10.1016/j.isatra.2012.11.008 |
| [8] Jin Yan, Anthony D'Amato and Dennis Bernstein (2012), doi:10.2514/6.2012-4448 |
| [9] (2006), doi:10.2514/5.9781600866852.0265.0294 |
| [10] Th.H. Göttsche, K.J. Hunt and T.A. Johansen (1998), doi:10.1016/S0378-4754(98)00083-4 |
| [11] B.A. Foss and T.A. Johansen (1992), doi:10.1016/S0066-4138(09)91010-2 |
| [12] Gregor Gregor i and Gordon Lightbody (2008), doi:10.1016/j.engappai.2007.11.004 |
| [13] S. C. Mcloone, S. Mcginnity and G. W. Irwin (2002), doi:10.1080/0020772021000046243 |
| [14] M. A. Unar and D. J. Murray-Smith (1999), doi:10.1002/(SICI)1099-1115(199906)13:4<203::AID-ACS544>3.0.CO;2-T |
| [15] Tor A. Johansen and Bjarne A. Foss (1995), doi:10.1016/0005-1098(94)00096-2 |
| [16] E. Ronco and P. J. Gawthrop (1999), doi:10.1049/ip-cta:19990720 |
| [17] K.J Hunt, R Haas and J.C Kalkkuhl (1996), doi:10.1016/0967-0661(96)00104-9 |
| [18] K.J. Hunt, M. Munih, N.de.N. Donaldson and F.M.D. Barr (1998), doi:10.1109/10.704868 |
| [19] Lior Rokach (2006), doi:10.1007/s10044-006-0041-y |
| [20] TOR A. JOHANSEN (1994), doi:10.1016/B978-0-08-042229-9.50028-8 |
| [21] B.A. Foss and T.A. Johansen (1993), doi:10.1016/B978-0-08-041898-8.50014-1 |
| [22] Lior Rokach (2010), doi:10.1007/s10462-009-9124-7 |
| [23] Séamus C. McLoone and George W. Irwin (2008), doi:10.1111/j.1934-6093.2003.tb00122.x |
| [24] Kirill R. Chernyshov (2009), doi:10.1109/SIBCON.2009.5044836 |
| [25] D. Neumerkel, R. Murray-Smith and H. Gollee (1993), doi:10.1109/IJCNN.1993.716995 |
| [26] K.J. Hunt, R. Haas and R. Murray-Smith (1994), doi:10.1109/CDC.1994.411597 |
| [27] L. Rokach and O. Mainon (2005), doi:10.1109/GRC.2005.1547369 |
| [28] K. Kiriakidis (1998), doi:10.1109/CDC.1998.758494 |
| [29] Neumerkel, Franz, Kruger and Hidiroglu (1994), doi:10.1109/CCA.1994.381407 |
| [30] K.C. Tan, Y. Li and M.L. Wang (2000), doi:10.1109/IECON.2000.972437 |
| [31] P.J. Gawthrop (1995), doi:10.1109/ICSMC.1995.537873 |
| [32] B.A. Foss and T.A. Johansen (1993), doi:10.1109/IFIS.1993.324209 |
| [33] Ruiyao Gao, A. O'dywer and E. Coyle (2002), doi:10.1109/WCICA.2002.1020140 |
| [34] Ahmed Abdelhadi, J. Barry Gomm, DingLi Yu and Kumaran Rajarathinam (2014), doi:10.1109/IConAC.2014.6935496 |
| [35] Ahmed Abdelhadi, J. Barry Gomm, DingLi Yu and Kumaran Rajarathinam (2014), doi:10.1109/CONTROL.2014.6915167 |
| [36] S.C. McLoone and G.W. Irwin (2001), doi:10.1109/ACC.2001.945959 |
| [37] (2015), doi:10.2514/5.9781624102790.0303.0334 |
| [38] Qinghao Rong, Seán F. McLoone and George W. Irwin (2002), doi:10.3182/20020721-6-ES-1901.00119 |
| [39] Rapeepong Rattanawaorahirunkul, Peerayot Sanposh and Chanin Panjapornpon (2016), doi:10.1109/ELINFOCOM.2016.7562975 |
| [40] Séamus c. McLoone, George W. Irwin and Seán F. McLoone (2001), doi:10.1016/S1474-6670(17)32923-3 |
| [41] Séamus Mc Loone and George Irwin (1998), doi:10.1016/S1474-6670(17)42149-5 |
| [42] Tor A. Johansen (1994), doi:10.1016/S1474-6670(17)48145-6 |
| [43] T.A. Johansen and B.A. Foss (1993), doi:10.1016/S1474-6670(17)48422-9 |
| [44] B.A. Foss and T.A. Johansen (1992), doi:10.1016/S1474-6670(17)50798-3 |
| [45] Ahmed Adebowale Adeniran and Sami El Ferik (2017), doi:10.1109/TSMC.2016.2560147 |
| [46] Tor A. Johansen and Bjarne A. Foss (1994), doi:10.1016/S1474-6670(17)47704-4 |
| [47] K.J. Hunt, R. Haas and J.C. Kalkkuhl (1996), doi:10.1016/S1474-6670(17)58997-1 |
| [48] Jantanee Rungrangpitayagon, Sirivat Poonvasin, Peerayot Sanposh, Rapeepong Rattanawaorahirunkul, Kanjanapan Sukvichai and Chanin Panjapornpon (2017), doi:10.1109/ICTEmSys.2017.7958775 |
| [49] Gregor Gregorcic, Florian Oberlechner and Peter Drage (2017), doi:10.1109/MED.2017.7984118 |
| [50] Zhengguang Xu, Weijian Kong and Mushu Wang (2019), doi:10.1007/978-981-13-2291-4_1 |
| [51] G. Prabhakar, P. Nedumal Pugazhenthi and S. Selvaperumal (2014), doi:10.4028/www.scientific.net/AMM.573.297 |
| [52] Lior Rokach and Oded Maimon (2009), doi:10.1007/978-0-387-09823-4_51 |
| [53] Oded Maimon and Lior Rokach (2005), doi:10.1007/0-387-25465-X_46 |
| [54] Hidenori Inaoka, Kozue Kobayashi, Satoru Nebuya, Hiroshi Kumagai, Harukazu Tsuruta and Yutaka Fukuoka (2019), doi:10.1002/tee.22920 |
| [55] Jessyca A. Bessa and Guilherme A. Barreto (2019), doi:10.1016/j.ifacol.2019.06.101 |
| [56] Hongxia Zhu, Gang Zhao, Li Sun and Kwang Y. Lee (2019), doi:10.3390/su11185102 |
| [57] Kiriakos Kiriakidis (2005), doi:10.1115/IMECE2005-81666 |
| [58] Asif Mahfuz, Mohammad Abdul Mannan and S. M. Muyeen (2022), doi:10.3390/electronics11050729 |
| [59] Jessyca A. Bessa, Guilherme A. Barreto and Ajalmar R. Rocha-Neto (2022), doi:10.1007/s11063-022-11040-z |
[1] ÅSTRÖM, K.J. WITTENMARK, B. (1989). Adaptive Control, Addison Wesley.
[2] CHEN, S. BILLINGS, S.A. (1989). Representation of non-linear systems: the NARMAX model, Int. J. Control, 49, 1013-1032.
[3] CHEN, S., BILLINGS, S.A. GRANT, P.M. (1990). Non-linear system identification using neural networks, Int. J. Control, 51, 1191-1214 doi:10.1080/00207179008934126
[4] CHEN, S., BILLINGS, S.A., COWAN, C.F.N. GRANT, P.M. (1990). Practical identification of NARMAX models using radial basis functions, Int. Journal of Control, 52, 1321-1350 doi:10.1080/00207179008953599
[5] HILHORST, R.A., VAN AMERONGEN, J. LÖHNBERG, P. (1991). Intelligent adaptive control of mode-switch processes, In Proc. IFAC International Symposium on Intelligent Tuning and Adaptive Control, Singapore, January 1991.
[6] JOHANSEN, T. A. FOSS, B.A. (1992). Nonlinear local model representation for adaptive systems, Int. Conf. on Intelligent Control and Instrumentation, February 1992, Vol. 2, 677-682 doi:10.1109/SICICI.1992.637617
[7] JOHANSEN, T.A. FOSS, B.A. (1992). Representing and learning unmodeled dynamics with neural network memories, To be presented at American Control Conference, Chicago, June 1992.
[8] JOHANSEN, T.A. FOSS, B.A. (1992). Constructing NARMAX models using ARMAX models, Submitted to Int. J. Control.
[9] JONES, R.D. et al. (1991). Nonlinear adaptive networks: A little theory, a few applications, Technical Report 91-273, Los Alamos National Lab., New Mexico.
[10] LEONTARITIS, I.J. BILLINGS, S.A. (1985). Input-output parametric models for non-linear systems, Int. Journal of Control, 41, 303-344 doi:10.1080/0020718508961129
[11] MOODY, J. DARKEN, C.J. (1989). Fast learning in networks of locally-tuned processing units, Neural Computation, 1, 281-294 doi:10.1162/neco.1989.1.2.281
[12] SKEPPSTEDT, A. (1988). Construction of Composite Models from Large Data-sets, PhD thesis, University of Linköping.
[13] SKEPPSTEDT, A., LJUNG, L. MILLNERT, M. (1992). Construction of composite models from observed data, Int. J. Control, 55, 141-152 doi:10.1080/00207179208934230
[14] SÖDERSTRÖM, T. STOICA, P. (1988). System Identification, Prentice Hall.
[15] SØRHEIM, E. (1990). A combined network architecture using ART2 and back propagation for adaptive estimation of dynamical processes, Modeling, Identification and Control, 11, 191-199 doi:10.4173/mic.1990.4.2
[16] STOKBRO, K., HERTZ, J.A. UMBERGER, D.K. (1990). Exploiting neurons with localized receptive fields to learn chaos, Preprint 28, Niels Bohr Institute and NORDITA, Copenhagen.
[17] WALLER, K.V. GUSTAFSSON, T.K. (1983). Fundamental properties of continuous pH control, ISA Transactions, 22, 25-34.
BibTeX:
@article{MIC-1992-1-3,
title={{A NARMAX model representation for adaptive control based on local models}},
author={Johansen, Tor A. and Foss, Bjarne A.},
journal={Modeling, Identification and Control},
volume={13},
number={1},
pages={25--39},
year={1992},
doi={10.4173/mic.1992.1.3},
publisher={Norwegian Society of Automatic Control}
};