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Data-driven Nonlinear System Identification Under Bounded Noise Using Kernel Learning-based Ellipsoidal Set-membership

Authors

DOI:

https://doi.org/10.26636/jtit.2026.4.2735

Keywords:

ellipsoidal outer-bounding, kernel methods, nonlinear system identification, online noise bound estimation, set-membership identification

Abstract

Nonlinear system identification under bounded interferences remains a challenging problem when the noise bound is unavailable a priori. This paper presents a recursive kernel-based set-membership identification algorithm that combines the ellipsoidal outer-bounding (EOB) set-membership method with kernel learning to address this issue. Instead of identifying the nonlinear system directly in the input space, the proposed method exploits a reproducing kernel Hilbert space (RKHS), where the nonlinear estimation problem is represented as a linear regression model. Furthermore, a recursive data-driven procedure is introduced to estimate the noise bound simultaneously with the model parameters. Theoretical convergence properties of the proposed algorithm are determined. The performance of the proposed algorithm is validated through numerical simulation.

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References

[1] F. Li, T. Zheng, and Q. Cao, "Modeling and Identification for Practical Nonlinear Process Using Neural Fuzzy Network-based Hammerstein System", Transactions of the Institute of Measurement and Control, vol. 45, pp. 2091-2102, 2023. DOI: https://doi.org/10.1177/01423312221143777
View in Google Scholar

[2] F. Li, L. Song, T. Wang, and R. Liu, "Parameter Identification for Nonlinear Hammerstein Models with Stacked Sparse Autoencoder Network", Engineering Applications of Artificial Intelligence, vol. 163, art. no. 113002, 2026. DOI: https://doi.org/10.1016/j.engappai.2025.113002
View in Google Scholar

[3] A. Bouklata et al., "Online Identification Method for Wiener Nonlinear Systems", International Journal of Dynamics and Control, vol. 13, art. no. 65, 2025. DOI: https://doi.org/10.1007/s40435-024-01569-3
View in Google Scholar

[4] F. Li, S. Qian, N. He, and B. Li, "Estimation of Wiener Nonlinear Systems with Measurement Noises Utilizing Correlation Analysis and Kalman Filter", International Journal of Robust and Nonlinear Control, vol. 34, pp. 4706-4718, 2024. DOI: https://doi.org/10.1002/rnc.7224
View in Google Scholar

[5] I. Constantin, J. Constantin, and A. Bigand, "A New Kernel RLS Algorithm for Systems with Bounded Noise", International Journal of Adaptive Control and Signal Processing, vol. 32, pp. 344-361, 2017. DOI: https://doi.org/10.1002/acs.2845
View in Google Scholar

[6] R. Fateh, A. Darif, A. Boumezzough, S. Safi, and M. Frikel, "A Novel Kernel Algorithm for Finite Impulse Response Channel Identification", Journal of Telecommunications and Information Technology, vol. 92, pp. 84-93, 2023. DOI: https://doi.org/10.26636/jtit.2023.169823
View in Google Scholar

[7] R. Fateh, A. Darif, and S. Safi, "Kernel and Linear Adaptive Methods for the BRAN Channels Identification", Advanced Intelligent Systems for Sustainable Development (AI2SD’2020), vol. 1418, pp. 579-591, 2022. DOI: https://doi.org/10.1007/978-3-030-90639-9_47
View in Google Scholar

[8] N. Aronszajn, "Theory of Reproducing Kernels", Transactions of the American Mathematical Society, vol. 68, pp. 337-404, 1950. DOI: https://doi.org/10.1090/S0002-9947-1950-0051437-7
View in Google Scholar

[9] Y. Engel, S. Mannor, and R. Meir, "The Kernel Recursive Least-squares Algorithm", IEEE Transactions on Signal Processing, vol. 52, pp. 2275-2285, 2004. DOI: https://doi.org/10.1109/TSP.2004.830985
View in Google Scholar

[10] B. Schölkopf, A. Smola, and K.R. Müller, "Nonlinear Component Analysis as a Kernel Eigenvalue Problem", Neural Computation, vol. 10, pp. 1299-1319, 1998. DOI: https://doi.org/10.1162/089976698300017467
View in Google Scholar

[11] M. Zhang, X. Wang, X. Chen, and A. Zhang, "The Kernel Conjugate Gradient Algorithms", IEEE Transactions on Signal Processing, vol. 66, pp. 4377-4387, 2018. DOI: https://doi.org/10.1109/TSP.2018.2853109
View in Google Scholar

[12] S. Zhao, B. Chen, and J.C. Principe, "Kernel Adaptive Filtering with Maximum Correntropy Criterion", International Joint Conference on Neural Networks (IJCNN), San Jose, USA, 2011. DOI: https://doi.org/10.1109/IJCNN.2011.6033473
View in Google Scholar

[13] J. Zhao, H. Zhang, and J.A. Zhang, "Gaussian Kernel Adaptive Filters with Adaptive Kernel Bandwidth", Signal Processing, vol. 166, art. no. 107270, 2020. DOI: https://doi.org/10.1016/j.sigpro.2019.107270
View in Google Scholar

[14] Y. Li et al., "Learning the Uncertainty Sets of Linear Control Systems via Set Membership: A Non-asymptotic Analysis", Forty-First International Conference on Machine Learning, Vienna, Austria, 2024 (https://proceedings.mlr.press/v235/li24ci.html).
View in Google Scholar

[15] D. Chen, Z. Zhou, J. Hu, and J. Liu, "Set-membership State Estimation for Delayed Switched Systems with Fading Measurement and Interval Uncertainty", Optimal Control Applications and Methods, vol. 45, pp. 1691-1715, 2024. DOI: https://doi.org/10.1002/oca.3118
View in Google Scholar

[16] M. Pouliquen, E. Pigeon, and O. Gehan, "Output Error Identification for Multi-input Multi-output Systems with Bounded Disturbances", 50th IEEE Conference on Decision and Control and European Control Conference, Orlando, Florida, 2011. DOI: https://doi.org/10.1109/CDC.2011.6160211
View in Google Scholar

[17] Y. Liu, Y. Zhao, and F. Wu, "Ellipsoidal State-bounding-based Set-membership Estimation for Linear Systems with Unknown-but-bounded Disturbances", IET Control Theory & Applications, vol. 10, pp. 431-442, 2016. DOI: https://doi.org/10.1049/iet-cta.2015.0654
View in Google Scholar

[18] H. El Maizi, M. Pouliquen, S. Safi, and M. Frikel, "Identification of Output Error Model with Bounded Disturbances", 11th IEEE International Conference on Systems and Control (ICSC), Sousse, Tunisia, 2023. DOI: https://doi.org/10.1109/ICSC58660.2023.10449868
View in Google Scholar

[19] M. Pouliquen et al., "Identification of ARMAX Systems with Bounded Noise", Journal of the Franklin Institute, vol. 362, art. no. 108061, 2025. DOI: https://doi.org/10.1016/j.jfranklin.2025.108061
View in Google Scholar

[20] H. El Maizi et al., "Kernel-based Machine Learning Ellipsoidal Outer Bounding for Non-line-of-sight Outdoor and Indoor Channel Identification", Telecommunication Systems, vol. 89, art. no. 40, 2026. DOI: https://doi.org/10.1007/s11235-026-01423-1
View in Google Scholar

[21] T.M. Lin, M. Nayeri, and J.R. Deller, "A Consistently Convergent OBE Algorithm with Automatic Estimation of Error Bounds", International Journal of Adaptive Control and Signal Processing, vol. 12, pp. 305-324, 1998. DOI: https://doi.org/10.1002/(SICI)1099-1115(199806)12:4<305::AID-ACS491>3.3.CO;2-M
View in Google Scholar

[22] L. Pronzato and E. Walter, "Minimal Volume Ellipsoids", International Journal of Adaptive Control and Signal Processing, vol. 8, pp. 15-30, 1994. DOI: https://doi.org/10.1002/acs.4480080103
View in Google Scholar

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Submitted

2026-07-21

Published

2026-10-07

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Copyright (c) 2026 Hasna El Maizi, Mathieu Pouliquen, Rachid Fateh, Miloud Frikel, Said Safi

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This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

[1]
H. El Maizi, M. Pouliquen, R. Fateh, M. Frikel, and S. Safi, “Data-driven Nonlinear System Identification Under Bounded Noise Using Kernel Learning-based Ellipsoidal Set-membership”, JTIT, vol. 106, no. 4, pp. 1–13, Oct. 2026, doi: 10.26636/jtit.2026.4.2735.

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