Discrete identification of continuous non-linear andnon-stationary dynamical systems that is insensitive to noise correlation and measurement outliers

• Autorzy: Kozłowski Janusz , Kowalczuk Zdzisław

Identyfikatory

DOI

10.24425/acs.2023.146281

• Języki publikacji: EN

Abstrakty

EN

The paper uses specific parameter estimation methods to identify the coefficients of continuous-time models represented by linear and non-linear ordinary differential equations. The necessary approximation of such systems in discrete time in the form of utility models is achieved by the use of properly tuned ‘integrating filters’ of the FIR type. The resulting discrete-time descriptions retain the original continuous parameterization and can be identified, for example, by the classical least squares procedure. Since in the presence of correlated noise, the estimated parameter values are burdened with an unavoidable systematic error (manifested by asymptotic bias of the estimates), in order to significantly improve the identification consistency, the method of instrumental variables is used here. In our research we use an estimation algorithm based on the least absolute values (LA) criterion of the least sum of absolute values, which is optimal in identifying linear and non-linear systems in the case of sporadic measurement errors. In the paper, we propose a procedure for determining the instrumental variable for a continuous model with non-linearity (related to the Wienerian system) in order to remove the evaluation bias, and a recursive sub-optimal version of the LA estmator. This algorithm is given in a simple (LA) version and in an instrumental variable version (IV-LA), which is robust to outliers, removes evaluation bias, and is suited to the task of identifying processes with non-linear dynamics (semi-Wienerian/NLID). In conclusion, the effectiveness of the proposed algorithmic solutions has been demonstrated by numerical simulations of the mechanical system, which is an essential part of the suspension system of a wheeled vehicle.

Słowa kluczowe

EN

instrumental variable; non-linear continuous-time models; optimization; supervisory systems; security systems; system identification

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2023
• Tom: Vol. 33, No. 2
• Strony: 391--411
• Opis fizyczny: Bibliogr. 36 poz., rys., wzory

Twórcy

autor

Kozłowski Janusz

• Gdansk University of Technology, WETI, Narutowicza 11/12, 80-952 Gdańsk

• https://orcid.org/0000-0002-8608-7754

autor

Kowalczuk Zdzisław

• Gdansk University of Technology, WETI, Narutowicza 11/12, 80-952 Gdańsk

• https://orcid.org/0000-0001-9174-546X

Bibliografia

• [1] S. Sagara and Z. Zhao: Numerical integration approach to on-line identification of continuous-time systems. Automatica, 26(1), (1990), 63-74. DOI: 10.1016/0005-1098(90)90158-E.
• [2] Z. Kowalczuk: Competitive identification for self-tuning control: robust estimation design and simulation experiments. Automatica, 28(1), (1992), 193-201. DOI: 10.1016/0005-1098(92)90021-7.
• [3] Z. Kowalczuk and J. Kozłowski: Continuous-time approaches to identification of continuous-time systems. Automatica, 36(8), (2000), 1229-1236. DOI: 10.1016/S0005-1098(00)00033-9.
• [4] S. Sagara, Z. Yang and K. Wada: Identification of continuous systems using digital low-pass filters. International Journal of Systems Science, 22(7), (1991), 1159-1176. DOI: 10.1080/00207729108910693.
• [5] Z. Kowalczuk and J. Kozłowski: Non-quadratic quality criteria in parameter estimation of continuous-time models. IET Control Theory and Applications, 5(13), (2011), 1494-1508. DOI: 10.1049/iet-cta.2010.0310.
• [6] E. Schlossmacher: An iterative technique for absolute deviations curve fitting. Journal of the American Statistical Association, 68(344), (1973), 857-865. DOI: 10.1080/01621459.1973.10481436.
• [7] P. Young: Parameter estimation for continuous-time models - a survey. Automatica, 17(1), (1981), 23-39. DOI: 10.1016/0005-1098(81)90082-0.
• [8] H. Unbehauen and G. Rao: Identification of Continuous Systems North Holland, Amsterdam, Netherlands, 1987.
• [9] R. Middleton and G. Goodwin: Digital Control and Estimation. A Unified Approach. Prentice-Hall, Upper Saddle River, NJ, USA, 1990.
• [10] J. Schoukens: Modeling of continuous time systems using a discrete time representation. Automatica, 26(3), (1990), 579-583. DOI: 10.1016/0005-1098(90)90029-H.
• [11] H. Unbehauen and G. Rao: Continuous-time approaches to system identification - a survey. Automatica, 26(1), (1990), 23-35. DOI: 10.1016/0005-1098(90)90155-B.
• [12] Z. Kowalczuk: Discrete approximation of continuous-time systems - a survey. IEE Proceedings G (Circuits, Devices and Systems), 140(4), (1993), 264-278. DOI: 10.1049/ip-g-2.1993.0045.
• [13] R. Johansson: Identification of continuous-time models. IEEE Transactions on Signal Processing, 42(4), (1994), 887-897. DOI: 10.1109/ 78.285652.
• [14] Z. Kowalczuk: Discrete-time realization of on-line continuous-time estimation algorithms. IASTED Journal on Control and Computers, 23(2), (1995), 33-37.
• [15] J. Schoukens and L. Ljung: Nonlinear system identification: a user-oriented road map. IEEE Control Systems Magazine, 39(6), (2019), 28-99. DOI: 10.1109/MCS.2019.2938121.
• [16] J. Kozłowski and Z. Kowalczuk: Intelligent monitoring the vertical dynamics of wheeled inspection vehicles. IFAC-PapersOnLine, 52(8), (2019), 251-256. DOI: 10.1016/j.ifacol.2019.08.079.
• [17] P. Suchomski and Z. Kowalczuk: Analytical design of stable delta-domain generalized predictive control. Optimal Control Applications and Methods, 23(5), (2002), 239-273. DOI: 10.1002/oca.712.
• [18] T. Söderström, H. Fan, B. Carlsson and S. Bigi: Least squares parameter estimation of continuous-time arx models from discrete-time data. IEEE Transactions on Automatic Control, 42(5), (1997), 659-673. DOI: 10.1109/9.580871.
• [19] Y. Chao, C. Chen and H. Huang: Recursive parameter estimation of transfer function matrix models via simpson’s integrating rules. International Journal of Systems Science, 18(5), (1987), 901-911. DOI: 10.1080/00207728708964017.
• [20] K. Inoue, K. Kumamaru, Y. Nakahashi, H. Nakamura and M. Uchida: A quick identification method of continuous-time nonlinear systems and its application to power plant control. Proceedings of the 10th IFAC Symposium on System Identification, 1 Copenhagen, Denmark, (1994), 319-324. DOI: 10.1016/S1474-6670(17)47729-9.
• [21] W. Byrski, M. Drapała and J. Byrski: An adaptive identification method based on the modulating functions technique and exact state observers for modeling and simulation of a nonlinear MISO glass melting process. International Journal of Applied Mathematics and Computer Science, 29(4), (2019), 739-757. DOI: 10.2478/amcs-2019-0055.
• [22] W. Byrski and M. Drapała: On-line process identification using the Modulating Functions Method and non-asymptotic state estimation. Archives of Control Sciences, 32(3), (2022), 535-555. DOI: 10.24425/acs.2022.142845.
• [23] M. Drapała and W. Byrski: Online continuous-time adaptive predictive control of the technological glass conditioning process. Archives of Control Sciences, 32(4), (2022), 755-782. DOI: 10.24425/acs.2022.143670.
• [24] J. Kozłowski and Z. Kowalczuk: Resistant to correlated noise and outliers discrete identification of continuous non-linear non-stationary dynamics objects. Intelligent and Safe Computer Systems in Control and Diagnostics, 545 of LNNS: Lecture Notes in Networks and Systems, Springer Nature AG, Cham, Switzerland, 2023, 317-327. DOI: 10.1007/978-3-031-16159-9 26.
• [25] L. Ljung: System Identification: Theory for the User. Prentice-Hall, Upper Saddle River, NJ, USA, 1987.
• [26] T. Söderström and P. Stoica: Comparison of some instrumental variable methods - consistency and accuracy aspects. Automatica, 17(1), (1981), 101-115. DOI: 10.1016/0005-1098(81)90087-X.
• [27] J. Craig: Introduction to Robotics: Mechanics and Control. Pearson Education, Cranbury, NJ, USA, 2014.
• [28] K. Janiszowski: Towards estimation in the sense of the least sum of absolute errors. IFAC Proceedings Volumes, 31(20), (1998), 605-610. DOI: 10.1016/S1474-6670(17)41862-3.
• [29] J. Kozłowski and Z. Kowalczuk: Robust to measurement faults, parameter estimation algorithms in problems of systems diagnostics. Intelligent Extraction of Information for Diagnostic Purposes, Pomorskie Wydawnictwo Naukowo-Techniczne, Gdańsk, Poland, (2007), 221-240.
• [30] Z. Kowalczuk: On discretization of continuous-time state-space models: A stable normal approach. IEEE Transactions, Circuits and Systems, 38(1), (1991), 1460-1477. DOI: 10.1109/31.108500.
• [31] S. Sagara and Z. Zhao: Recursive identification of transfer function matrix in continuous systems via linear integral filter. International Journal of Control, 50(2), (1989), 457-477. DOI: 10.1080/00207178908953377.
• [32] Z. Zhao and S. Sagara: Consistent estimation of time delay in continuous-time systems. Transactions of the Society of Instrument and Control Engineers, 27(1), (1991), 64-69. DOI: 10.9746/sicetr1965.27.64.
• [33] S. Sagara and Z. Zhao: Identification of system parameters in distributed parameter systems. Proceedings of the 11th IFAC World Congress, IFAC, Tallinn, Estonia, (1990), 471-476. DOI: 10.1016/S1474-6670(17)51960-6.
• [34] D. Goldberg: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Reading, MA, USA, 1989.
• [35] M. Willis, G. Montague, C. Di Massimo, M. Tham and A. Morris: Artificial neural networks in process estimation and control. Automatica, 28(6), (1992), 1181-1188. DOI: 10.1016/0005-1098(92)90059-O.
• [36] D. Uciński and M. Patan: Sensor network design for the estimation of spatially distributed processes. Internarional Journal of Applied Mathematics and Computer Science, 20(3), (2010), 459-481. DOI: 10.2478/v10006-010-0034-2.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).