Volume 16, Issue 3 (Journal of Control, V.16, N.3 Fall 2022)                   JoC 2022, 16(3): 47-58 | Back to browse issues page

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Hajatipour M, Kashefi S. New Optimal Observer Design Based on State Prediction for a Class of Non-linear Systems Through Approximation. JoC 2022; 16 (3) :47-58
URL: http://joc.kntu.ac.ir/article-1-923-en.html
1- University of Kashan, Kashan
Abstract:   (686 Views)
This paper deals with the optimal state observer of non-linear systems based on a new strategy. Despite the development of state prediction in linear systems, state prediction for non-linear systems is still challenging. In this paper, to obtain a future estimation of the system states, initially Taylor series expansion of states in their receding horizons was achieved to any specified order and then an analytic solution was developed for the prediction error problem, which resulted in a closed-form for non-linear optimal observer. In the proposed observer, the observer gain was optimally chosen among gains obtained from the analytic solution of the prediction error problem and satisfied the stability condition. Finally, the qualitative simulation results showed the effectiveness of the proposed method in the state observation.
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Type of Article: Research paper | Subject: Special
Received: 2022/02/20 | Accepted: 2022/09/13 | ePublished ahead of print: 2022/09/19

1. [1] Luenberger, D.G., 1964, "Observing the state of a linear system", IEEE Transactions on Military Electronics, 8(2), 74-80. [DOI:10.1109/TME.1964.4323124]
2. [2] Luenberger, D.G., 1966, "Observers for multivariable systems", IEEE Transaction on Automatic Control, 11(2), 190-197. [DOI:10.1109/TAC.1966.1098323]
3. [3] Luenberger, D.G., 1971, "An introduction to observers", IEEE Transaction on Automatic Control, 16(6), 596-602. [DOI:10.1109/TAC.1971.1099826]
4. [4] Thau, F.E., 1973, "Observing the state of non-linear dynamic systems", International Journal of Control, 17, 471-479. [DOI:10.1080/00207177308932395]
5. [5] Kou, S.R., Elliot, D.L. and Tarn, T.J., 1975, "Exponential observers for non-linear dynamic systems", Information and Control, 29, 204-216. [DOI:10.1016/S0019-9958(75)90382-4]
6. [6] Zheng, G., Boutat, D. and Wang, H., 2017, "A non-linear Luenberger-like observer for non-linear singular systems", Automatica, 86, 11-17. [DOI:10.1016/j.automatica.2017.08.018]
7. [7] Hajatipour, M. and Farrokhi, M., 2010, "Chattering free with noise reduction in sliding mode observers using frequency domain analysis", Journal of Process Control 20(8), 912- 921. [DOI:10.1016/j.jprocont.2010.06.015]
8. [8] Modarres, A.A. and Momeni, H.R., 2010, "A New Sliding Mode Observer Design for Linear System with Unknown Input and Time-varying Delay", Journal of Control, 4(4), 24-31. (In Persian)
9. [9] Ahrens, J.H. and Khalil, K.H., 2009, "High-gain observers in the presence of measurement noise: A switched-gain approach", Automatica, 45(4), 936-943. [DOI:10.1016/j.automatica.2008.11.012]
10. [10] Khalil, H.K., 2017, "High-gain observers in feedback control: Application to permanent magnet synchronous motors", IEEE Control System, 37(3), 25-41. [DOI:10.1109/MCS.2017.2674438]
11. [11] Adil, A., Hamaz, A., N'Doye, I., Zemouche, A., Laleg-Kirati, T.-M. and Bedouhene, F., "On high-gain observer design for nonlinear systems with delayed output measurements", Automatica, 141, 2022,110281. [DOI:10.1016/j.automatica.2022.110281]
12. [12] Moraal, PE. and Grizzle, J.W., 1995, "Observer design for non-linear systems with discrete-time measurement", IEEE Transaction on Automatic Control, 40(3), 395-404. [DOI:10.1109/9.376051]
13. [13] Rao, C.V., Rawlings, J.B. and Mayne, D.Q., 2003, "Constrained state estimation for non-linear discrete-time systems: Stability and moving horizon approximation", IEEE Transaction on Automatic Control, 48(2), 246-258. [DOI:10.1109/TAC.2002.808470]
14. [14] Kühl, P., Diehl, M., Kraus, T., Schlöder, J.P. and Bock, H.G., 2011, "A real-time algorithm for moving horizon state and parameter estimation", Computer and Chemical Engineering, 35, 71-83. [DOI:10.1016/j.compchemeng.2010.07.012]
15. [15] Alessandri, A., Baglietto, M. and Battistelli, G., 2003, "Receding horizon estimation for discrete time linear systems", IEEE Transaction on Automatic Control, 48(3), 473-478. [DOI:10.1109/TAC.2003.809155]
16. [16] Almir, M., 2007, "Non-linear Moving Horizon Observers: Theory and Real-Time Implementation. In: Besançon G Non-linear Observers and Applications", Lecture Notes in Control and Information Sciences, Springer, Berlin, Heidelberg, 139-179. [DOI:10.1007/978-3-540-73503-8_5]
17. [17] Almir, M., 2013, "A new identification framework for off-Line computation of moving-horizon observers", IEEE Transaction on Automatic Control, 58(6), 1877-1882. [DOI:10.1109/TAC.2013.2256016]
18. [18] Alessandri, A., Baglietto, M. and Battistelli, G., 2008, "Moving-horizon state estimation for non-linear discrete-time systems: New stability results and approximation schemes", Automatica. 44(7), 1753-1765. [DOI:10.1016/j.automatica.2007.11.020]
19. [19] Alessandri, A., Baglietto, M., Battistelli, G. and Gaggero, M., 2011, "Moving-horizon state estimation for non-linear systems using neural networks", IEEE Transaction on Neural Networks, 22(5), 768-780. [DOI:10.1109/TNN.2011.2116803]
20. [20] Ramar, K. and Gourishankar, V., 1976, "Optimal observers with specified eigenvalues", International Journal of Control, 27(2), 239-244. [DOI:10.1080/00207177808922361]
21. [21] Chou, Fu.I. and Cheng, M.Y., 2019, "Optimal design of reduced-order observers with specified eigenvalues and performance measurement of minimizing estimation errors using evolutionary optimization", Journal of Low Frequency Noise, Vibration and Active Control, 38(2), 728-739. [DOI:10.1177/1461348419830226]
22. [22] Na, J., Herrmann, G. and Vamvoudakis, K., "Adaptive optimal observer design via approximate dynamic programming", In: American Control Conference IEEE, Seattle, USA, 24-26 May 2017, 3288-3293. Washington: IEEE. [DOI:10.23919/ACC.2017.7963454]
23. [23] Chakrabarty, A. and Benosman, M., 2021, "Safe learning-based observers for unknown nonlinear systems using Bayesian optimization", Automatica, 133, 109760. [DOI:10.1016/j.automatica.2021.109860]
24. [24] Besan¸con, G., Georges, D. and Benayache, Z., 2007, "Asymptotic state prediction for continuous-time systems with delayed input and application to control", In: Control conference (ecc), European, 2007, 1786-1791. [DOI:10.23919/ECC.2007.7068540]
25. [25] Najafi, M., Hosseinnia, S., Sheikholeslam, F. and Karimadini, M., 2013, "Closed-loop control of dead time systems via sequential sub-predictors", International Journal of Control, 86 (4), 599-609. [DOI:10.1080/00207179.2012.751627]
26. [26] Najafi, M., Sheikholeslam, F., Wang, Q.G. and Hosseinnia, S., 2014, "Robust H∞ control of single input-delay systems based on sequential sub-predictors", IET Control Theory and Applications, 8 (13), 1175-1184. [DOI:10.1049/iet-cta.2012.1004]
27. [27] Ahmed-Ali, T., Cherrier, E. and Lamnabhi-Lagarrigue, F. 2012, "Cascade high gain predictors for a class of nonlinear systems", IEEE Transactions on Automatic Control, 57 (1), 221-226. [DOI:10.1109/TAC.2011.2161795]
28. [28] Mazenc, F. and Malisoff, M., 2016 "New prediction approach for stabilizing time-varying systems under time-varying input delay. In Decision and control (CDC) ", In: IEEE 55th conference, 3178-3182. [DOI:10.1109/CDC.2016.7798746]
29. [29] Sanz, R., Garcia, P., Fridman, E. and Albertos, P., 2018, "Rejection of mismatched disturbances for systems with input delay via a predictive extended state observer", International Journal of Robust and Nonlinear Control. [DOI:10.1002/rnc.4027]
30. [30] Sanz, R., García, P., Fridman E. and P. Albertos P., 2018 "Robust Predictive Extended State Observer for a Class of Nonlinear Systems with Time-Varying Input Delay", Journal of control, 93(2), 1-18. [DOI:10.1080/00207179.2018.1562204]
31. [31] Zhu, Y., Fridman E., 2021, Sub-predictors for network-based control under uncertain large delays. Automatica 123, 109350. [DOI:10.1016/j.automatica.2020.109350]
32. [32] Koshkouei, A.J. and Zinober, A.S.I., 2004, "Sliding mode state observation for non-linear systems", International Journal of Control, 77(2), 118-127. [DOI:10.1080/00207170310001643249]
33. [33] Young, H.K., Frank, L.L. and Chaouki, T.A., 1997, "A dynamic recurrent neural-network-based adaptive observer for a class of nonlinear systems", Automatica, 33(8), 1539-1543. [DOI:10.1016/S0005-1098(97)00065-4]
34. [34] Ruiqi, W. and Zhujun, J., 2004, "Chaos control of chaotic pendulum system", Chaos, Solitons and Fractals, 21, 201-207. [DOI:10.1016/j.chaos.2003.10.011]
35. [35] Arthur, J.K. and Mingqing, X., "Non-linear observer design in the SIEGEL domain", SIAM Journal on Control and Optimization, 41(3), 2002, 932-953. [DOI:10.1137/S0363012900375330]

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