| Title:
|
Robust sampled-data observer design for Lipschitz nonlinear systems (English) |
| Author:
|
Yu, Yu |
| Author:
|
Shen, Yanjun |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
54 |
| Issue:
|
4 |
| Year:
|
2018 |
| Pages:
|
699-717 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, a robust sampled-data observer is proposed for Lipschitz nonlinear systems. Under the minimum-phase condition, it is shown that there always exists a sampling period such that the estimation errors converge to zero for whatever large Lipschitz constant. The optimal sampling period can also be achieved by solving an optimal problem based on linear matrix inequalities (LMIs). The design methods are extended to Lipschitz nonlinear systems with large external disturbances as well. In such a case, the estimation errors converge to a small region of the origin. The size of the region can be small enough by selecting a proper parameter. Compared with the existing results, the design parameters can be easily obtained by solving LMIs. (English) |
| Keyword:
|
sampled-data observer |
| Keyword:
|
nonlinear systems |
| Keyword:
|
Lipschitz |
| Keyword:
|
sampling period |
| Keyword:
|
LMIs |
| MSC:
|
93B51 |
| MSC:
|
93C57 |
| idZBL:
|
Zbl 06987029 |
| idMR:
|
MR3863251 |
| DOI:
|
10.14736/kyb-2018-4-0699 |
| . |
| Date available:
|
2018-10-30T14:42:47Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147419 |
| . |
| Reference:
|
[1] Ahrens, J., Tan, X., Khalil, H.: Multirate sampled-data output feedback control with application to smart material actuated systems..IEEE Trans. Automat. Control 54 (2009), 2518-2529. MR 2571917, 10.1109/tac.2009.2031204 |
| Reference:
|
[2] Boutat, D.: Extended nonlinear observer normal forms for a class of nonlinear dynamical systems..Int. J. Robust Nonlinear Control 25 (2015), 461-474. MR 3304211, 10.1002/rnc.3102 |
| Reference:
|
[3] Boyd, S., Ghaoui, L., al., E. Feron et: Linear Matrix Inequalities in System and Control Theory..Society for Industrial and Applied Mathematics, ch. 1.2, Philadelphia 1994. MR 1284712, 10.1137/1.9781611970777 |
| Reference:
|
[4] Chen, M., Chen, C.: Robust nonlinear observer for Lipschitz nonlinear systems subject to disturbances..IEEE Trans. Automat. Control 52 (2007), 2365-2369. MR 2374276, 10.1109/tac.2007.910724 |
| Reference:
|
[5] Dezuo, T., Trofino, A.: LMI conditions for designing rational nonlinear observers..In: 2014 American Control Conference. 47 (2014), 5343-5348. 10.1109/acc.2014.6858805 |
| Reference:
|
[6] Dinh, T., Andrieu, V., Nadri, M., al., et: Continuous-discrete time observer design for Lipschitz systems with sampled measurements..IEEE Trans. Automat. Control 60 (2015), 787-792. MR 3318404, 10.1109/tac.2014.2329211 |
| Reference:
|
[7] Dong, Y., Liu, J., Mei, S.: Observer design for a class of nonlinear discrete-time systems with time-delay..Kybernetika 49 (2013), 341-358. Zbl 1264.93144, MR 3085400 |
| Reference:
|
[8] Doyle, J., Stein, G.: Robustness with observers..IEEE Trans. Automatic Control 24 (1979), 607-611. MR 0538818, 10.1109/tac.1979.1102095 |
| Reference:
|
[9] Ekramian, M., Sheikholeslam, F., al., S. Hosseinnia et: Adaptive state observer for Lipschitz nonlinear systems..Systems Control Lett. 62 (2013), 319-323. MR 3031101, 10.1016/j.sysconle.2013.01.002 |
| Reference:
|
[10] Gupta, M., Tomar, N., Bhaumik, S.: Observer Design for Descriptor Systems with Lipschitz Nonlinearities: An LMI Approach..Nonlinear Dynamics Systems Theory 14 (2014), 291-301. MR 3560210 |
| Reference:
|
[11] Kang, W., Krener, A., al., M. Xiao et: A survey of observers for nonlinear dynamical systems..In: Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications, Vol. II, Springer Berlin Heidelberg 2013, pp. 1-25. 10.1007/978-3-642-35088-7\_1 |
| Reference:
|
[12] Khalil, H.: Nonlinear System..Upper Saddle River, Prentice Hall, ch. 14.5, NJ 2000. |
| Reference:
|
[13] Kwakernaak, H., Sivan, R.: Linear Optimal Control Systems..Wiley, ch. 3, Theorem 3.14, New York 1972. MR 0406607 |
| Reference:
|
[14] Lewis, F.: Applied Optimal Control and Estimation..Englewood Cliffs, Prentice-Hall, ch. 3, Theorem 2, NJ 1992. |
| Reference:
|
[15] Marino, R., Tomei, P.: Nonlinear control design..Automatica 33 (2009), 1769-1770. 10.1016/s0005-1098(97)82237-6 |
| Reference:
|
[16] Nešić, D., Teel, A.: A framework for stabilization of nonlinear sampled-data systems based on their approximate discrete-time models..IEEE Trans. Automat. Control 49 (2004), 1103-1122. MR 2071938, 10.1109/tac.2004.831175 |
| Reference:
|
[17] Oucief, N., Tadjine, M., Labiod, S.: Adaptive observer-based fault estimation for a class of Lipschitz nonlinear systems..Archives Control Sci. 26 (2016), 245-259. MR 3530358, 10.1515/acsc-2016-0014 |
| Reference:
|
[18] Pan, J., Meng, M., Feng, J.: A note on observers design for one-sided Lipschitz nonlinear systems..In: Control Conference IEEE (2015), pp. 1003-1007. 10.1109/chicc.2015.7259771 |
| Reference:
|
[19] Perez, C., Mera, M.: Robust observer-based control of switched nonlinear systems with quantized and sample output..Kybernetika 54 (2015), 59-80. MR 3333833, 10.14736/kyb-2015-1-0059 |
| Reference:
|
[20] Rehák, B.: Sum-of-squares based observer design for polynomial systems with a known fixed time delay..Kybernetika 51 (2015), 856-873. MR 3445988, 10.14736/kyb-2015-5-0856 |
| Reference:
|
[21] Saberi, A., Sannuti, P., Chen, B.: $H_2$ Optimal Control..Englewood Cliffs, Prentice-Hall, ch. 4, Theorem 4.1.2, NJ 1995. |
| Reference:
|
[22] Shen, Y., Zhang, D., Xia, X.: Continuous output feedback stabilization for nonlinear systems based on sampled and delayed output measurements..Internat. J. Robust and Nonlinear Control 26 (2016), 3075-3087. Zbl 1346.93320, MR 3537171, 10.1002/rnc.3491 |
| Reference:
|
[23] Shen, Y., Zhang, D., Xia, X.: Continuous observer design for a class of multi-output nonlinear systems with multi-rate sampled and delayed output measurements..Automatica 75 (2017), 127-132. MR 3582161, 10.1016/j.automatica.2016.09.028 |
| Reference:
|
[24] Stein, G., Athans, M.: The LQG/LTR procedure for multivariable feedback control design..IEEE Trans. Automat. Control 32 (1987), 105-114. 10.1109/tac.1987.1104550 |
| Reference:
|
[25] Tahir, A., Magri, A., Ahmed-Ali, T., al., et: Sampled-data nonlinear observer design for sensorless synchronous PMSM..IFAC-Papers OnLine 48 (2015), 327-332. 10.1016/j.ifacol.2015.09.206 |
| Reference:
|
[26] Thau, F.: Observing the state if nonlinear dynamic systems..Int. J. Control 17 (1973), 471-479. 10.1080/00207177308932395 |
| Reference:
|
[27] Wang, Y., Liu, X., Xiao, J., Shen, Y.: Output formation-containment of interacted heterogeneous linear systems by distributed hybrid active control..Automatica 93 (2018), 26-32. MR 3810889, 10.1016/j.automatica.2018.03.020 |
| Reference:
|
[28] Yu, L.: Robust Control: Linear Matrix Inequality Approach..Tsinghua University Press 2002. |
| Reference:
|
[29] Zemouche, A., Boutayeb, M.: On LMI conditions to design observers for Lipschitz nonlinear systems..Automatica 49 (2013), 585-591. MR 3004728, 10.1016/j.automatica.2012.11.029 |
| Reference:
|
[30] Zhang, D., Shen, Y. J.: Continuous sampled-data observer design for nonlinear systems with time delay larger or samller than the sampling period..IEEE Trans. Automat. Control 62 (2017), 5822-5829. MR 3730959, 10.1109/tac.2016.2638043 |
| Reference:
|
[31] Zhang, D., Shen, Y., Xia, X.: Globally uniformly ultimately bounded observer design for a class of nonlinear systems with sampled and delayed measurements..Kybernetika 52 (2016), 441-460. MR 3532516, 10.14736/kyb-2016-3-0441 |
| Reference:
|
[32] Zhang, W., Su, H., al., S. Su et: Nonlinear $H_\infty$ observer design for one-sided Lipschitz systems..Neurocomputing (2014), 505-511. |
| Reference:
|
[33] Zhang, W., Su, H., al., F. Zhu et: A note on observers for discrete-time Lipschitz nonlinear systems..IEEE Trans. Circuits Systems II Express Briefs 29 (2012), 123-127. 10.1109/tcsii.2011.2174671 |
| Reference:
|
[34] Zhou, Y., Soh, Y., Shen, J.: High-gain observer with higher order sliding mode for state and unknown disturbance estimations..Int. J. Robust abd Nonlinear Control 24 (2016), 2136-2151. MR 3259380, 10.1002/rnc.2982 |
| . |
