Observer-based Iterative and Repetitive Learning Control for a Class of Nonlinear Systems

Sheng Zhu; Xuejie Wang; Hong Liu

doi:10.1109/JAS.2017.7510463

Volume 5 Issue 5

Aug. 2018

IEEE/CAA Journal of Automatica Sinica

JCR Impact Factor: 15.3, Top 1 (SCI Q1)

CiteScore: 23.5, Top 2% (Q1)
Google Scholar h5-index: 77， TOP 5

Turn off MathJax

Article Contents

Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2018 > 5(5): 990-998

Sheng Zhu, Xuejie Wang and Hong Liu, "Observer-based Iterative and Repetitive Learning Control for a Class of Nonlinear Systems," IEEE/CAA J. Autom. Sinica, vol. 5, no. 5, pp. 990-998, Sept. 2018. doi: 10.1109/JAS.2017.7510463

Citation:

Sheng Zhu, Xuejie Wang and Hong Liu, "Observer-based Iterative and Repetitive Learning Control for a Class of Nonlinear Systems," IEEE/CAA J. Autom. Sinica, vol. 5, no. 5, pp. 990-998, Sept. 2018. doi: 10.1109/JAS.2017.7510463

Citation:

PDF( 1151 KB)

Observer-based Iterative and Repetitive Learning Control for a Class of Nonlinear Systems

doi: 10.1109/JAS.2017.7510463

Department of Information and Electrical Engineering, Zhejiang University City College, Hangzhou 310015, China

Funds:

the Third Level of Hangzhou 131 Young Talent Cultivation Plan Funding, and 2018 Soft Science Research Project of Zhejiang Provincial Science and Technology Department Zhejiang Province Construction and participate in the "The Belt and Road" Technology Innovation Community Path Research 2018C35029

More Information

Abstract

Abstract

In this paper, both output-feedback iterative learning control (ILC) and repetitive learning control (RLC) schemes are proposed for trajectory tracking of nonlinear systems with state-dependent time-varying uncertainties. An iterative learning controller, together with a state observer and a fully-saturated learning mechanism, through Lyapunov-like synthesis, is designed to deal with time-varying parametric uncertainties. The estimations for outputs, instead of system outputs themselves, are applied to form the error equation, which helps to establish convergence of the system outputs to the desired ones. This method is then extended to repetitive learning controller design. The boundedness of all the signals in the closed-loop is guaranteed and asymptotic convergence of both the state estimation error and the tracking error is established in both cases of ILC and RLC. Numerical results are presented to verify the effectiveness of the proposed methods.
- Iterative learning control (ILC),
- observers,
- repetitive learning control (RLC),
- time-varying parametrization

FullText(HTML)

References(25)

References

[1]	S. Arimoto, S. Kawamura, and F. Miyazaki, "Bettering operation of robots by learning, " J. Robot. Syst., vol. 1, no. 2, pp. 123-140, Jun. 1984. http://www.mendeley.com/catalog/bettering-operation-robots-learning/
[2]	T. Inoue, M. Nakano, and S. Iwai, "High accuracy control of servomechanism for repeated contouring, " in Proc. 10th Annu. Symposium on Incremental Motion Control Systems and Devices, Oxford, England, 1981, pp. 282-292.
[3]	T. Kuc and J. S. Lee, "An adaptive learning control of uncertain robotic systems, " in Proc. 30th IEEE Conf. Decision Control, Britain, UK, 1991, pp. 1206-1211. http://xueshu.baidu.com/s?wd=paperuri%3A%280b4d1429a87f48e277f45a49eae8159e%29&filter=sc_long_sign&tn=SE_xueshusource_2kduw22v&sc_vurl=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D261560&ie=utf-8&sc_us=4311581159098582858
[4]	C. Ham, Z. Qu, and J. Kaloust, " A new framework of learning control for a class of nonlinear systems, " in Proc. American Control Conf., Seattle, USA, 1995, pp. 3024-3028. http://xueshu.baidu.com/s?wd=paperuri%3A%282ee75f5e918b6ab4481d1c4b92a88ead%29&filter=sc_long_sign&tn=SE_xueshusource_2kduw22v&sc_vurl=http%3A%2F%2Flibra.msra.cn%2FPublication%2F50027489%2Fa-new-framework-of-learning-control-for-a-class-of-nonlinear-systems&ie=utf-8&sc_us=10398511950872274498
[5]	B. H. Park, T. Y. Kuc, and J. S. Lee, "Adaptive learning control of uncertain robotic systems, " Int. J. Control, vol. 65, no. 5, pp. 725-744, 1996. doi: 10.1080/00207179608921719
[6]	N. Sadegh, R. Horowitz, W. W. Kao, and M. Tomizuka, "A unified approach to the design of adaptive and repetitive controllers for robotic manipulators, " J. Dyn. Sys., Meas., Control, vol. 112, no. 4, pp. 618-629, Dec. 1990. http://xueshu.baidu.com/s?wd=paperuri%3A%28c87521dcb0db95e84db6ebf306552a15%29&filter=sc_long_sign&tn=SE_xueshusource_2kduw22v&sc_vurl=http%3A%2F%2Fdx.doi.org%2F10.1115%2F1.2896187&ie=utf-8&sc_us=11064356641441691675
[7]	W. Messner, R. Horowitz, W. W. Kao, and M. Boals, "A new adaptive learning rule, " IEEE Trans. Autom. Control, vol. 36, no. 2, pp. 188-197, Feb. 1991. http://www.mendeley.com/research/new-adaptive-learning-rule/
[8]	J. X. Xu and Y. Tan, "A composite energy function-based learning control approach for nonlinear systems with time-varying parametric uncertainties, " IEEE Trans. Autom. Control, vol. 37, no. 11, pp. 1940-1945, Nov. 2002. http://xueshu.baidu.com/s?wd=paperuri%3A%285ebeb655c13f44fc6649486ce024676c%29&filter=sc_long_sign&tn=SE_xueshusource_2kduw22v&sc_vurl=http%3A%2F%2Fdx.doi.org%2F10.1109%2FTAC.2003.817004&ie=utf-8&sc_us=5774042070062982352
[9]	J. X. Xu, Y. Tan, and T. H. Lee, "Iterative learning control design based on composite energy function with input saturation, " Automatica, vol. 40, no. 8, pp. 1371-1377, Aug. 2004. http://www.mendeley.com/research/iterative-learning-control-design-based-composite-energy-function-input-saturation-1/
[10]	A. Gelb, "Iterative learning control design based on composite energy function with input saturation, " MA: MIT PRESS, 1974. http://www.mendeley.com/research/iterative-learning-control-design-based-composite-energy-function-input-saturation-1/
[11]	D. G. Luenberger, "Observing the state of a linear system, " IEEE Trans. Milit. Electron., vol. 8, no. 2, pp. 74-80, Apr. 1964. http://xueshu.baidu.com/s?wd=paperuri%3A%286e029b21a5d73f415ca45719eebee3e5%29&filter=sc_long_sign&tn=SE_xueshusource_2kduw22v&sc_vurl=http%3A%2F%2Fdx.doi.org%2F10.1109%2FTME.1964.4323124&ie=utf-8&sc_us=3116668829177157849
[12]	G. Besançon, "Remarks on nonlinear adaptive observer design, " Syst. Control Lett., vol. 41, no. 4, pp. 271-280, Nov. 2000. http://www.ixueshu.com/document/7358692e393e0106318947a18e7f9386.html
[13]	D. Fissore, "Robust control in presence of parametric uncertainties: Observer-based feedback controller design, " Chem. Eng. Sci., vol. 63, no. 7, pp. 1890-1900, Apr. 2008. http://xueshu.baidu.com/s?wd=paperuri%3A%28771b5313b048968522e5ad71ea334cf3%29&filter=sc_long_sign&tn=SE_xueshusource_2kduw22v&sc_vurl=http%3A%2F%2Fdx.doi.org%2F10.1016%2Fj.ces.2007.12.019&ie=utf-8&sc_us=9734836141484680245
[14]	C. Edwards, S. K. Spurgenon, and R. J. Patton, "Sliding mode observers for fault detection and isolation, " Automatica, vol. 36, no. 4, pp. 541-553, Apr. 2000. http://lra.le.ac.uk/handle/2381/30204
[15]	T. Poznyak, I. Chairez, and A. Poznyak, "Application of a neural observer to phenols ozonation in water: Simulation and kinetic parameters identification, " Water Res., vol. 39, no. 12, pp. 2611-2620, Jul. 2005. http://med.wanfangdata.com.cn/Paper/Detail/PeriodicalPaper_PM15996710
[16]	J. H. Park, G. T. Park, S. H. Kim, and C. J. Moon, "Output-feedback control of uncertain nonlinear systems using a self-structuring adaptive fuzzy observer, " Fuzzy Sets Syst., vol. 151, no. 1, pp. 21-42, Apr. 2005. http://xueshu.baidu.com/s?wd=paperuri%3A%287126d127853bac52000744eb59c96010%29&filter=sc_long_sign&tn=SE_xueshusource_2kduw22v&sc_vurl=http%3A%2F%2Fdx.doi.org%2F10.1016%2Fj.fss.2004.07.007&ie=utf-8&sc_us=14952449194194341963
[17]	C. J. Chien and C. Y. Yao, "Iterative learning of model reference adaptive controller for uncertain nonlinear systems with only output measurement, " Automatica, vol. 40, no. 5, pp. 855-864, May 2004. http://cat.inist.fr/?aModele=afficheN&cpsidt=15621344
[18]	M. French and E. Rogers, "Non-linear iterative learning by an adaptive Lyapunov technique, " Int. J. Control, vol. 73, no. 10, pp. 840-850, Jul. 2000. http://xueshu.baidu.com/s?wd=paperuri%3A%2849e828640aedd43693b6b5437ec9ea2f%29&filter=sc_long_sign&tn=SE_xueshusource_2kduw22v&sc_vurl=http%3A%2F%2Fwww.ingentaconnect.com%2Fcontent%2Ftandf%2Ftcon%2F2000%2F00000073%2F00000010%2Fart00004&ie=utf-8&sc_us=3427499935881186778
[19]	A. Tayebi and J. X. Xu, "Observer-based iterative learning control for a class of time-varying nonlinear systems, " IEEE Trans. Circ. Syst. I: Fund. Theor. Appl., vol. 50, no. 3, pp. 452-455, Mar. 2003. http://xueshu.baidu.com/s?wd=paperuri%3A%28244492969f83045e571420660e8d4e6d%29&filter=sc_long_sign&tn=SE_xueshusource_2kduw22v&sc_vurl=http%3A%2F%2Fwww.ingentaconnect.com%2Fcontent%2Fiee%2F10577122%2F2003%2F00000050%2F00000003%2Fart00016&ie=utf-8&sc_us=9506852684151117913
[20]	J. X. Xu and J. Xu, "Observer based learning control for a class of nonlinear systems with time-varying parametric uncertainties, " IEEE Trans. Autom. Control, vol. 49, no. 2, pp. 275-281, Feb. 2004. http://www.mendeley.com/research/observer-based-learning-control-class-nonlinear-systems-timevarying-parametric-uncertainties/
[21]	W. E. Dixon, E. Zergeroglu, D. M. Dawson, and B. T. Costic, "Repetitive learning control: A Lyapunov-based approach, " IEEE Trans. Syst. Man Cybernet. B: Cybernet., vol. 32, no. 4, pp. 538-545, Aug. 2002. http://xueshu.baidu.com/s?wd=paperuri%3A%28efce6c4c7118667d0c4ce9e515cd12be%29&filter=sc_long_sign&tn=SE_xueshusource_2kduw22v&sc_vurl=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpubmed%2F18238149&ie=utf-8&sc_us=381651049142266413
[22]	J. X. Xu and Z. H. Qu, "Robust iterative learning control for a class of nonlinear systems, " Automatica, vol. 34, no. 8, pp. 983-988, Aug. 1998. http://www.mysciencework.com/publication/show/robust-iterative-learning-control-for-a-class-of-nonlinear-systems
[23]	M. X. Sun, "A barbalat-like lemma with its application to learning control, " IEEE Trans. Autom. Control, vol. 54, no. 9, pp. 2222-2225, Sep. 2009. http://www.mendeley.com/research/barbalatlike-lemma-application-learning-control/
[24]	M. X. Sun, S. S. Ge, and I. M. Y. Mareels, "Adaptive repetitive learning control of robotic manipulators without the requirement for initial repositioning, " IEEE Trans. Robot., vol. 22, no. 3, pp. 563-568, Jun. 2006.
[25]	M. X. Sun, D. W. Wang, and P. N. Chen, "Repetitive learning control of nonlinear systems over finite intervals, " Sci. China Ser. F, vol. 53, no. 1, pp. 115-128, Jan. 2010. http://xueshu.baidu.com/s?wd=paperuri%3A%28e09ed33c25a801df2d5b1843ee0b4272%29&filter=sc_long_sign&tn=SE_xueshusource_2kduw22v&sc_vurl=http%3A%2F%2Fen.cnki.com.cn%2FArticle_en%2FCJFDTOTAL-JFXG201001010.htm&ie=utf-8&sc_us=3332271224393366824

Supplements(0)

Cited By

Proportional views

Proportional views

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Figures(8)

Get Citation

PDF

XML

Article Metrics

Article views (1646) PDF downloads(100)

Observer-based Iterative and Repetitive Learning Control for a Class of Nonlinear Systems

doi: 10.1109/JAS.2017.7510463

Abstract

References

Proportional views

Catalog

通讯作者: 陈斌, bchen63@163.com

Article Metrics

Export File

Citation

Format

Content