Robust Output Feedback Control for Fractional Order Nonlinear Systems with Time-varying Delays

Changchun Hua; Tong Zhang; Yafeng Li; Xinping Guan

Volume 3 Issue 4

Oct. 2016

IEEE/CAA Journal of Automatica Sinica

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Changchun Hua, Tong Zhang, Yafeng Li and Xinping Guan, "Robust Output Feedback Control for Fractional Order Nonlinear Systems with Time-varying Delays," IEEE/CAA J. Autom. Sinica, vol. 3, no. 4, pp. 477-482, Oct. 2016.

Citation:

Changchun Hua, Tong Zhang, Yafeng Li and Xinping Guan, "Robust Output Feedback Control for Fractional Order Nonlinear Systems with Time-varying Delays," IEEE/CAA J. Autom. Sinica, vol. 3, no. 4, pp. 477-482, Oct. 2016.

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Robust Output Feedback Control for Fractional Order Nonlinear Systems with Time-varying Delays

1.
Institute of Electrical Engineering, Yanshan University, Qinhuangdao 066004, China
2.
Department of Automation, Shanghai Jiao Tong University, Shanghai 200030, China

Funds:

National Natural Science Foundation of China 61290322, 61273222, 61322303, 61473248, 61403335

Hebei Province Applied Basis Research Project 15967629D

Top Talents Project of Hebei Province and Yanshan University Project 13LGA020

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Author Bio:
Tong Zhang received the B. S. degree in electrical engineering from Yanshan University, Qinhuangdao, China, in 2014. She is currently working toward the M. S. degree in electrical engineering. Her research interests include fractional order system control.(13230929204@163.com)

Yafeng Li received the B. S. degree in electrical engineering from Hebei University of Science and Technology, Shijiazhuang, China, in 2013. He is currently working toward the Ph. D. degree in Yanshan University. His research interests include nonlinear system control and multi-agent system control.(y.f.li@foxmail.com)

Xinping Guan received the B. S. degree in mathematics from Harbin Normal University, Harbin, China, and the M. S. degree in applied mathematics and the Ph. D. degree in electrical engineering, both from Harbin Institute of Technology, in 1986, 1991, and 1999, respectively. He is with the Department of Automation, Shanghai Jiao Tong University. He is the (co)author of more than 200 papers in mathematical, technical journals, and conferences. As (a)an (co)-investigator, he has finished more than 20 projects supported by National Natural Science Foundation of China (NSFC), the National Education Committee Foundation of China, and other important foundations. He is Cheung Kong Scholars Programme Special appointment professor. His current research interests include networked control systems, robust control and intelligent control for complex systems and their applications. Dr. Guan is serving as a reviewer of Mathematic Review of America, a member of the Council of Chinese Artificial Intelligence Committee, and chairman of Automation Society of Hebei Province, China.(e-mail: xpguan@ysu.edu.cn)
Corresponding author: Changchun Hua received the Ph. D. degree in electrical engineering from Yanshan University, Qinhuangdao, China, in 2005. He was a research fellow in National University of Singapore from 2006 to 2007. From 2007 to 2009, he worked in Carleton University, Canada, funded by Province of Ontario Ministry of Research and Innovation Program. From 2009 to 2011, he worked in University of Duisburg- Essen, Germany, funded by Alexander von Humboldt Foundation. Now he is a full professor at Yanshan University, China. He is the author or coauthor of more than 110 papers in mathematical, technical journals, and conferences. He has been involved in more than 10 projects supported by the National Natural Science Foundation of China, the National Education Committee Foundation of China, and other important foundations. His research interests include nonlinear control systems, control systems design over network, teleoperation systems, and intelligent control. Corresponding author of this paper.(email:cch@ysu.edu.cn).
Received Date: 2015-09-08
Revised Date: 2016-03-03

Abstract

Abstract

Robust controller design problem is investigated for a class of fractional order nonlinear systems with time varying delays. Firstly, a reduced-order observer is designed. Then, an output feedback controller is designed. Both the designed observer and controller are independent of time delays. By choosing appropriate Lyapunov functions, we prove the designed controller can render the fractional order system asymptotically stable. A simulation example is given to verify the effectiveness of the proposed approach.
- Fractional order systems,
- time-varying delays,
- Laypunov function,
- backstepping

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References

[1]	Podlubny I. Fractional Differential Equations:An Introduction to Fractional Derivatives, Fractional Differential Equations, Some Methods of Their Solution and Some of Their Applications. San Diego:Academic Press, 1999.
[2]	Pan I, Das S. Intelligent Fractional Order Systems and Control. Berlin Heidelberg:Springer, 2013.
[3]	Kilbas A A, Srivastava H M, Trujillo J J. Theory and Applications of Fractional Differential Equations, Volume 204(North-Holland Mathematics Studies). New York:Elsevier Science Inc., 2006.
[4]	Lakshmikantham V, Leela S, Vasundhara Devi J. Theory of Fractional Dynamic Systems. Cambridge, UK:Cambridge Scientific Publishers, 2009.
[5]	Diethelm K. The Analysis of Fractional Differential Equations. Berlin:Springer, 2010.
[6]	Lakshmikantham V, Vatsala A S. Basic theory of fractional differential equations. Nonlinear Analysis:Theory, Methods and Applications, 2008, 69(8):2677-2682 doi: 10.1016/j.na.2007.08.042
[7]	Matignon D. Stability results for fractional differential equations with applications to control processing. Computational Engineering in Systems Applications, 1996, 2:963-968 http://cn.bing.com/academic/profile?id=56786142&encoded=0&v=paper_preview&mkt=zh-cn
[8]	Lu J G, Chen Y Q. Robust stability and stabilization of fractional-order interval systems with the fractional order α:the 0 << α << 1 case. IEEE Transactions on Automatic Control, 2010, 55(1):152-158 doi: 10.1109/TAC.2009.2033738
[9]	Lu J G, Chen G R. Robust stability and stabilization of fractional-order interval systems:an LMI approach. IEEE Transactions on Automatic Control, 2009, 54(6):1294-1299 doi: 10.1109/TAC.2009.2013056
[10]	Zhang X F, Liu L, Feng G, Wang Y Z. Asymptotical stabilization of fractional-order linear systems in triangular form. Automatica, 2013, 49(11):3315-3321 doi: 10.1016/j.automatica.2013.08.002
[11]	Lim Y H, Oh K K, Ahn H S. Stability and stabilization of fractionalorder linear systems subject to input saturation. IEEE Transactions on Automatic Control, 2013, 58(4):1062-1067 doi: 10.1109/TAC.2012.2218064
[12]	Aguila-Camacho N, Duarte-Mermoud M A, Gallegos J A. Lyapunov functions for fractional order systems. Communications in Nonlinear Science and Numerical Simulation, 2014, 19(9):2951-2957 doi: 10.1016/j.cnsns.2014.01.022
[13]	Wen X J, Wu Z M, Lu J G. Stability analysis of a class of nonlinear fractional-order systems. IEEE Transactions on Circuits and Systems Ⅱ:Express Briefs, 2008, 55(11):1178-1182 doi: 10.1109/TCSII.2008.2002571
[14]	Delavari H, Baleanu D, Sadati J. Stability analysis of Caputo fractionalorder nonlinear systems revisited. Nonlinear Dynamics, 2012, 67(4):2433-2439 doi: 10.1007/s11071-011-0157-5
[15]	Li Y, Chen Y Q, Podlubny I. Stability of fractional-order nonlinear dynamic systems:Lyapunov direct method and generalized MittagLeffler stability. Computers and Mathematics with Applications, 2010, 59(5):1810-1821 doi: 10.1016/j.camwa.2009.08.019
[16]	Hua C C, Guan X P, Shi P. Robust backstepping control for a class of time delayed systems. IEEE Transactions on Automatic Control, 2005, 50(6):894-899 doi: 10.1109/TAC.2005.849255
[17]	Bonnet C, Partington J R. Coprime factorizations and stability of fractional differential systems. Systems and Control Letters, 2000, 41(3):167-174 doi: 10.1016/S0167-6911(00)00050-5
[18]	Deng W H, Li C P, Lv J H. Stability analysis of linear fractional differential system with multiple time delays. Nonlinear Dynamics, 2007, 48(4):409-416 doi: 10.1007/s11071-006-9094-0
[19]	Kheirizad I, Tavazoei M S, Jalali A A. Stability criteria for a class of fractional order systems. Nonlinear Dynamics, 2010, 61(1-2):153-161 doi: 10.1007/s11071-009-9638-1
[20]	Zhang F R, Li C P. Stability analysis of fractional differential systems with order lying in (1, 2). Advances in Difference Equations, 2011, 2011:Article ID 213485 http://cn.bing.com/academic/profile?id=2058317840&encoded=0&v=paper_preview&mkt=zh-cn
[21]	Wen Y H, Zhou X F, Zhang Z X, Liu S. Lyapunov method for nonlinear fractional differential systems with delay. Nonlinear Dynamics, 2015, 82(1-2):1015-1025 doi: 10.1007/s11071-015-2214-y
[22]	Yu W, Li T Z. Stability analysis of fractional-order nonlinear systems with delay. Mathematical Problems in Engineering, 2014, 2014(4):Article ID 301235 http://cn.bing.com/academic/profile?id=2033083367&encoded=0&v=paper_preview&mkt=zh-cn
[23]	Wei Y H, Chen Y Q, Liang S, Wang Y. A novel algorithm on adaptive backstepping control of fractional order systems. Neurocomputing, 2015, 165:395-402 doi: 10.1016/j.neucom.2015.03.029
[24]	Ding D S, Qi D L, Meng Y, Xu L. Adaptive Mittag-Leffler stabilization of commensurate fractional-order nonlinear systems. In:Proceedings of the 53rd IEEE Conference on Decision and Control (CDC). Los Angeles, CA:IEEE, 2014. 6920-6926
[25]	Syta A, Litak G, Lenci S, Scheffler M. Chaotic vibrations of the duffing system with fractional damping. Chaos:An Interdisciplinary Journal of Nonlinear Science, 2014, 24(1):013107 doi: 10.1063/1.4861942

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Robust Output Feedback Control for Fractional Order Nonlinear Systems with Time-varying Delays

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