Finite-time Sliding Mode Control Design for a Class of Uncertain Conic Nonlinear Systems

Shuping He; Jun Song

doi:10.1109/JAS.2017.7510643

Volume 4 Issue 4

Oct. 2017

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 > 2017 > 4(4): 809-816

Shuping He and Jun Song, "Finite-time Sliding Mode Control Design for a Class of Uncertain Conic Nonlinear Systems," IEEE/CAA J. Autom. Sinica, vol. 4, no. 4, pp. 809-816, Oct. 2017. doi: 10.1109/JAS.2017.7510643

Citation:

Shuping He and Jun Song, "Finite-time Sliding Mode Control Design for a Class of Uncertain Conic Nonlinear Systems," IEEE/CAA J. Autom. Sinica, vol. 4, no. 4, pp. 809-816, Oct. 2017. doi: 10.1109/JAS.2017.7510643

Citation:

PDF( 1682 KB)

Finite-time Sliding Mode Control Design for a Class of Uncertain Conic Nonlinear Systems

doi: 10.1109/JAS.2017.7510643

Shuping He^,,
Jun Song

School of Electrical Engineering and Automation, Anhui University, Hefei 230601, China

Funds:

the National Natural Science Foundation of China 61673001

the National Natural Science Foundation of China 61203051

the Foundation for Distinguished Young Scholars of Anhui Province 1608085J05

the Key Support Program of University Outstanding Youth Talent of Anhui Province gxydZD201701

More Information

Author Bio:
Shuping He (M'2017) received the B.S. degree in automation and the Ph.D. degree in control theory and control engineering at Jiangnan University, Wuxi, China in 2005 and 2011, respectively. From 2010 to 2011, he was a Visiting Scholar with the Control Systems Centre, School of Electrical and Electronic Engineering, the University of Manchester, UK. From 2011 to 2013, he was successively a Senior Lecturer at Anhui University. Since 2013, he has been a Professor with the School of Electrical Engineering and Automation, Anhui University, Hefei, China. His research interests include control theory and applications, including robust control of stochastic systems, nonlinear and optimal control of nonlinear systems and complex system modeling, control, filtering, fault detection and their applications. Dr. He was a recipient of the Outstanding Youth Funds Award of Anhui Province in 2016, and the Honor of Excellent Young Talents in University of Anhui Province in 2017. He has authored or coauthored more than 80 papers in professional journals, conference proceedings, and technical reports in these related areas and coauthored a book about stochastic systems. (e-mail: shuping.he@ahu.edu.cn)

Jun Song received the B.S. degree in electronic science and technology and the master degree in pattern recognition and intelligent system at Anhui University, Hefei China in 2011 and 2014, respectively. Currently, he is now a Ph.D. candidate at the School of Information Science and Engineering, East China University of Science and Technology, Shanghai, China. His research interests include adaptive control, stochastic control, and optimal control.(e-mail: jun_song@mail.ecust.edu.cn)
Corresponding author: Shuping He, e-mail:shuping.he@ahu.edu.cn
Recommended by Associate Editor Haibo Ji
Received Date: 2014-10-11
Accepted Date: 2015-03-02

Abstract

Abstract

This paper studies the sliding mode controller design problems for a class of nonlinear system. The nonlinear function is considered to satisfy conic-type constraint condition. A novel finite-time boundedness (FTB) based sliding mode controller design theory is proposed. And then a sufficient condition is obtained in terms of linear matrix inequalities (LMIs), which guarantees the resulted sliding mode dynamics to be FTB wrt some predefined scalars. Thereafter, a FTB-based sliding mode control (SMC) law is synthesized to ensure the state of the controlled system is driven into a novel desired switching surface s(t)=c (c is a constant) in a finite time. Simulation results illustrate the validity of the proposed FTB-based SMC design theory.
- Conic nonlinear system,
- finite-time boundedness (FTB),
- sliding mode control (SMC),
- state-feedback

FullText(HTML)

Recommended by Associate Editor Haibo Ji

References(25)

References

[1]	P. Dorato, "Short time stability in linear time-varying systems, " in Proc. the IRE Int. Conv. Rec. , New York, UK, 1961, pp. 83-87.
[2]	F. Amato, G. de Tommasi, and A. Pironti, "Necessary and sufficient conditions for finite-time stability of impulsive dynamical linear systems, " Automatica, vol. 49, no. 8, pp. 2546-2550, Aug. 2013. http://www.ams.org/mathscinet-getitem?mr=3072649
[3]	Y. Guo, Y. Yao, S. C. Wang, K. M. Ma, K. Liu, and J. Guo, "Input-output finite-time stabilization of linear systems with finite-time boundedness, " ISA Trans. , vol. 53, no. 4, pp. 977-982, Jul. 2014. http://europepmc.org/abstract/med/24947432
[4]	Z. G. Yan, G. S. Zhang, and W. H. Zhang, "Finite-time stability and stabilization of linear Itô stochastic systems with state and control-dependent noise, " Asian J. Control, vol. 15, no. 1, pp. 270-281, May 2013. doi: 10.1002/asjc.v15.1
[5]	F. Amato, R. Ambrosino, C. Cosentino, and de G. Tommasi, "Inputoutput finite time stabilization of linear systems, " Automatica, vol. 46, no. 9, pp. 1558-1562, Sep. 2010. http://www.sciencedirect.com/science/article/pii/S0005109810002554
[6]	F. Amato, M. Ariola, and P. Dorato, "Finite-time control of linear systems subject to parametric uncertainties and disturbances, " Automatica, vol. 37, no. 9, pp. 1459-1463, Sep. 2001. http://www.sciencedirect.com/science/article/pii/S0005109801000875
[7]	W. M. Xiang and J. Xiao, "H_∞ finite-time control for switched nonlinear discrete-time systems with norm-bounded disturbance, " J. Franklin Inst. , vol. 348, no. 2, pp. 331-352, Jun. 2011. http://www.ams.org/mathscinet-getitem?mr=2771844
[8]	M. N. ElBsat and E. E. Yaz, "Robust and resilient finite-time control of a class of continuous-time nonlinear systems, " IFAC Proc. Volumes, vol. 45, no. 13, pp. 15-20, 2012. doi: 10.3182/20120620-3-DK-2025.00145
[9]	M. N. ElBsat and E. E. Yaz, "Robust and resilient finite-time bounded control of discrete-time uncertain nonlinear systems, " Automatica, vol. 49, no. 7, pp. 2292-2296, Jul. 2013. http://www.sciencedirect.com/science/article/pii/S0005109813002033
[10]	Y. G. Niu and D. W. C. Ho, "Robust observer design for Itô stochastic time-delay systems via sliding mode control, " Syst. Control Lett. , vol. 55, no. 10, pp. 781-793, Oct. 2006. http://www.sciencedirect.com/science/article/pii/S0167691106000570
[11]	Y. G. Niu and D. W. C. Ho, "Design of sliding mode control subject to packet losses, " IEEE Trans. Automat. Control, vol. 55, no. 11, pp. 2623-2628, Nov. 2010. http://ieeexplore.ieee.org/document/5555974/
[12]	Y. Xia, G. P. Liu, P. Shi, J. Chen, D. Rees, and J. Liang, "Sliding mode control of uncertain linear discrete time systems with input delay, " IET Control Theory Appl. , vol. 1, no. 4, pp. 1169-1175, Jul. 2007. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4271426
[13]	F. Gouaisbaut, M. Dambrine, and J. R. Richard, "Robust control of delay systems: a sliding mode control design via LMI, " Syst. Control Lett. , vol. 46, no. 4, pp. 219-230, Jul. 2002. http://www.sciencedirect.com/science/article/pii/S0167691101001992
[14]	B. Chen, Y. G. Niu, and Y. Y. Zou, "Adaptive sliding mode control for stochastic Markovian jumping systems with actuator degradation, " Automatica, vol. 49, no. 6, pp. 1748-1754, Jun. 2013. http://www.sciencedirect.com/science/article/pii/S0005109813000782
[15]	L. G. Wu and W. X. Zheng, "Passivity-based sliding mode control of uncertain singular time-delay systems, " Automaica, vol. 45, no. 9, pp. 2120-2127, Sep. 2009. http://www.sciencedirect.com/science/article/pii/S0005109809002611
[16]	Y. G. Niu, D. W. C. Ho, and J. Lam, "Robust integral sliding mode control for uncertain stochastic systems with time-varying delay, " Automatica, vol. 41, no. 5, pp. 873-880, May 2005. doi: 10.1016/j.automatica.2004.11.035
[17]	W. Perruquetti and J. P. Barbot, Sliding Mode Control in Engineering, New York:Marcel Dekker, 2002.
[18]	F. Feng, C. S. Jeong, E. E. Yaz, S. C. Schneider, and Y. I. Yaz, "Robust controller design with general criteria for uncertain conic nonlinear systems with disturbances, " Proc. 2013 American Control Conf. , Washington, DC, USA, 2013, 5869-5874. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6580758
[19]	C. D. Johnson, "Disturbance-accomodation control:An overview of the subject, " J. Interdiscipl. Mod. Simulat., vol. 3, no. 1, pp. 1-29, 1980.
[20]	I. R. Petersen and R. Tempo, "Robust control of uncertain systems:Classical results and recent developments, " Automatica, vol. 50, no. 5, pp. 1315-1335, May 2014. doi: 10.1016/j.automatica.2014.02.042
[21]	A. Zemouche and M. Boutayeb, "On LMI conditions to design observers for Lipschitz nonlinear systems, " Automatica, vol. 49, no. 2, pp. 585-591, Feb. 2013. http://www.sciencedirect.com/science/article/pii/S0005109812005651
[22]	G. P. Lu, D. W. C. Ho, and L. Zhou, "A note on the existence of a solution and stability for Lipschitz discrete-time descriptor systems, " Automatica, vol. 47, no. 7, pp. 1525-1529, Jul. 2011. http://www.sciencedirect.com/science/article/pii/S0005109811002214
[23]	J. Song and S. P. He, "Observer-based finite-time passive control for a class of uncertain time-delayed Lipschitz nonlinear systems, " Trans. Inst. Meas. Control, vol. 36, no. 6, pp. 797-804, Mar. 2014. doi: 10.1177/0142331214524266
[24]	L. Huang and X. Mao, "SMC design for robust H_∞ control of uncertain stochastic delay systems, " Automatica, vol. 46, no. 2, pp. 405-412, Feb. 2010. http://www.sciencedirect.com/science/article/pii/S0005109809005378
[25]	P. P. Khargonekar, I. R. Petersen, and K. Zhou, "Robust stabilization of uncertain linear systems: quadratic stabilizability and H_∞ control theory, " IEEE Trans. Automat. Control, vol. 35, no. 3, pp. 356-361, Mar. 1990.

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(2)

Get Citation

PDF

XML

Article Metrics

Article views (805) PDF downloads(188)

Finite-time Sliding Mode Control Design for a Class of Uncertain Conic Nonlinear Systems

doi: 10.1109/JAS.2017.7510643

Abstract

References

Proportional views

Catalog

通讯作者: 陈斌, bchen63@163.com

Article Metrics

Export File

Citation

Format

Content