Asynchronous Observer Design for Switched Linear Systems: A Tube-Based Approach

Minghao Han; Ruixian Zhang; Lixian Zhang; Ye Zhao; Wei Pan

doi:10.1109/JAS.2019.1911822

Volume 7 Issue 1

Jan. 2020

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 > 2020 > 7(1): 70-81

Minghao Han, Ruixian Zhang, Lixian Zhang, Ye Zhao and Wei Pan, "Asynchronous Observer Design for Switched Linear Systems: A Tube-Based Approach," IEEE/CAA J. Autom. Sinica, vol. 7, no. 1, pp. 70-81, Jan. 2020. doi: 10.1109/JAS.2019.1911822

Citation:

Minghao Han, Ruixian Zhang, Lixian Zhang, Ye Zhao and Wei Pan, "Asynchronous Observer Design for Switched Linear Systems: A Tube-Based Approach," IEEE/CAA J. Autom. Sinica, vol. 7, no. 1, pp. 70-81, Jan. 2020. doi: 10.1109/JAS.2019.1911822

Citation:

PDF( 1808 KB)

Asynchronous Observer Design for Switched Linear Systems: A Tube-Based Approach

doi: 10.1109/JAS.2019.1911822

Funds: This work was supported in part by the National Defense Basic Scientific Research Program of China (JCKY2018603C 015), and Cultivation Plan of Major Research Program of Harbin Institute of Technology (ZDXMPY20180101)

More Information

Author Bio:
Minghao Han (S’17) received the B.S. degree in the Department of Control Science and Engineering from Harbin Institution of Technology, China, in 2017. He was a visiting student in the Department of Electrical and Computer Engineering, National University of Singapore, Singapore, in 2016. He is currently pursuing the Ph.D. degree in control science and engineering at the Research Institute of Intelligence Control and Systems, Harbin Institution of Technology. His research interests include switched systems and reinforcement learning

Ruixian Zhang received the B.S. degree from Harbin Institution of Technology, China, in 2017. He is currently pursuing the Ph.D. degree in control science and engineering at the Research Institute of Intelligence Control and Systems, Harbin Institution of Technology. His research interests cover robotic application and reinforcement learning

Lixian Zhang (F’17) received the Ph.D. degree in control science and engineering from Harbin Institute of Technology, Harbin, China, in 2006. From January 2007 to September 2008, he was a Postdoctoral Fellow in the Department Mechanical Engineering at the Ecole Polytechnique de Montreal, Canada. He was a Visiting Professor at the Process Systems Engineering Laboratory, Massachusetts Institute of Technology (MIT), Cambridge, MA, USA, from February 2012 to March 2013. Since January 2009, he has been with Harbin Institute of Technology, where he is currently Full Professor and Vice Director at the Research Institute of Intelligent Control and Systems, School of Astronautics. His research interests include nondeterministic switched systems, networked control systems, model predictive control and their applications. Dr. Zhang serves as an Associate Editor for various peer-reviewed journals, including the IEEE Transactions on Automatic Control, IEEE Transactions on Cybernetics, etc., and was a leading Guest Editor for the Special Section on Advances in Theories and Industrial Applications of Networked Control Systems in the IEEE Transactions On Industrial Informatics. He was named to the list of Thomson Reuters Highly Cited Researchers in 2014, 2015, 2016 and 2017

Ye Zhao (S’10–M’19) received the B.E. degree in control science and engineering from Harbin Institute of Technology, Harbin, China, in 2011 and the M.S. and Ph.D. degrees in mechanical engineering from the University of Texas at Austin, Austin, TX, USA, in 2013 and 2016, respectively, where he also received the UT Robotics Graduate Portfolio Program degree in 2016. He was a Postdoctoral Fellow with the John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA. His research interests include robust motion planning and contact-rich trajectory optimization, high-level task planning, decision-making algorithms, and legged robotic systems. He is currently an Assistant Professor at the George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology. He is affiliated to the Institute for Robotics and Intelligent Machines (IRIM). Dr. Zhao was a Co-Chair of the IEEE Robotics and Automation Society (RAS) Student Activities Committee and a Committee Member of IEEE-RAS Member Activities Board. He is also an ICT Chair of the 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems, and serves as an Associate Editor of IROS and Humanoids Conferences

Wei Pan (S’11–M’19) received the B.E. degree in automation from Harbin Institute of Technology in 2008, the M.S. degree in biomedical engineering from University of Science and Technology of China in 2011, and the Ph.D. degree in bioengineering from Imperial College London in 2015. He is currently an Assistant Professor at Robot Dynamics Group as part of the Department of Cognitive Robotics, Delft University of Technology. Until May 2018, he was a Project Leader at DJI, China, responsible for machine learning research for DJI drones and AI accelerator. He is the recipient of Dorothy Hodgkin’s Postgraduate Awards, Microsoft Research Ph.D. Scholarship and Chinese Government Award for Outstanding Students Abroad, Shenzhen Peacock Plan Award. His research interests include machine learning and control theory and their unification to build intelligent and trustworthy machines
Corresponding author: M. H. Han, R. X. Zhang, and L. X. Zhang are with the School of Astronautics, Harbin Institute of Technology, Harbin 150080, China (e-mail: mhhan@hit.edu.cn; ruixianzhang@stu.hit.edu.cn; lixianzhang@hit.edu.cn)
Received Date: 2019-05-28
Revised Date: 2019-07-19
Accepted Date: 2019-08-20

Available Online: 2019-10-22

Abstract

Abstract

This paper proposes a tube-based method for the asynchronous observation problem of discrete-time switched linear systems in the presence of amplitude-bounded disturbances. Sufficient stability conditions of the nominal observer error system under mode-dependent persistent dwell-time (MPDT) switching are first established. Taking the disturbances into account, a novel asynchronous MPDT robust positive invariant (RPI) set and an asynchronous MPDT generalized RPI (GRPI) set are determined for the difference system between the nominal and disturbed observer error systems. Further, the global uniform asymptotical stability of the observer error system is established in the sense of converging to the asynchronous MPDT GRPI set, i.e., the cross section of the tube of the observer error system. Finally, the proposed results are validated on a space robot manipulator example.

FullText(HTML)

References(31)

References

[1]	L. Ni and D. W. Wang, " A gain-switching control scheme for positionerror-based bilateral teleoperation: Contact stability analysis and controller design,” The Int. J. Robotics Research, vol. 23, no. 3, pp. 255–274, 2004. doi: 10.1177/0278364904041563
[2]	K. S. Narendra, J. Balakrishnan, and M. K. Ciliz, " Adaptation and learning using multiple models, switching, and tuning,” IEEE Control Systems, vol. 15, no. 3, pp. 37–51, 1995. doi: 10.1109/37.387616
[3]	Y. Kang, D. H. Zhai, G. P. Liu, Y. B. Zhao, and P. Zhao, " Stability analysis of a class of hybrid stochastic retarded systems under asynchronous switching,” IEEE Trans. Automatic Control, vol. 59, no. 6, pp. 1511–1523, 2014. doi: 10.1109/TAC.2014.2305931
[4]	X. Zhao, L. Zhang, P. Shi, and M. Liu, " Stability and stabilization of switched linear systems with mode-dependent average dwell time,” IEEE Trans. Automatic Control, vol. 57, no. 7, pp. 1809–1815, 2012. doi: 10.1109/TAC.2011.2178629
[5]	Y. Kang, D. H. Zhai, G. P. Liu, and Y. B. Zhao, " On input-to-state stability of switched stochastic nonlinear systems under extended asynchronous switching,” IEEE Trans. Cybernetics, vol. 46, no. 5, pp. 1092–1105, 2016. doi: 10.1109/TCYB.2015.2423553
[6]	S. Yuan, L. Zhang, B. De Schutter, and S. Baldi, " A novel Lyapunov function for a non-weighted L₂ gain of asynchronously switched linear systems,” Automatica, vol. 87, pp. 310–317, 2018. doi: 10.1016/j.automatica.2017.10.018
[7]	D. Ma and J. Zhao, " Stabilization of networked switched linear systems: an asynchronous switching delay system approach,” Systems and Control Letters, vol. 77, pp. 46–54, 2015.
[8]	J. Lin, S. Fei, and Z. Gao, " Stabilization of discrete-time switched singular time-delay systems under asynchronous switching,” J. the Franklin Institute, vol. 349, no. 5, pp. 1808–1827, 2012. doi: 10.1016/j.jfranklin.2012.02.009
[9]	Y. E. Wang, J. Zhao, and B. Jiang, " Stabilization of a class of switched linear neutral systems under asynchronous switching,” IEEE Trans. Automatic Control, vol. 58, no. 8, pp. 2114–2119, 2013. doi: 10.1109/TAC.2013.2250076
[10]	Z. Xiang, R. Wang, and Q. Chen, " Robust reliable stabilization of stochastic switched nonlinear systems under asynchronous switching,” Applied Mathematics and Computation, vol. 217, no. 19, pp. 7725–7736, 2011. doi: 10.1016/j.amc.2011.02.076
[11]	G. Zong, R. Wang, W. X. Zheng, and L. Hou, " Finite-time stabilization for a class of switched time-delay systems under asynchronous switching,” Applied Mathematics and Computation, vol. 219, no. 11, pp. 5757–5771, 2013. doi: 10.1016/j.amc.2012.11.078
[12]	H. Liu, Y. Shen, and X. Zhao, " Delay-dependent observer-based H_∞ finite-time control for switched systems with time-varying delay,” Nonlinear Analysis:Hybrid Systems, vol. 6, no. 3, pp. 885–898, 2012. doi: 10.1016/j.nahs.2012.03.001
[13]	J. Lian and Y. Ge, " Robust H_∞ output tracking control for switched systems under asynchronous switching,” Nonlinear Analysis:Hybrid Systems, vol. 8, pp. 57–68, 2013. doi: 10.1016/j.nahs.2012.10.003
[14]	H. Liu, Y. Shen, and X. Zhao, " Asynchronous finite-time H_∞ control for switched linear systems via mode-dependent dynamic state-feedback,” Nonlinear Analysis:Hybrid Systems, vol. 8, pp. 109–120, 2013. doi: 10.1016/j.nahs.2012.12.001
[15]	D. Zhang, L. Yu, Q. G. Wang, and C. J. Ong, " Estimator design for discrete-time switched neural networks with asynchronous switching and time-varying delay,” IEEE Trans. Neural Networks and Learning Systems, vol. 23, no. 5, pp. 827–834, 2012. doi: 10.1109/TNNLS.2012.2186824
[16]	B. Niu and J. Zhao, " Robust h control for a class of switched nonlinear cascade systems via multiple lyapunov functions approach,” Applied Mathematics and Computation, vol. 218, no. 11, pp. 6330–6339, 2012. doi: 10.1016/j.amc.2011.09.059
[17]	L. Zhang, S. Zhuang, and P. Shi, " Non-weighted quasi-time-dependent H_∞ filtering for switched linear systems with persistent dwell-time,” Automatica, vol. 54, pp. 201–209, 2015. doi: 10.1016/j.automatica.2015.02.010
[18]	N. Vafamand, M. H. Asemani, and A. Khayatian, " Robust L₁ observerbased non-PDC controller design for persistent bounded disturbed TS fuzzy systems,” IEEE Trans. Fuzzy Systems, 2017.
[19]	J. H. Kim, S. M. Hur, and Y. Oh, " Performance analysis for bounded persistent disturbances in PD/PID-controlled robotic systems with its experimental demonstrations,” Int. J. Control, vol. 91, no. 3, pp. 688–705, 2018. doi: 10.1080/00207179.2017.1288301
[20]	Y. Li, Q. Zhang, X. Zhou, and X. Luo, " Basis-dependent and delaydependent results on robust L₁ filtering for networked control systems,” J. the Franklin Institute, vol. 353, no. 14, pp. 3368–3385, 2016. doi: 10.1016/j.jfranklin.2016.06.005
[21]	L. Zhang, S. Zhuang, P. Shi, and Y. Zhu, " Uniform tube based stabilization of switched linear systems with mode-dependent persistent dwell-time,” IEEE Trans. Automatic Control, vol. 60, no. 11, pp. 2994–2999, 2015. doi: 10.1109/TAC.2015.2414813
[22]	L. Zhang, S. Zhuang, and R. D. Braatz, " Switched model predictive control of switched linear systems: feasibility, stability and robustness,” Automatica, vol. 67, pp. 8–21, 2016. doi: 10.1016/j.automatica.2016.01.010
[23]	M. Dehghan and C. J. Ong, " Characterization and computation of disturbance invariant sets for constrained switched linear systems with dwell time restriction,” Automatica, vol. 48, no. 9, pp. 2175–2181, 2012. doi: 10.1016/j.automatica.2012.06.007
[24]	Y. Ren, M. J. Er, and G. Sun, " Switched systems with average dwell time: Computation of the robust positive invariant set,” Automatica, vol. 85, pp. 306–313, 2017. doi: 10.1016/j.automatica.2017.07.066
[25]	C.-K. Lin, " H_∞ reinforcement learning control of robot manipulators using fuzzy wavelet networks,” Fuzzy Sets and Systems, vol. 160, no. 12, pp. 1765–1786, 2009. doi: 10.1016/j.fss.2008.09.010
[26]	D. Q. Mayne, M. M. Seron, and S. Raković, " Robust model predictive control of constrained linear systems with bounded disturbances,” Automatica, vol. 41, no. 2, pp. 219–224, 2005. doi: 10.1016/j.automatica.2004.08.019
[27]	F. Blanchini, D. Casagrande, and S. Miani, " Modal and transition dwell time computation in switching systems: a set-theoretic approach,” Automatica, vol. 46, no. 9, pp. 1477–1482, 2010. doi: 10.1016/j.automatica.2010.06.006
[28]	L. Zhang, N. Cui, M. Liu, and Y. Zhao, " Asynchronous filtering of discrete-time switched linear systems with average dwell time,” IEEE Trans. Circuits and Systems, vol. 58, no. 5, pp. 1109–1118, 2011. doi: 10.1109/TCSI.2010.2092151
[29]	J. B. Rawlings and D. Q. Mayne, Model Predictive Control: Theory and Design. Nob Hill Pub., 2009.
[30]	D. Liberzon, Switching in Systems and Control. Springer Science and Business Media, 2012.
[31]	S. Kanev and M. Verhaegen, " Controller reconfiguration for non-linear systems,” Control Engineering Practice, vol. 8, no. 11, pp. 1223–1235, 2000. doi: 10.1016/S0967-0661(00)00074-5

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(7)

Get Citation

PDF

XML

Article Metrics

Article views (2566) PDF downloads(130)

Highlights

Sufficient stability conditions of the nominal observer error system under asynchronous MPDT switching are proposed and algorithm is designed to determine the asynchronous observer solution.
The RPI and GRPI sets in the asynchronous MPDT switching case are first determined in this paper and the corresponding algorithm is designed.
Based on the determined asynchronous MPDT GRPI set, the stability condition of the disturbed observer error system is obtained.

Asynchronous Observer Design for Switched Linear Systems: A Tube-Based Approach

doi: 10.1109/JAS.2019.1911822

Abstract

References

Proportional views

Catalog

通讯作者: 陈斌, bchen63@163.com

Article Metrics

Highlights

Export File

Citation

Format

Content