Further Result on the Observer Design for
One-Sided Lipschitz Systems

doi:10.1007/s12204-020-2252-6

Abstract

Abstract: This paper investigates the problem of observer design for a class of control systems. Different from current works, the nonlinear functions in the system only satisfy the property of the one-sided Lipschitz (OSL) condition but not quadratic inner-boundedness (QIB). Moreover, the case where the OSL constant is negative is specially investigated. Firstly, a full-order observer is constructed for the original system. Then, a reduced-order observer is also designed by using the decomposition method. The advantage and effectiveness of the proposed design scheme are shown in a numerical simulation.

Key words: control systems, one-sided Lipschitz (OSL) systems, full-order observers, reduced-order observers

CLC Number:

O 231

YANG Ming1 (杨明), HUANG Jun1∗ (黄俊), ZHANG Wei2 (章伟). Further Result on the Observer Design for One-Sided Lipschitz Systems[J]. J Shanghai Jiaotong Univ Sci, 2022, 27(6): 817-822.

References 27

[1]	THAU F E. Observing the state of nonlinear dynamic systems [J]. International Journal of Control, 1973, 17(3): 471-479.
[2]	RAJAMANI R. Observers for Lipschitz nonlinear systems [J]. IEEE Transactions on Automatic Control, 1998, 43(3): 397-401.
[3]	ZHU F, HAN Z. A note on observers for Lipschitz nonlinear systems [J]. IEEE Transactions on Automatic Control, 2002, 47(10): 1751-1754.
[4]	ZHANG W, SU H S, ZHU F L, et al. Observer-based H ∞ synchronization and unknown input recovery for a class of digital nonlinear systems [J]. Circuits, Systems, and Signal Processing,2013, 32(6): 2867-2881.
[5]	HU G D. Observers for one-sided Lipschitz nonlinear systems [J]. IMA Journal of Mathematical Control and Information, 2006, 23(4): 395-401.
[6]	ABBASZADEH M, MARQUEZ H J. Nonlinear observer design for one-sided Lipschitz systems [C]//2010 American Control Conference. Baltimore, MD, USA, 2010: 5284-5289.
[7]	ZHANG W, SU H S, ZHU F L, et al. A note on observers for discrete-time Lipschitz nonlinear systems [J]. IEEE Transactions on Circuits and Systems II: Express Briefs, 2012, 59(2): 123-127.
[8]	ZHANG W, SU H S, LIANG Y, et al. Non-linear observer design for one-sided Lipschitz systems: An linear matrix inequality approach [J]. IET Control Theory and Applications, 2012, 6(9):1297-1303.
[9]	LIU L J, KARIMI H R, ZHAO X D. New approaches to positive observer design for discrete-time positive linear systems [J]. Journal of the Franklin Institute, 2018, 355(10): 4336-4350.
[10]	LIU L J, ZHAO X D, SUN X M, et al. LP-based observer design for switched positive linear time-delay systems [J]. Transactions of the Institute of Measurement and Control, 2019, 41(9): 2419-2427.
[11]	LIU L J, ZHAO X D. Design of multiple-mode observer and multiple-mode controller for switched positive linear systems [J]. IET Control Theory & Applications, 2019, 13(9): 1320-1328.
[12]	BARBATA A, ZASADZINSKI M, SOULEY ALI H, et al. Exponential observer for a class of one-sided Lipschitz stochastic nonlinear systems [J]. IEEE Transactions on Automatic Control, 2015, 60(1): 259-264.
[13]	ZHANG W, SU H S, ZHU F L, et al. Unknown input observer design for one-sided Lipschitz nonlinear systems [J]. Nonlinear Dynamics, 2015, 79(2): 1469-1479.
[14]	NGUYEN M C, TRINH H. Unknown input observer design for one-sided Lipschitz discrete-time systems subject to time-delay [J]. Applied Mathematics and Computation, 2016, 286(5): 57-71.
[15]	DONG Y L, LIU W J, LIANG S. Nonlinear observer design for one-sided Lipschitz systems with time-varying delay and uncertainties [J]. International Journal of Robust and Nonlinear Control, 2017, 27(11): 1974-1998.
[16]	BEIKZADEH H, MARQUEZ H J. Observer-based H ∞ control using the incremental gain for one-sided Lipschitz nonlinear systems [C]//2014 American Control Conference. Portland, OR, USA: IEEE, 2014: 4653-4658.
[17]	AHMAD S, REHAN M. On observer-based control of one-sided Lipschitz systems [J]. Journal of the Franklin Institute, 2016, 353(4): 903-916.
[18]	AHMAD S, REHAN M, HONG K S. Observer-based robust control of one-sided Lipschitz nonlinear systems [J]. ISA Transactions, 2016, 65: 230-240.
[19]	FU Q, LI X D, DU L L, et al. Consensus control for multi-agent systems with quasi-one-sided Lipschitz nonlinear dynamics via iterative learning algorithm [J]. Nonlinear Dynamics, 2018, 91(4): 2621-2630.
[20]	REHAN M, JAMEEL A, AHN C K. Distributed consensus control of one-sided Lipschitz nonlinear multi-agent systems [J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2018, 48(8): 1297-1308.
[21]	SHI M J, HUANG J, CHEN L, et al. Adaptive fullorder and reduced-order observers for one-sided Lur’e systems with set-valued mappings [J]. IMA Journal of Mathematical Control and Information, 2018, 35(2): 569-589.
[22]	GU P P, TIAN S P. D-type iterative learning control for one-sided Lipschitz nonlinear systems [J]. International Journal of Robust and Nonlinear Control, 2019, 29(9): 2546-2560.
[23]	ZHANG W, SU H S, ZHU F L, et al. Improved exponential observer design for one-sided Lipschitz nonlinear systems [J]. International Journal of Robust and Nonlinear Control, 2016, 26(18): 3958-3973.
[24]	ABBASZADEH M, MARQUEZ H J. Nonlinear observer design for one-sided Lipschitz systems [C]//Proceedings of the 2010 American Control Conference. Baltimore, MD, USA: IEEE, 2010: 5284-5289.
[25]	CHANG X H, YANG G H. New results on output feedback H ∞ control for linear discrete-time systems [J]. IEEE Transactions on Automatic Control, 2014, 59(5): 1355-1359.
[26]	BOYD S, EI GHAOUI L, FERON E, et al. Linear matrix inequalities in system and control theory [M]. Philadelphia, PA, USA: SIAM, 1994.
[27]	EL GHAOUI L, NIKOUKHAH R, DELEBECQUE F. LMITOOL: A package for LMI optimization [C]//Proceedings of 1995 34th IEEE Conference on Decision and Control. New Orleans, LA, USA: IEEE, 1995: 3096-3101.

Further Result on the Observer Design for One-Sided Lipschitz Systems

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References 27

Related Articles 4

Recommended Articles

Metrics

Comments

[1]	JI Xiukun (冀秀坤), HAI Jintao (海金涛), LUO Wenguang (罗文广), LIN Cuixia (林翠霞), XIONG Yu(熊禹), OU Zengkai (殴增开), WEN Jiayan(文家燕). Obstacle Avoidance in Multi-Agent Formation Process Based on Deep Reinforcement Learning [J]. J Shanghai Jiaotong Univ Sci, 2021, 26(5): 680-685.
[2]	QIAO Xing, MA Dan, YAO Xuliang, FENG Baolin. Stability and Numerical Analysis of a Standby System [J]. J Shanghai Jiaotong Univ Sci, 2020, 25(6): 769-778.
[3]	CHANG Lu, SHAN Liang, LI Jun, DAI Yuewei . Sliding Mode Control of T-Shaped Pedestrian Channel [J]. Journal of Shanghai Jiao Tong University(Science), 2020, 25(4): 478-485.
[4]	WANG Limin (王立敏), WANG Runze (王润泽), XIONG Yuting (熊玉婷), WANG Haosen (王浩森), ZHU Lin (朱琳), ZHANG Ke (张可), GAO Furong (高福荣). Guaranteed Cost Iterative Learning Control for Multi-Phase Batch Processes [J]. Journal of Shanghai Jiao Tong University (Science), 2018, 23(6): 811-819.