Exact uncertainty compensation of linear systems by continuous fixed-time output-feedback controller

doi:10.23919/JSEE.2022.000065

Journal of Systems Engineering and Electronics ›› 2022, Vol. 33 ›› Issue (3): 706-715.doi: 10.23919/JSEE.2022.000065

• CONTROL THEORY AND APPLICATION • Previous Articles Next Articles

Exact uncertainty compensation of linear systems by continuous fixed-time output-feedback controller

Shang SHI^1,²(), Guosheng ZHANG¹(), Huifang MIN^3,*(), Yinlong HU¹(), Yonghui SUN¹()

¹ College of Energy and Electrical Engineering, Hohai University, Nanjing 211100, China
² School of Automation, Southeast University, Nanjing 234299, China
³ School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China

Received:2020-12-12 Online:2022-06-18 Published:2022-06-24
Contact: Huifang MIN E-mail:shishangshang@foxmail.com;zgs15295770291@163.com;jiejie1043640772@126.com;yinlonghu@outlook.com;sunyonghui168@163.com
About author:|SHI Shang was born in 1990. He received his B.S. and M.S. degrees in control theory from Jiangsu University, Zhenjiang, China, in 2013 and 2015, respectively. He received his Ph.D. degree with the School of Automation, Nanjing University of Science and Technology, Nanjing, China. He is now a lecture in the College of Energy and Electrical Engineering, Hohai University. His research interests include sliding mode control, finite-time control, fixed-time control, and time-delay systems. E-mail: shishangshang@yahoo.com||ZHANG Guosheng was born in 1997. He received his B.S. degree in automation from Hohai University, Nanjing, China, in 2021. He is currently working toward his M.S. degree with the College of Energy and Electrical Engineering, Hohai University. His research interests include fixed-time control of wheeled mobile robots and sliding mode control. E-mail: zgs15295770291@163.com||MIN Huifang was born in 1990. She received her M.S. degree from the School of Electrical Engineering and Automation, Jiangsu Normal University, Xuzhou, China, in 2015, and her Ph.D. degree from the School of Automation, Nanjing University of Science and Technology, Nanjing, China, in 2019. She is now a professor in the School of Automation, Nanjing University of Science and Technology, Nanjing. Her research interests include nonlinear adaptive control and stochastic nonlinear control. E-mail: jiejie1043640772@126.com||HU Yinlong was born in 1987. He is now an associate professor in the College of Energy and Electrical Engineering, Hohai University. He received his B.S. degree in electrical engineering and automation in 2010, and his Ph.D. degree in control theory in 2016, from the School of Automation, Nanjing University of Science and Technology, Nanjing, China. His research interests include passive and semi-active vibration control, nonlinear intelligent control theory and its applications in mechanical and electrical systems. E-mail: yinlonghu@outlook.com||SUN Yonghui was born in 1980. He received his Ph.D. degree from City University of Hong Kong, Hong Kong, in 2010. He is currently a professor with the College of Energy and Electrical Engineering, Hohai University, Nanjing, China. He has authored more than 80 papers in refereed international journals. His research interests include stability analysis and control of power systems, optimal planning and operation of integrated energy system, optimization algorithms, and data analysis. E-mail: sunyonghui168@163.com
Supported by:
This work was supported by the National Natural Science Foundation of China (62003131; 62073121; 62173125) and the Natural Science Foundation of Jiangsu Province (BK20200520) .

Abstract

Abstract:

This paper studies the fixed-time output-feedback control for a class of linear systems subject to matched uncertainties. To estimate the uncertainties and system states, we design a composite observer which consists of a high-order sliding mode observer and a Luenberger observer. Then, a robust output-feedback controller with fixed-time convergence guarantee is constructed. Rigorous theoretical proof shows that with the proposed controller, the system states can converge to zero in fixed-time free of the initial conditions. Finally, simulation comparison with existing algorithms is given. Simulation results verify the effectiveness of the proposed controller in terms of its fixed-time convergence and perfect disturbance rejection.

Key words: linear system, output feedback, matched uncertainty, fixed-time control, observer

Shang SHI, Guosheng ZHANG, Huifang MIN, Yinlong HU, Yonghui SUN. Exact uncertainty compensation of linear systems by continuous fixed-time output-feedback controller[J]. Journal of Systems Engineering and Electronics, 2022, 33(3): 706-715.

Figures/Tables 6

References 34

1	GONG X, FU Y B, JIANG L X, et al Application of super-twisting extended state observer in fault reconfiguration of quadrotor aircraft. Systems Engineering and Electronics, 2020, 42 (9): 2077- 2084.
2	ZHAO Y, DONG L L Adaptive back-stepping control on container ships for path following. Journal of Systems Engineering and Electronics, 2020, 31 (4): 780- 791. doi: 10.23919/JSEE.2020.000053
3	MIN H F, XU S Y, ZHANG Z Q Adaptive finite-time stabilization of stochastic nonlinear systems subject to full-state constraints and input saturation. IEEE Trans. on Automatic Control, 2021, 66 (3): 1306- 1313. doi: 10.1109/TAC.2020.2990173
4	MIN H F, XU S Y, ZHANG B Y, et al Globally adaptive control for stochastic nonlinear time-delay systems with perturbations and its application. Automatica, 2019, 102, 105- 110. doi: 10.1016/j.automatica.2019.01.004
5	UTKIN V, Sliding modes in control and optimization. Berlin: Springer-Verlag, 1992.
6	LEVANT A Higher-order sliding modes, differentiation and output-feedback control. International Journal of Control, 2003, 76 (9/10): 924- 941. doi: 10.1080/0020717031000099029
7	DING S H, LEVANT A, LI S H Simple homogeneous sliding-mode controller. Automatica, 2016, 67, 22- 32. doi: 10.1016/j.automatica.2016.01.017
8	SHI S, XU S Y, GU J, et al Global high-order sliding mode controller design subject to mismatched terms: application to buck converter. IEEE Trans. on Circuits Systems-I: Regular Papers, 2019, 66 (12): 4840- 4849. doi: 10.1109/TCSI.2019.2933164
9	MIN H F, XU S Y, MA Q, et al Composite-observer-based output-feedback control for nonlinear time-delay systems with input saturation and its application. IEEE Trans. on Industrial Electronics, 2018, 65 (7): 5856- 5863. doi: 10.1109/TIE.2017.2784347
10	MIN H F, XU S Y, ZHANG B Y, et al Output-feedback control for stochastic nonlinear systems subject to input saturation and time-varying delay. IEEE Trans. on Automatic Control, 2018, 64 (1): 359- 364.
11	BEJARANO F, FRIDMAN L, POZNYAK A Exact state estimation for linear systems with unknown inputs based on hierarchical super-twisting algorithm. International Journal of Robust Nonlinear Control, 2007, 17 (18): 1734- 1753. doi: 10.1002/rnc.1190
12	LOZA A, BEJARANO F, FRIDMAN L Unmatched uncertainties compensation based on high-order sliding mode observation. International Journal of Robust Nonlinear Control, 2013, 23 (7): 754- 764. doi: 10.1002/rnc.2795
13	FERREIRA A, BEJARANO F, FRIDMAN L Robust control with exact uncertainties compensation: with or without chattering? IEEE Trans. on Control Systems Technology, 2011, 19 (5): 965- 975.
14	BASIN M, PANATHULA C, SHTESSEL Y, et al Continuous finite-time higher order output regulators for systems with unmatched unbounded disturbances. IEEE Trans. on Industrial Electronics, 2016, 63 (8): 5036- 5043.
15	SHI S, XU S Y, YU X, et al Robust output-feedback finite-time regulator of systems with mismatched uncertainties bounded by positive functions. IET Control Theory and Application, 2017, 11 (17): 3107- 3114. doi: 10.1049/iet-cta.2017.0291
16	MIN H F, XU S Y, ZHANG B Y, et al Practically finite-time control for nonlinear systems with mismatching conditions and application to a robot system. IEEE Trans. on Systems, Man, and Cybernetics: Systems, 2020, 50 (2): 2168- 2216.
17	YANG R M, PEI W H, HAN Y Z, et al Finite-time adaptive robust simultaneous stabilization of nonlinear delay systems by the Hamiltonian function method. Science China: Information Science, 2021, 64 (6): 169201. doi: 10.1007/s11432-019-2804-2
18	ANDRIEU V, PRALY L, ASTOLFI A Homogeneous approximation, recursive observer and output feedback. SIAM Journal on Control and Optimization, 2008, 47 (4): 1814- 1850. doi: 10.1137/060675861
19	POLYAKOV A Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans. on Automatic Control, 2012, 57 (8): 2106- 2110. doi: 10.1109/TAC.2011.2179869
20	NING B D, HAN Q L Prescribed finite-time consensus tracking for multi-agent systems with nonholonomic chained-form dynamics. IEEE Trans. on Automatic Control, 2019, 64 (4): 1686- 1693. doi: 10.1109/TAC.2018.2852605
21	ZUO Z Y, HAN Q L, NING B D, et al An overview of recent advances in fixed-time cooperative control of multiagent systems. IEEE Trans. on Industrial Electronics, 2018, 14 (6): 2322- 2334. doi: 10.1109/TII.2018.2817248
22	SHI S, GU J, XU S Y, et al Globally fixed-time high-order sliding mode control for new sliding mode systems subject to mismatched terms and its application. IEEE Trans. on Industrial Electronics, 2019, 67 (12): 10776- 10786.
23	SHI S, MIN H F, DING S H Observer-based adaptive scheme for fixed-time frequency estimation of biased sinusoidal signals. Automatica, 2021, 127, 109559. doi: 10.1016/j.automatica.2021.109559
24	BASIN M, SHTESSEL Y, ALDUKALI F Continuous finite-and fixed-time high-order regulators. Journal of the Franklin Institute, 2016, 353 (18): 5001- 5012. doi: 10.1016/j.jfranklin.2016.09.026
25	TIAN B L, ZUO Z Y, YAN X M, et al Fixed-time output feedback control scheme for double integrator systems. Automatica, 2017, 80, 17- 24. doi: 10.1016/j.automatica.2017.01.007
26	NI J K, LIU L, LIU C X, et al Fast fixed-time nonsingular terminal sliding mode control and its application to chaos suppression in power system. IEEE Trans. on Circuits Systems-II: Express Briefs, 2016, 64 (2): 151- 155.
27	CRUZ-ZAVALA E, MORENO J, FRIDMAN L Lyapunov-based design for a class of variable-gain 2nd-sliding controllers with the desired convergence rate. International Journal of Robust and Nonlinear Control, 2018, 28 (17): 5279- 5296. doi: 10.1002/rnc.4310
28	SHI S, GU J, XU S Y, et al Variable-gain second-order sliding mode controller with globally fixed-time stability guarantees. IEEE Trans. on Circuits Systems-II: Express Briefs, 2020, 67 (28): 1414- 1418.
29	LOPEZ-RAMIREZ F, POLYAKOV A, EFIMOV D, et al Finite-time and fixed-time observer design: implicit Lyapunov function approach. Automatica, 2018, 87, 52- 60. doi: 10.1016/j.automatica.2017.09.007
30	MENARD T, MOULAY E, PERRUQUETTI W Fixed-time observer with simple gains for uncertain systems. Automatica, 2017, 81, 438- 446. doi: 10.1016/j.automatica.2017.04.009
31	RIOS H, TEEL A A hybrid fixed-time observer for state estimation of linear systems. Automatica, 2018, 87, 103- 112. doi: 10.1016/j.automatica.2017.09.019
32	BHAT S, BERNSTEIN D Finite-time stability of continuous autonomous systems. SIAM Journal on Control and Optimization, 2000, 38 (3): 751- 766. doi: 10.1137/S0363012997321358
33	FILIPPOV A F. Mathematics and its applications. Differential equations with discontinuous right-hand sides. ARSCott F M, ed. Dordrecht: Kluwer Academic Publishers, 1988.
34	ANGULO M, MORENO J, FRIDMAN L Robust exact uniformly convergent arbitrary order differentiator. Automatica, 2013, 49 (8): 2489- 2495. doi: 10.1016/j.automatica.2013.04.034

[1]	Xinjian MA, Shiqian LIU, Huihui CHENG. Civil aircraft fault tolerant attitude tracking based on extended state observers and nonlinear dynamic inversion [J]. Journal of Systems Engineering and Electronics, 2022, 33(1): 180-187.
[2]	Steven Xianchuan DING, Linlin LI, Bin JIANG. Unified control and detection framework and its applications: a review, some new results, and future perspectives [J]. Journal of Systems Engineering and Electronics, 2021, 32(5): 995-1013.
[3]	Abdollah AZIZI, Mehdi FOROUZANFAR. Stabilizing controller design for nonlinear fractional order systems with time varying delays [J]. Journal of Systems Engineering and Electronics, 2021, 32(3): 681-689.
[4]	Sheng LIU, He LIAO, Jinjin XIE, Yufei XU, Yi XU, Zhongxin TANG, Chuang YAO. A non-contact spacecraft architecture with extended stochastic state observer based control for gravity mission [J]. Journal of Systems Engineering and Electronics, 2021, 32(2): 460-472.
[5]	Zhen SHI, Yaen XIE, Chengchen DENG, Kun ZHAO, Yushan HE, Yong HAO. Disturbance observer based finite-time coordinated attitude tracking control for spacecraft on SO(3) [J]. Journal of Systems Engineering and Electronics, 2020, 31(6): 1274-1285.
[6]	Hongwei WANG, Penglong FENG. Fuzzy modeling of multirate sampled nonlinear systems based on multi-model method [J]. Journal of Systems Engineering and Electronics, 2020, 31(4): 761-769.
[7]	Yiru ZOU, Chunsheng LIU, Ke LU. Extended state observer based smooth switching control for tilt-rotor aircraft [J]. Journal of Systems Engineering and Electronics, 2020, 31(4): 815-825.
[8]	Lixiong LIN, Qing WANG, Bingwei HE, Xiafu PENG. Evaluation of fault diagnosability for nonlinear uncertain systems with multiple faults occurring simultaneously [J]. Journal of Systems Engineering and Electronics, 2020, 31(3): 634-646.
[9]	Junjie LIU, Mingwei SUN, Zengqiang CHEN, Qinglin SUN. High AOA decoupling control for aircraft based on ADRC [J]. Journal of Systems Engineering and Electronics, 2020, 31(2): 393-402.
[10]	Yandong LI, Ling ZHU, Yuan GUO. Observer-based multivariable fixed-time formation control of mobile robots [J]. Journal of Systems Engineering and Electronics, 2020, 31(2): 403-414.
[11]	Tianqing CHANG, Quandong WANG, Lei ZHANG, Na HAO, Wenjun DAI. Battlefield dynamic scanning and staring imaging system based on fast steering mirror [J]. Journal of Systems Engineering and Electronics, 2019, 30(1): 37-56.
[12]	Ligang GONG, Qing WANG, Chaoyang DONG. Switching disturbance rejection attitude control of near space vehicles with variable structure [J]. Journal of Systems Engineering and Electronics, 2019, 30(1): 167-179.
[13]	Ping MA, Denghui ZHANG, Songyan WANG, Tao CHAO. Integrated guidance and control design method based on finite-time state observer [J]. Journal of Systems Engineering and Electronics, 2018, 29(6): 1251-1262.
[14]	Jiayi TIAN, Shifeng ZHANG. Active disturbance rejected predictive functional control for space vehicles with RCS [J]. Journal of Systems Engineering and Electronics, 2018, 29(5): 1022-1035.
[15]	Xiaoyan LIN, Lingmei CHEN, Dongyun LIN, Weiyao LAN. Output regulation of singular linear systems with input saturation by composite nonlinear feedback control [J]. Journal of Systems Engineering and Electronics, 2018, 29(4): 834-843.

Exact uncertainty compensation of linear systems by continuous fixed-time output-feedback controller

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

Share this article

Figures/Tables 6

References 34

Related Articles 15

Recommended Articles

Metrics

Comments