Revised barrier function-based adaptive finite- and fixed-time convergence super-twisting control

doi:10.23919/JSEE.2023.000071

Abstract

Abstract:

This paper presents an adaptive gain, finite- and fixed-time convergence super-twisting-like algorithm based on a revised barrier function, which is robust to perturbations with unknown bounds. It is shown that this algorithm can ensure a finite- and fixed-time convergence of the sliding variable to the equilibrium, no matter what the initial conditions of the system states are, and maintain it there in a predefined vicinity of the origin without violation. Also, the proposed method avoids the problem of overestimation of the control gain that exists in the current fixed-time adaptive control. Moreover, it shows that the revised barrier function can effectively reduce the computation load by obviating the need of increasing the magnitude of sampling step compared with the conventional barrier function. This feature will be beneficial when the algorithm is implemented in practice. After that, the estimation of the fixed convergence time of the proposed method is derived and the impractical requirement of the preceding fixed-time adaptive control that the adaptive gains must be large enough to engender the sliding mode at time $ t = 0 $ is discarded. Finally, the outperformance of the proposed method over the existing counterpart method is demonstrated with a numerical simulation.

Key words: super-twisting algorithm, barrier function, fixed-time sliding mode control, adaptive control

Dakai LIU, Sven ESCHE. Revised barrier function-based adaptive finite- and fixed-time convergence super-twisting control[J]. Journal of Systems Engineering and Electronics, 2023, 34(3): 775-782.

Figures/Tables 10

Fig 1

Fig 2

Fig 3

Fig 4

Fig 5

Fig 6

Fig 7

Fig 8

Fig 9

Fig 10

References 26

1	EDWARDS C, SPURGEON S. Sliding mode control: theory and applications. Florida: CRC Press, 1998.
2	UTKIN V I. Sliding modes in optimization and control problems. New York: Springer Verlag, 1992.
3	EDWARDS C, SHTESSEL Y B Enhanced continuous higher order sliding mode control with adaptation. Journal of the Franklin Institute, 2019, 356 (9): 4773- 4784. doi: 10.1016/j.jfranklin.2018.12.026
4	UTKIN V I, POZNYAK A S Adaptive sliding mode control with application to super-twist algorithm: equivalent control method. Automatica, 2013, 49, 39- 47. doi: 10.1016/j.automatica.2012.09.008
5	SHTESSEL Y B, SHKOLNIKOV I A, LEVANT A Smooth second-order sliding modes: missile guidance application. Automatica, 2007, 43, 1470- 1476. doi: 10.1016/j.automatica.2007.01.008
6	LIU D K, ESCHE S, WANG M G An adaptive super-twisting algorithm based on conditioning technique. Transactions of the Institute of Measurement and Control, 2022, 44 (2): 497- 505. doi: 10.1177/01423312211040317
7	SHTESSEL Y B, MORENO J A, PLESTAN F, et al. Super-twisting adaptive sliding mode control: a Lyapunov design. Proc. of the 49th IEEE Conference on Decision and Control, 2010: 5109−5113.
8	EDWARDS C, SHTESSEL Y B Adaptive dual-layer super-twisting control and observation. International Journal of Control, 2016, 89 (9): 1759- 1766. doi: 10.1080/00207179.2016.1175030
9	EDWARDS C, SHTESSEL Y B Adaptive continuous higher order sliding mode control. Automatica, 2016, 65, 183- 190. doi: 10.1016/j.automatica.2015.11.038
10	OLIVEIRA T R, CUNHA J P V, HSU L. Adaptive sliding mode control for disturbances with unknown bounds. Proc. of the 14th International Workshop on Variable Structure Systems, 2016: 59−64.
11	TIAN B L, CUI J, LU H C, et al Adaptive finite-time attitude tracking of quadrotors with experiments and comparisons. IEEE Trans. on Industrial Electronics, 2019, 66, 9428- 9438. doi: 10.1109/TIE.2019.2892698
12	NEGRETE-CHAVEZ D Y, MORENO J A Second-order sliding mode output feedback controller with adaptation. International Journal of Adaptive Control and Signal Processing, 2016, 30 (8−10): 1523- 1543. doi: 10.1002/acs.2662
13	BASIN M, PANATHULA C B, SHTESSEL Y Adaptive uniform finite-/fixed-time convergent second-order sliding-mode control. International Journal of Control, 2016, 89 (9): 1777- 1787. doi: 10.1080/00207179.2016.1184759
14	PLESTAN F, SHTESSEL Y, BREGEAULT V, et al New methodologies for adaptive sliding mode control. International Journal of Control, 2010, 83 (9): 1907- 1919. doi: 10.1080/00207179.2010.501385
15	SHTESSEL Y, TALEB M, PLESTAN F A novel adaptive-gain supertwisting sliding mode controller: methodology and application. Automatica, 2012, 48, 759- 769. doi: 10.1016/j.automatica.2012.02.024
16	OBEID H, FRIDMAN L, LAGHROUCHE S, et al. Barrier function-based adaptive twisting controller. Proc. of the 15th International Workshop on Variable Structure Systems, 2018: 198−202.
17	OBEID H, FRIDMAN L, LAGHROUCHE S, et al Adaptation of Levant’s differentiator based on barrier function. International Journal of Control, 2018, 91 (9): 2019- 2027. doi: 10.1080/00207179.2017.1406149
18	OBEID H, FRIDMAN L M, LAGHROUCHE S, et al Barrier function-based adaptive sliding mode control. Automatica, 2018, 93, 540- 544. doi: 10.1016/j.automatica.2018.03.078
19	OBEID H, LAGHROUCHE S, FRIDMAN L, et al Barrier function-based variable gain super-twisting controller. IEEE Trans. on Automatic Control, 2020, 65, 4928- 4933. doi: 10.1109/TAC.2020.2974390
20	OBEID H, LAGHROUCHE S, FRIDMAN L. A barrier function based-adaptive super-twisting controller for wind energy conversion system. Proc. of the 58th Conference on Decision and Control, 2019: 7869−7874.
21	BASIN M, RODRIGUEZ-RAMIREZ P, DING S X, et al Continuous fixed-time convergent regulator for dynamic systems with unbounded disturbances. Journal of the Franklin Institute, 2018, 355 (5): 2762- 2778. doi: 10.1016/j.jfranklin.2018.01.010
22	BASIN M Finite-and fixed-time convergent algorithms: Design and convergence time estimation. Annual Reviews in Control, 2019, 48, 209- 221. doi: 10.1016/j.arcontrol.2019.05.007
23	BASIN M, PANATHULA C B, SHTESSEL Y Multivariable continuous fixed-time second-order sliding mode control: design and convergence time estimation. IET Control Theory & Applications, 2017, 11 (8): 1104- 1111.
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	BASIN M, RODRIGUEZ-RAMIREZ P, GARZA-ALONSO A Continuous fixed-time convergent super-twisting algorithm in case of unknown state and disturbance initial conditions. Asian Journal of Control, 2019, 21 (1): 323- 338. doi: 10.1002/asjc.1924
26	FILIPPOV A F. Differential equations with discontinuous righthand sides: control systems. Berlin: Springer Science & Business Media, 2013.

[1]	Fan WANG, Pengfei FAN, Yonghua FAN, Bin XU, Jie YAN. Robust adaptive control of hypersonic vehicle considering inlet unstart [J]. Journal of Systems Engineering and Electronics, 2022, 33(1): 188-196.
[2]	Zhaoying LI, Shuai SHI, Hao LIU. Trajectory tracking of tail-sitter aircraft by $ {\cal{L}}_1$ adaptive fault tolerant control [J]. Journal of Systems Engineering and Electronics, 2021, 32(6): 1477-1489.
[3]	Fuhui GUO, Pingli LU. Fast self-adapting high-order sliding mode control for a class of uncertain nonlinear systems [J]. Journal of Systems Engineering and Electronics, 2021, 32(3): 690-699.
[4]	Yang LI, Mingyong LIU, Xiaojian ZHANG, Xingguang PENG. Global approximation based adaptive RBF neural network control for supercavitating vehicles [J]. Journal of Systems Engineering and Electronics, 2018, 29(4): 797-804.
[5]	Ri Liu, Xiuxia Sun, Wenhan Dong, and Dong Wang. Finite-time adaptive sliding mode control for heavyweight airdrop operations [J]. Systems Engineering and Electronics, 2017, 28(2): 338-346.
[6]	Jiaoru Huang, Fucai Qian, Guo Xie, and Hengzhan Yang. Robust adaptive control for dynamic systems with mixed uncertainties [J]. Systems Engineering and Electronics, 2016, 27(3): 656-663.
[7]	Xuemei Zheng, Peng Li, Haoyu Li, and Danmei Ding. Adaptive backstepping-based NTSM control for unmatched uncertain nonlinear systems [J]. Systems Engineering and Electronics, 2015, 26(3): 557-564.
[8]	Yong Guo, Shenmin Song, and Liwei Deng. Finite-time coordination control for formation flying spacecraft [J]. Journal of Systems Engineering and Electronics, 2014, 25(5): 859-867.
[9]	Xuelian Yao, Gang Tao, and Ruiyun Qi. Adaptive actuator failure compensation and disturbance rejection scheme for spacecraft [J]. Journal of Systems Engineering and Electronics, 2014, 25(4): 648-.
[10]	Lei Li and Zhizhong Mao. Direct adaptive control for a class of MIMO nonlinear discrete-time systems [J]. Journal of Systems Engineering and Electronics, 2014, 25(1): 129-137.
[11]	Wenli Sun, Hong Cai, and Fu Zhao. FBFN-based adaptive repetitive control of nonlinearly parameterized systems [J]. Journal of Systems Engineering and Electronics, 2013, 24(6): 1003-1010.
[12]	Xunhong Lv, Bin Jiang, Ruiyun Qi, and Jing Zhao. Survey on nonlinear reconfigurable flight control [J]. Journal of Systems Engineering and Electronics, 2013, 24(6): 971-983.
[13]	Haibin Sun, Shihua Li, and Changyin Sun. Adaptive fault-tolerant controller design for airbreathing hypersonic vehicle with input saturation [J]. Journal of Systems Engineering and Electronics, 2013, 24(3): 488-.
[14]	Xiyuan Huang, Qing Wang, Yali Wang, Yanze Hou, and Chaoyang Dong. Adaptive augmentation of gain-scheduled controller for aerospace vehicles [J]. Journal of Systems Engineering and Electronics, 2013, 24(2): 272-280.
[15]	Chunsheng Liu and Shaojie Zhang. Novel robust control framework for morphing aircraft [J]. Journal of Systems Engineering and Electronics, 2013, 24(2): 281-287.