一类具有未知幂次的高阶不确定非线性系统的自适应控制

刘玉发; 刘勇华; 苏春翌; 鲁仁全

doi:10.16383/j.aas.c200893

一类具有未知幂次的高阶不确定非线性系统的自适应控制

doi: 10.16383/j.aas.c200893

刘玉发^{1, 2,},
刘勇华^{1, 2,},
苏春翌^{1, 2,},
鲁仁全^{1, 2,}

1.
广东工业大学自动化学院广州 510006
2.
广东省智能决策与协同控制重点实验室广州 510006

基金项目: 国家自然科学基金 (61803097, U2013601), 广东省特支计划本土创新创业团队项目基金(2019BT02X353)资助

详细信息

作者简介:
刘玉发：广东工业大学自动化学院硕士研究生. 主要研究方向为自适应控制. E-mail: yufa.liu@outlook.com

刘勇华：广东工业大学自动化学院副教授. 主要研究方向为非线性控制与智能控制. 本文通信作者. E-mail: yonghua.liu@outlook.com

苏春翌：广东工业大学自动化学院教授. 主要研究方向为控制理论及其在机电系统中的应用. E-mail: chunyi.su@concordia.ca

鲁仁全：广东工业大学自动化学院教授. 主要研究方向为网络化控制系统理论及应用, 医疗大数据分析, 智能制造. E-mail: rqlu@gdut.edu.cn

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出版历程
- 收稿日期: 2020-10-25
- 录用日期: 2021-04-16
- 网络出版日期: 2021-07-01
- 刊出日期: 2022-06-01

Adaptive Control for a Class of High-order Uncertain Nonlinear Systems With Unknown Powers

LIU Yu-Fa^{1, 2
,},
LIU Yong-Hua^{1, 2
,},
SU Chun-Yi^{1, 2
,},
LU Ren-Quan^{1, 2
,}

1.
School of Automation, Guangdong University of Technology, Guangzhou 510006
2.
Guangdong Province Key Laboratory of Intelligent Decision and Cooperative Control, Guangzhou 510006

Funds: Supported by National Natural Science Foundation of China (61803097, U2013601) and Local Innovative and Research Teams Project of Guangdong Special Support Program (2019BT02X353)

More Information

Author Bio:
LIU Yu-Fa　Master student at the School of Automation, Guangdong University of Technology. His main research interest is adaptive control

LIU Yong-Hua　Associate professor at the School of Automation, Guangdong University of Technology. His research interest covers nonlinear and intelligent control. Corresponding author of this paper

SU Chun-Yi　Professor at the School of Automation, Guangdong University of Technology. His research interest covers control theory and its applications to mechanical systems

LU Ren-Quan　Professor at the School of Automation, Guangdong University of Technology. His research interest covers theory and application of networked control system, medical big data analysis, and intelligent manufacturing

摘要

摘要: 研究了一类具有未知幂次的高阶不确定非线性系统的自适应跟踪控制问题. 在无需系统函数先验知识的条件下, 采用积分反推技术和障碍李雅普诺夫函数, 提出了一种新颖的自适应跟踪控制算法. 该控制算法的显著特点是所设计的自适应控制器均与系统幂次无关, 并且能够保证闭环系统的所有信号皆有界. 仿真算例验证了该控制算法的有效性.
- 高阶非线性系统 /
- 输出跟踪 /
- 自适应控制 /
- 障碍函数 /
- 未知幂次
Abstract: This paper studies the problem of adaptive output tracking for a class of high-order uncertain nonlinear systems with unknown powers. Without incorporating a priori information of system functions, a novel adaptive tracking control algorithm is proposed by combining integrator backstepping technique and barrier Lyapunov functions. The remarkable feature of the proposed algorithm is that the designed adaptive controller does not rely on the powers and ensures the global uniform boundedness of all the closed-loop signals. Simulation studies are stated to perform the effectiveness of the control algorithm.
- High-order nonlinear systems /
- output tracking /
- adaptive control /
- barrier function /
- unknown powers

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图 1 具有未知幂次的控制系统框图

Fig. 1 Block diagram of the control system with unknown powers

下载: 全尺寸图片幻灯片

图 2 系统$\Sigma_1$和$\Sigma_2$的输出跟踪误差$y-y_r$

Fig. 2 Output tracking errors $y-y_r$ of systems $\Sigma_1$ and $\Sigma_2$

下载: 全尺寸图片幻灯片

图 3 系统$\Sigma_1$和$\Sigma_2$的控制信号$u$

Fig. 3 Control signals $u$ of systems $\Sigma_1$ and $\Sigma_2$

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图 4 系统$\Sigma_1$和$\Sigma_2$的自适应参数$\hat{\vartheta}_1$和$\ \hat{\vartheta}_2$

Fig. 4 Adaptive parameters $\hat{\vartheta}_1$ and $\hat{\vartheta}_2$ of systems $\Sigma_1$ and $\Sigma_2$

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图 5 系统$\Sigma_1$在不同幂次下的跟踪误差$y-y_r$

Fig. 5 Output tracking errors $y-y_r$ of system $\Sigma_1$ under various powers

下载: 全尺寸图片幻灯片

图 6 系统$\Sigma_1$在不同幂次下的控制信号$u$

Fig. 6 Control signals $u$ of system $\Sigma_1$ under various powers

下载: 全尺寸图片幻灯片

参考文献(35)

[1]	Rui C L, Reyhangolu M, Kolmanovsky I, Cho S, McClamroch N H. Nonsmooth stabilization of an underactuated unstable two degrees of freedom mechanical system. In: Proceedings of the 36th IEEE Conference on Decision and Control. California, USA: IEEE, 1997. 3998−4003
[2]	Su Z G, Qian C J, Wang Q, Wang Z. Reduced-order observer and controller design for a 1 000 mw ultra-supercritical unit. In: Proceedings of the 58th ISA Power Generation Division Symposium. Florida, USA: ISA, 2015. 129−140
[3]	Lin W, Qian C. Adding one power integrator: a tool for global stabilization of high-order lower-triangular systems. Systems and Control Letters, 2000, 39(5): 339-351 doi: 10.1016/S0167-6911(99)00115-2
[4]	Lin W, Qian C. Adaptive regulation of high-order lowertriangular systems: an adding a power integrator technique. Systems and Control Letters, 2000, 39(5): 353-364 doi: 10.1016/S0167-6911(99)00114-0
[5]	Qian C, Lin W. A continuous feedback approach to global strong stabilization of nonlinear systems. IEEE Transactions on Automatic Control, 2001, 46(7): 1061-1079 doi: 10.1109/9.935058
[6]	Lin W, Qian C J. Adaptive control of nonlinearly parameterized systems: A nonsmooth feedback framework. IEEE Transactions on Automatic Control, 2002, 47(5): 757-774 doi: 10.1109/TAC.2002.1000270
[7]	Qian C J, Lin W. Practical output tracking of nonlinear systems with uncontrollable unstable linearization. IEEE Transactions on Automatic Control, 2002, 47(1): 21-36 doi: 10.1109/9.981720
[8]	Lin W, Pongvuthithum R. Adaptive output tracking of inherently nonlinear systems with nonlinear parameterization. IEEE Transactions on Automatic Control, 2003, 48(10): 1737-1749 doi: 10.1109/TAC.2003.817922
[9]	Yang B, Lin W. Homogeneous observers, iterative design, and global stabilization of high-order nonlinear systems by smooth output feedback. IEEE Transactions on Automatic Control, 2004, 49(7): 1069-1080 doi: 10.1109/TAC.2004.831186
[10]	Back J, Cheong S G, Shim H, Seo J H. Nonsmooth feedback stabilizer for strict-feedback nonlinear systems that may not be linearizable at the origin. Systems and Control Letters, 2007, 56(11-12): 742-752 doi: 10.1016/j.sysconle.2007.04.009
[11]	Yan X H, Liu Y G. Global practical tracking for high-order uncertain nonlinear systems with unknown control directions. SIAM Journal on Control and Optimization, 2010, 48(7): 4453-4473 doi: 10.1137/090769727
[12]	Fu J, Ma R, Chai T. Global finite-time stabilization of a class of switched nonlinear systems with the powers of positive odd rational numbers. Automatica, 2015, 54: 360-373 doi: 10.1016/j.automatica.2015.02.023
[13]	Sun Z Y, Xue L R, Zhang K. A new approach to finitetime adaptive stabilization of high-order uncertain nonlinear system. Automatica, 2015, 58: 60-66 doi: 10.1016/j.automatica.2015.05.005
[14]	Fu J, Ma R, Chai T. Adaptive finite-time stabilization of a class of uncertain nonlinear systems via logic-based switchings. IEEE Transactions on Automatic Control, 2017, 62(11): 5998-6003 doi: 10.1109/TAC.2017.2705287
[15]	Sun Z Y, Shao Y, Chen C C. Fast finite-time stability and its application in adaptive control of high-order nonlinear system. Automatica, 2019, 106: 339-348 doi: 10.1016/j.automatica.2019.05.018
[16]	段纳, 解学军. 具有iISS未建模动态的非线性系统的状态反馈调节. 自动化学报, 2010, 36(7): 1033-1036 doi: 10.3724/SP.J.1004.2010.01033 Duan Na, Xie Xue Jun. State-feedback Regulation of Nonlinear Systems with iISS Unmodeled Dynamics. Acta Automatica Sinca, 2010, 36(7): 1033-1036 doi: 10.3724/SP.J.1004.2010.01033
[17]	张健, 刘允刚. 一类不确定非线性系统无过参数自适应控制设计新方法. 中国科学: 信息科学, 2011, 41(7): 892-902 Jian Zhang, Liu Yun-Gang. A new approach to adaptive control design without overparametrization for a class of uncertain nonlinear systems. Science China Information Sciences, 2011, 41(7): 892-902
[18]	满永超, 刘允刚. 高阶不确定非线性系统线性状态反馈自适应控制设计. 自动化学报, 2014, 40(1): 24-32 Man Yong-Chao, Liu Yun-Gang. Adaptive Control Design via Linear State-feedback for High-order Uncertain Nonlinear Systems. Acta Automatica Sinca, 2014, 40(1): 24-32
[19]	孙丞, 孙鹤旭, 刁心薇. 一类非齐次高阶非线性系统的连续反馈控制设计. 自动化学报, 2014, 40(1): 151-155 Sun Cheng, Sun He-Xu, Diao Xin-Wei. Continuous Feedback Control Design for a Class of Non-homogeneous Highorder Nonlinear Systems. Acta Automatica Sinca, 2014, 40(1): 151-155
[20]	Su Zhigang, Qian Chunjiang, Shen Jiong. Interval homogeneity-based control for a class of nonlinear systems with unknown power drifts. IEEE Transactions on Automatic Control, 2017, 62(3): 1445-1450 doi: 10.1109/TAC.2016.2575819
[21]	Chen C C, Qian C, Lin X, Sun Z Y, Liang Y W. Smooth output feedback stabilization for a class of nonlinear systems with time-varying powers. International Journal of Robust and Nonlinear Control, 2017, 27(18): 5113-5128 doi: 10.1002/rnc.3826
[22]	Man Yong-Chao, Liu Yun-Gang. Global adaptive stabilization and practical tracking for nonlinear systems with unknown powers. Automatica, 2019, 100: 171-181 doi: 10.1016/j.automatica.2018.11.011
[23]	Guo C, Xie R, Xie X J. Adaptive control of full-state constrained high-order nonlinear systems with time-varying powers. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019, doi: 10.1109/TSMC.2019.2946350
[24]	Wang M, Liu Y, Man Y. Switching adaptive controller for the nonlinear systems with uncertainties from unknown powers. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2020, 50(7): 2375-2385 doi: 10.1109/TSMC.2018.2814345
[25]	Man Y, Liu Y. Global adaptive stabilization for planar nonlinear systems with unknown input powers. Science China Information Sciences, 2021, 64: 199204:1-199204:3 doi: 10.1007/s11432-018-9774-y
[26]	Tee K P, Ge S S, Tay E H. Barrier Lyapunov functions for the control of output-constrained nonlinear systems. Automatica, 2009, 45(4): 918-927 doi: 10.1016/j.automatica.2008.11.017
[27]	Jankovic M. Robust control barrier functions for constrained stabilization of nonlinear systems. Automatica, 2018, 96: 359-367 doi: 10.1016/j.automatica.2018.07.004
[28]	Khalil H K. Nonlinear Systems, 3rd Edition. Englewood Cliffs: Prentice-Hall, 2002.
[29]	Qian C, Lin W. Non-Lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization. Systems and Control Letters, 2015, 42(3): 185-200
[30]	Hardy G H, Littlewood J E, Pólya G. Inequalities. London: Cambridge University Press. 1934.
[31]	Wang C, Zuo Z. Adaptive trajectory tracking control of output constrained multi-rotors systems. IET Control Theory and Applications, 2014, 8(13): 1163-1174 doi: 10.1049/iet-cta.2013.0949
[32]	Ren B, Ge S S, Tee K P, Lee T H. Adaptive neural control for output feedback nonlinear systems using a barrier Lyapunov function. IEEE Transactions on Neural Networks, 2010, 21(8): 1339-1345 doi: 10.1109/TNN.2010.2047115
[33]	Logemann M, Ryan E P. Ordinary Differential Equations: Analysis, Qualitative Theory and Control. London, UK: Springer. 2014.
[34]	Liu Y H, Su C Y, Li H, Adaptive output feedback funnel control of uncertain nonlinear systems with arbitrary relative degree. IEEE Transactions on Automatic Control, 2020, doi: 10.1109/TAC.2020.3012027.
[35]	Liu Y H, Liu Y, Liu Y F, Su C Y, Zhou Q, Lu R, Adaptive approximation-based tracking control for a class of unknown high-order nonlinear systems with unknown powers. IEEE Transactions on Cybernetics, 2020, doi: 10.1109/TCYB.2020.3030310.