Adaptive control design for nonlinear systems with multiple uncertainties
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- 英文论文题名：Adaptive control design for nonlinear systems with multiple uncertainties
- 论文作者：Yaxin Huang ; Yungang Liu
- 英文论文作者：Yaxin Huang ; Yungang Liu ; School of Control Science and Engineering ; Shandong University
- 年：2017
- 作者机构：School of Control Science and Engineering,Shandong University;
- 英文论文关键词：Uncertain nonlinear systems ; State feedback ; Unknown control directions ; Adaptive technique ; Unknown input bias
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（A）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（A）
- 语种：英文
- 分类号：O231
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：6
- 文件大小：228k
- 原文格式：D
- 会议级别：全国
摘要
This paper considers the global state-feedback stabilization for a class of nonlinear systems with multiple uncertainties.Different from the existing related literature, the systems under investigation are subjected to unknown input bias, and allow unknown control directions and parametric uncertainties. In this paper, an adaptive state-feedback scheme is proposed, not only to deal with the multiple uncertainties, but also to achieve the global stabilization of the systems. Detailedly, a state-feedback controller is designed by the backstepping approach, where the Nussbaum-type gain approach and estimation-based adaptive technique are incorporated to handle the unknown control directions and parametric uncertainties, respectively. It is shown that all the signals of the resulting closed-loop system are bounded, and the original system states converge to zero. A simulation example on the model of ship steering is given to demonstrate the effectiveness of the theoretical results.
This paper considers the global state-feedback stabilization for a class of nonlinear systems with multiple uncertainties.Different from the existing related literature, the systems under investigation are subjected to unknown input bias, and allow unknown control directions and parametric uncertainties. In this paper, an adaptive state-feedback scheme is proposed, not only to deal with the multiple uncertainties, but also to achieve the global stabilization of the systems. Detailedly, a state-feedback controller is designed by the backstepping approach, where the Nussbaum-type gain approach and estimation-based adaptive technique are incorporated to handle the unknown control directions and parametric uncertainties, respectively. It is shown that all the signals of the resulting closed-loop system are bounded, and the original system states converge to zero. A simulation example on the model of ship steering is given to demonstrate the effectiveness of the theoretical results.
This paper considers the global state-feedback stabilization for a class of nonlinear systems with multiple uncertainties.Different from the existing related literature, the systems under investigation are subjected to unknown input bias, and allow unknown control directions and parametric uncertainties. In this paper, an adaptive state-feedback scheme is proposed, not only to deal with the multiple uncertainties, but also to achieve the global stabilization of the systems. Detailedly, a state-feedback controller is designed by the backstepping approach, where the Nussbaum-type gain approach and estimation-based adaptive technique are incorporated to handle the unknown control directions and parametric uncertainties, respectively. It is shown that all the signals of the resulting closed-loop system are bounded, and the original system states converge to zero. A simulation example on the model of ship steering is given to demonstrate the effectiveness of the theoretical results.
引文
[1]R.Brockett,“New issues in the mathematics of control,”Mathematics Unlimited–2001 and Beyond,189–220,2001.
[2]K.J.?Astrm,Model Uncertainty and Feedback,London:Springer,2002.
[3]Z.P.Jiang,I.Mareels,D.J.Hill and J.Huang,“A unifying framework for global regulation via nonlinear output feedback:from ISS to i ISS,”IEEE Transactions on Automatic Control,49(4):549–562,2004.
[4]Z.T.Ding,“Global adaptive output feedback stabilization of nonlinear systems of any relative degree with unknown high frequency gains,”IEEE Transactions on Automatic Control,43(10):1442–1446,1998.
[5]X.D.Ye,“Adaptive nonlinear output-feedback control with unknown high-frequency gain sign,”IEEE Transactions on Automatic Control,46(1):112–115,2001.
[6]Y.G.Liu,“Output-feedback adaptive control for a class of nonlinear systems with unknown control directions,”Acta Automatica Sinca,33(12):1306–1312,2007.
[7]Q.C.Zhao,Y.M.Li and Y.Lin,“Adaptive nonlinear output-feedback dynamic surface control with unknown highfrequency gain sign,”International Journal of Control,86(12):2203–2214,2013.
[8]L.Praly and Z.P.Jiang,“Linear output feedback with dynamic high gain for nonlinear systems,”Systems&Control Letters,53(2):107–116,2004.
[9]R.D.Nussbaum,“Some remarks on a conjecture in parameter adaptive control,”Systems&Control Letters,3(5):243–246,1983.
[10]X.D.Ye and J.P.Jiang,“Adaptive nonlinear design without a priori knowledge of control directions,”IEEE Transactions on Automatic Control,43(11):1617–1621,1998.
[11]A.Astolfi and L.Lanari,“Disturbance attenuation and setpoint regulation of rigid robots via H∞control,”Proceedings of the 33rd Conference on Decision and Control,Lake Buena Vita,FL,USA:2578–2583,1994.
[12]W.G.Wu,H.T.Chen,Y.J.Wang and P.Y.Woo,“Adaptive exponential stabilization of mobile robots with unknown constant-input disturbance,”Journal of Robotic Systems,18(6):289–294,2001.
[13]B.Martensson,“Remarks on adaptive stabilization of first order nonlinear systems,”Systems&Control Letters,14(1):1–7,1990.
[14]X.D.Ye,“Asymptotic regulation of time-varying uncertain nonlinear systems with unknown control directions,”Automatica,35(5):929–935,1999.
[15]Y.Zhang,C.Y.Wen and Y.C.Soh,“Adaptive backstepping control design for systems with unkonwn high-frequency gain,”IEEE Transactions on Automatic Control,45(12):2350–2354,2000.
[16]H.X.Yan and Y.G.Liu,“Global practical tracking for highorder uncertain nonlinear systems with unknown control directions,”SIAM Journal on Control and Optimization,48(7):4453–4473,2010.
[17]Y.Y.Min and Y.G.Liu,“Barbalat Lemma and its application in analysis of system stability,”Journal of Shandong University(Engineering Science),37(1):551–554,2007(in Chinese).
[18]J.L.Du,A.Abraham,S.H.Yu and J.Zhao,“Adaptive dynamic surface control with Nussbaum gain for course-keeping of ships,”Engineering Applications of Artificial Intelligence,27:236–240,2014.
[2]K.J.?Astrm,Model Uncertainty and Feedback,London:Springer,2002.
[3]Z.P.Jiang,I.Mareels,D.J.Hill and J.Huang,“A unifying framework for global regulation via nonlinear output feedback:from ISS to i ISS,”IEEE Transactions on Automatic Control,49(4):549–562,2004.
[4]Z.T.Ding,“Global adaptive output feedback stabilization of nonlinear systems of any relative degree with unknown high frequency gains,”IEEE Transactions on Automatic Control,43(10):1442–1446,1998.
[5]X.D.Ye,“Adaptive nonlinear output-feedback control with unknown high-frequency gain sign,”IEEE Transactions on Automatic Control,46(1):112–115,2001.
[6]Y.G.Liu,“Output-feedback adaptive control for a class of nonlinear systems with unknown control directions,”Acta Automatica Sinca,33(12):1306–1312,2007.
[7]Q.C.Zhao,Y.M.Li and Y.Lin,“Adaptive nonlinear output-feedback dynamic surface control with unknown highfrequency gain sign,”International Journal of Control,86(12):2203–2214,2013.
[8]L.Praly and Z.P.Jiang,“Linear output feedback with dynamic high gain for nonlinear systems,”Systems&Control Letters,53(2):107–116,2004.
[9]R.D.Nussbaum,“Some remarks on a conjecture in parameter adaptive control,”Systems&Control Letters,3(5):243–246,1983.
[10]X.D.Ye and J.P.Jiang,“Adaptive nonlinear design without a priori knowledge of control directions,”IEEE Transactions on Automatic Control,43(11):1617–1621,1998.
[11]A.Astolfi and L.Lanari,“Disturbance attenuation and setpoint regulation of rigid robots via H∞control,”Proceedings of the 33rd Conference on Decision and Control,Lake Buena Vita,FL,USA:2578–2583,1994.
[12]W.G.Wu,H.T.Chen,Y.J.Wang and P.Y.Woo,“Adaptive exponential stabilization of mobile robots with unknown constant-input disturbance,”Journal of Robotic Systems,18(6):289–294,2001.
[13]B.Martensson,“Remarks on adaptive stabilization of first order nonlinear systems,”Systems&Control Letters,14(1):1–7,1990.
[14]X.D.Ye,“Asymptotic regulation of time-varying uncertain nonlinear systems with unknown control directions,”Automatica,35(5):929–935,1999.
[15]Y.Zhang,C.Y.Wen and Y.C.Soh,“Adaptive backstepping control design for systems with unkonwn high-frequency gain,”IEEE Transactions on Automatic Control,45(12):2350–2354,2000.
[16]H.X.Yan and Y.G.Liu,“Global practical tracking for highorder uncertain nonlinear systems with unknown control directions,”SIAM Journal on Control and Optimization,48(7):4453–4473,2010.
[17]Y.Y.Min and Y.G.Liu,“Barbalat Lemma and its application in analysis of system stability,”Journal of Shandong University(Engineering Science),37(1):551–554,2007(in Chinese).
[18]J.L.Du,A.Abraham,S.H.Yu and J.Zhao,“Adaptive dynamic surface control with Nussbaum gain for course-keeping of ships,”Engineering Applications of Artificial Intelligence,27:236–240,2014.