Nonsmooth Feedback Adaptive Stabilization for High-Order Nonlinear Systems Subject to State Delay
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- 英文论文题名：Nonsmooth Feedback Adaptive Stabilization for High-Order Nonlinear Systems Subject to State Delay
- 论文作者：Xianglei Jia ; Junfeng Zhang ; Yun Chen ; Ridong Zhang
- 英文论文作者：Xianglei Jia ; Junfeng Zhang ; Yun Chen ; Ridong Zhang ; School of Automation ; Hangzhou Dianzi University
- 年：2017
- 作者机构：School of Automation,Hangzhou Dianzi University;
- 英文论文关键词：Backstepping ; Nonsmooth ; Dynamic Gains ; Time-Delay Systems ; Lyapunov-Krasovskii Functional
- 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：5
- 文件大小：241k
- 原文格式：D
- 会议级别：全国
摘要
This paper proposes a nonsmooth control scheme for high-order nonlinear time-delay systems without extra assumptions,which can be regarded as an expansion of the backstepping method based on dynamic gains. With the help of the LyapunovKrasovskii theorem, a continuous and memoryless controller is explicitly constructed, which guarantees that all the closed-loop signals are globally uniformly ultimately bounded while the original system states asymptotically converge to zero. Finally, an example is given to illustrate the usefulness of our result.
This paper proposes a nonsmooth control scheme for high-order nonlinear time-delay systems without extra assumptions,which can be regarded as an expansion of the backstepping method based on dynamic gains. With the help of the LyapunovKrasovskii theorem, a continuous and memoryless controller is explicitly constructed, which guarantees that all the closed-loop signals are globally uniformly ultimately bounded while the original system states asymptotically converge to zero. Finally, an example is given to illustrate the usefulness of our result.
This paper proposes a nonsmooth control scheme for high-order nonlinear time-delay systems without extra assumptions,which can be regarded as an expansion of the backstepping method based on dynamic gains. With the help of the LyapunovKrasovskii theorem, a continuous and memoryless controller is explicitly constructed, which guarantees that all the closed-loop signals are globally uniformly ultimately bounded while the original system states asymptotically converge to zero. Finally, an example is given to illustrate the usefulness of our result.
引文
[1]Praly,L.,Andrea-Novel,B.D.,&Coron,J.M.,Lyapunov design of stabilizing controllers for cascaded systems,IEEE Transactions on Automatic Control,36(10),1177–1181,1991.
[2]Coron,J.M.,&Praly,L.,Adding an integrator for the stabilization problem,Systems&Control Letters,17(2),89–104,1991.
[3]Kanellakopoulos,I.,Kokotovic,P.V.,&Morse,A.S.,Systematic design of adaptive controllers for feedback linearizable systems,IEEE Transactions on Automatic Control,36(11),1241–1253,1991.
[4]Tzamtzi,M.&Tsinias,J.,Explicit formulas of feedback stabilizers for a class of triangular systems with uncontrollable linearization,Systems&control letters,38(2),115–126,1999.
[5]Lin,W.,&Qian,C.,Adding one power integrator:a tool for global stabilization of high-order lower-triangular systems,Systems&Control Letters,39(5),339–351,2000.
[6]Qian,C.&Lin,W.,A continuous feedback approach to global strong stabilization of nonlinear systems,IEEE Transactions on Automatic Control,46(7),1061–1079,2001.
[7]Ge,S.S.,Hong,F.,&Lee,T.H.,Robust adaptive control of nonlinear systems with unknown time delays,Automatica,41(7),1181–1190,2005.
[8]Hua,C.,Feng,G.,&Guan,X.,Robust controller design of a class of nonlinear time delay systems via backstepping method,Automatica,44(2),567–573,2008.
[9]Dashkovskiy,S.N.&Pavlichkov,S.S.,Robust stabilization of the generalized triangular form nonlinear systems with disturbances,IEEE Transactions on Automatic Control,59(6),1577–1582,2014.
[10]Zhang,X.&Lin,Y.,Global stabilization of high-order nonlinear time-delay systems by state feedback,Systems&Control Letters,65,89–95,2014.
[11]Zhang,X.&Lin,Y.,Adaptive control of nonlinear time-delay systems with application to a two-stage chemical reactor,IEEE Transactions on Automatic Control,60(4):1074–1079,2015.
[12]Zhang,X.,Lin,W.,Lin,Y.,Nonsmooth feedback control of time-delay systems:A dynamic gain based approach,IEEE Transactions on Automatic Control,62(1):438–444,2017.
[2]Coron,J.M.,&Praly,L.,Adding an integrator for the stabilization problem,Systems&Control Letters,17(2),89–104,1991.
[3]Kanellakopoulos,I.,Kokotovic,P.V.,&Morse,A.S.,Systematic design of adaptive controllers for feedback linearizable systems,IEEE Transactions on Automatic Control,36(11),1241–1253,1991.
[4]Tzamtzi,M.&Tsinias,J.,Explicit formulas of feedback stabilizers for a class of triangular systems with uncontrollable linearization,Systems&control letters,38(2),115–126,1999.
[5]Lin,W.,&Qian,C.,Adding one power integrator:a tool for global stabilization of high-order lower-triangular systems,Systems&Control Letters,39(5),339–351,2000.
[6]Qian,C.&Lin,W.,A continuous feedback approach to global strong stabilization of nonlinear systems,IEEE Transactions on Automatic Control,46(7),1061–1079,2001.
[7]Ge,S.S.,Hong,F.,&Lee,T.H.,Robust adaptive control of nonlinear systems with unknown time delays,Automatica,41(7),1181–1190,2005.
[8]Hua,C.,Feng,G.,&Guan,X.,Robust controller design of a class of nonlinear time delay systems via backstepping method,Automatica,44(2),567–573,2008.
[9]Dashkovskiy,S.N.&Pavlichkov,S.S.,Robust stabilization of the generalized triangular form nonlinear systems with disturbances,IEEE Transactions on Automatic Control,59(6),1577–1582,2014.
[10]Zhang,X.&Lin,Y.,Global stabilization of high-order nonlinear time-delay systems by state feedback,Systems&Control Letters,65,89–95,2014.
[11]Zhang,X.&Lin,Y.,Adaptive control of nonlinear time-delay systems with application to a two-stage chemical reactor,IEEE Transactions on Automatic Control,60(4):1074–1079,2015.
[12]Zhang,X.,Lin,W.,Lin,Y.,Nonsmooth feedback control of time-delay systems:A dynamic gain based approach,IEEE Transactions on Automatic Control,62(1):438–444,2017.