Passivity-based Stabilization for a Strict-feedback Nonlinear System under a Proper State-dependent Switching
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- 英文论文题名：Passivity-based Stabilization for a Strict-feedback Nonlinear System under a Proper State-dependent Switching
- 论文作者：Yaowei Sun ; Jun Zhao
- 英文论文作者：Yaowei Sun ; Jun Zhao ; State Key Laboratory of Synthetical Automation for Process Industries (Northeastern University) ; College of Information Science and Engineering ; Northeastern University ; College of Mathematics and Statistics ; Zhoukou Normal University
- 年：2017
- 作者机构：State Key Laboratory of Synthetical Automation for Process Industries (Northeastern University),College of Information Science and Engineering,Northeastern University;College of Mathematics and Statistics,Zhoukou Normal University;
- 英文论文关键词：Switched nonlinear systems ; Passivity ; Recursive backstepping
- 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（B）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（B）
- 语种：英文
- 分类号：TP273
- 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：312k
- 原文格式：D
- 会议级别：全国
摘要
In this paper, the passivity-based stabilization problem of a strict-feedback nonlinear system under a proper statedependent switching law is investigated. Here, the feedback passification problem of each subsystem does not need to be solvable. First, by using the recursive backstepping technique, a sufficient condition under which the closed-loop switched system with designed state feedback controllers is strictly passive from the new input to a designed virtual output is given under a state-dependent switching law. Moreover, the asymptotical stability property of the switched system is achieved by redesigning the introduced new input based on passivity. Finally, a numeral example shows the effectiveness of the proposed method.
In this paper, the passivity-based stabilization problem of a strict-feedback nonlinear system under a proper statedependent switching law is investigated. Here, the feedback passification problem of each subsystem does not need to be solvable. First, by using the recursive backstepping technique, a sufficient condition under which the closed-loop switched system with designed state feedback controllers is strictly passive from the new input to a designed virtual output is given under a state-dependent switching law. Moreover, the asymptotical stability property of the switched system is achieved by redesigning the introduced new input based on passivity. Finally, a numeral example shows the effectiveness of the proposed method.
In this paper, the passivity-based stabilization problem of a strict-feedback nonlinear system under a proper statedependent switching law is investigated. Here, the feedback passification problem of each subsystem does not need to be solvable. First, by using the recursive backstepping technique, a sufficient condition under which the closed-loop switched system with designed state feedback controllers is strictly passive from the new input to a designed virtual output is given under a state-dependent switching law. Moreover, the asymptotical stability property of the switched system is achieved by redesigning the introduced new input based on passivity. Finally, a numeral example shows the effectiveness of the proposed method.
引文
[1]S.Dashkovskiy,S.Pavlichkov,Constructive design of adaptive controllers for nonlinear MIMO systems with arbitrary switchings,IEEE Trans.Autom.Control,61(7):2001-2007,2016.
[2]R.C.Ma,J.Zhao,Backstepping design for global stabilization of switched nonlinear systems in lower triangular form under arbitrary switchings,Automatica,46(11):1819-1823,2010.
[3]B.Niu,J.Zhao,Barrier Lyapunov functions for the output tracking control of constrained nonlinear switched systems,Syst.Control Lett.,62(10):963-971,2013.
[4]J.P.Hespanha,A,S.Morse,Stability of switched systems with average dwell-time,in Proceedings of the 38rd IEEE Conference on Decision and Control,1999:2655-2660.
[5]D.Liberzon,Switching in Systems and Control,Boston:Birkhauser,2003.
[6]B.Niu,H.R.Karimi,H.Q.Wang,and Y.L.Liu,Adaptive output-feedback controller design for switched nonlinear stochastic systems with a modified average dwell-time method,IEEE Trans.Syst.,Man,Cybern.B,Cybern.,DOI:10.1109/TSMC.2016.2597305.
[7]L.X.Zhang,P.Shi,Stability,L2-gain and asynchronous H∞control of discrete-time switched systems with average dwell time,IEEE Trans.Autom.Control,54(9):2193-2200,2009.
[8]Y.E.Wang,X.M.Sun,and F.Mazenc,Stability of switched nonlinear systems with delay and disturbance,Automatica,69(C):78-86,2016.
[9]X.D.Zhao,P.Shi,Y.F.Yin and S.K.Nguang,New results on stability of slowly switched systems:a multiple discontinuous Lyapunov function approach,IEEE Trans.Autom.Control,DOI 10.1109/TAC.2016.2614911.
[10]L.L.Long,J.Zhao,An integral-type multiple Lyapunov functions approach for switched nonlinear systems,IEEE Trans.Automat.Control,61(7):1979-1986,2016.
[11]J.Zhao D.J.Hill,On stability L2-gain and H∞control for switched systems,Automatica,44(5):1220-1232,2008.
[12]J.C.Willems,Dissipative dynamical systems,Eur.J.Control,13(2-3):134-151,2007.
[13]D.J.Hill,P.J.Moylan,The stability of nonlinear dissipative systems,IEEE Trans.Autom.Control,21(5):708-711,1976.
[14]T.Rajpurohit,W.M.Haddad,Dissipativity theory for nonlinear stochastic dynamical systems:input-output and state properties,and stability of feedback interconnections,IEEE Trans.Autom.Control,DOI 10.1109/TAC.2016.2598474.
[15]Z.J.Wu,H.R.Karimi and P.Shi,Dissipativity-based smallgain theorems for stochastic network systems,IEEE Trans.Autom.Control,61(8):2065-2077,2016.
[16]C.I.Byrnes,A.Isidori and J.C.Willems,Passivity,feedback equivalence,and the global stabilization of minimum phase nonlinear systems,IEEE Trans.Autom.Control,36(11):1228-1240,1991.
[17]W.Lin,T.L.Shen,Robust passivity and feedback design for minimum-phase nonlinear systems with structural uncertainty,Automatica,35(1):35-47,1999.
[18]Z.P.Jiang,D.J.Hill and A.L.Fradkov,A passification approach to adaptive nonlinear stabilization,Syst.Control Lett.,28(2):73-84,1996.
[19]C.S.Li,J.Zhao,Robust passivity-based H∞control for uncertain switched nonlinear systems,Int.J.Robust Nonlin.Control,26(24):3186-3206,2016.
[20]L.G.Wu,W.X.Zheng ang H.J.Gao,Dissipativity-based sliding mode control of switched stochastic systems,IEEE Trans.Autom.Control,58(3):785-791,2013.
[21]J.Zhao,D.J.Hill,Dissipativity theory for switched systems,IEEE Trans.Autom.Control,53(4):941-953,2008.
[22]A.Bemporad,G.Bianchini and F.Brogi,Passivity analysis and passification of discrete-time hybrid systems[J],IEEE Trans.Autom.Control,53(4):1004-1009,2008.
[23]H.B.Pang,J.Zhao,Robust passivity,feedback passification and global robust stabilisation for switched non-linear systems with structural uncertainty,IET Control Theory Appl.,9(11):1723-1730,2015.
[24]H.B.Pang,J.Zhao,Adaptive passification and stabilization for switched nonlinearly parameterized systems,Int.J.Robust Nonlin.Control,27:1147-1170,2017.
[25]Y.Y.Liu,G.S.Stojanovski,M.J.Stankovski,G.M.Dimirovski and J.Zhao,Feedback passification of switched nonlinear systems using storage-like functions,Int.J.Control,Autom.Syst.9(5):980-986,2011.
[26]H.B.Jiang,Hybrid adaptive and impulsive synchronisation of uncertain complex dynamical networks by the generalised Barbalat‘s lemma,IET Control Theory Appl.,3(10),1330-1340,2009.
[2]R.C.Ma,J.Zhao,Backstepping design for global stabilization of switched nonlinear systems in lower triangular form under arbitrary switchings,Automatica,46(11):1819-1823,2010.
[3]B.Niu,J.Zhao,Barrier Lyapunov functions for the output tracking control of constrained nonlinear switched systems,Syst.Control Lett.,62(10):963-971,2013.
[4]J.P.Hespanha,A,S.Morse,Stability of switched systems with average dwell-time,in Proceedings of the 38rd IEEE Conference on Decision and Control,1999:2655-2660.
[5]D.Liberzon,Switching in Systems and Control,Boston:Birkhauser,2003.
[6]B.Niu,H.R.Karimi,H.Q.Wang,and Y.L.Liu,Adaptive output-feedback controller design for switched nonlinear stochastic systems with a modified average dwell-time method,IEEE Trans.Syst.,Man,Cybern.B,Cybern.,DOI:10.1109/TSMC.2016.2597305.
[7]L.X.Zhang,P.Shi,Stability,L2-gain and asynchronous H∞control of discrete-time switched systems with average dwell time,IEEE Trans.Autom.Control,54(9):2193-2200,2009.
[8]Y.E.Wang,X.M.Sun,and F.Mazenc,Stability of switched nonlinear systems with delay and disturbance,Automatica,69(C):78-86,2016.
[9]X.D.Zhao,P.Shi,Y.F.Yin and S.K.Nguang,New results on stability of slowly switched systems:a multiple discontinuous Lyapunov function approach,IEEE Trans.Autom.Control,DOI 10.1109/TAC.2016.2614911.
[10]L.L.Long,J.Zhao,An integral-type multiple Lyapunov functions approach for switched nonlinear systems,IEEE Trans.Automat.Control,61(7):1979-1986,2016.
[11]J.Zhao D.J.Hill,On stability L2-gain and H∞control for switched systems,Automatica,44(5):1220-1232,2008.
[12]J.C.Willems,Dissipative dynamical systems,Eur.J.Control,13(2-3):134-151,2007.
[13]D.J.Hill,P.J.Moylan,The stability of nonlinear dissipative systems,IEEE Trans.Autom.Control,21(5):708-711,1976.
[14]T.Rajpurohit,W.M.Haddad,Dissipativity theory for nonlinear stochastic dynamical systems:input-output and state properties,and stability of feedback interconnections,IEEE Trans.Autom.Control,DOI 10.1109/TAC.2016.2598474.
[15]Z.J.Wu,H.R.Karimi and P.Shi,Dissipativity-based smallgain theorems for stochastic network systems,IEEE Trans.Autom.Control,61(8):2065-2077,2016.
[16]C.I.Byrnes,A.Isidori and J.C.Willems,Passivity,feedback equivalence,and the global stabilization of minimum phase nonlinear systems,IEEE Trans.Autom.Control,36(11):1228-1240,1991.
[17]W.Lin,T.L.Shen,Robust passivity and feedback design for minimum-phase nonlinear systems with structural uncertainty,Automatica,35(1):35-47,1999.
[18]Z.P.Jiang,D.J.Hill and A.L.Fradkov,A passification approach to adaptive nonlinear stabilization,Syst.Control Lett.,28(2):73-84,1996.
[19]C.S.Li,J.Zhao,Robust passivity-based H∞control for uncertain switched nonlinear systems,Int.J.Robust Nonlin.Control,26(24):3186-3206,2016.
[20]L.G.Wu,W.X.Zheng ang H.J.Gao,Dissipativity-based sliding mode control of switched stochastic systems,IEEE Trans.Autom.Control,58(3):785-791,2013.
[21]J.Zhao,D.J.Hill,Dissipativity theory for switched systems,IEEE Trans.Autom.Control,53(4):941-953,2008.
[22]A.Bemporad,G.Bianchini and F.Brogi,Passivity analysis and passification of discrete-time hybrid systems[J],IEEE Trans.Autom.Control,53(4):1004-1009,2008.
[23]H.B.Pang,J.Zhao,Robust passivity,feedback passification and global robust stabilisation for switched non-linear systems with structural uncertainty,IET Control Theory Appl.,9(11):1723-1730,2015.
[24]H.B.Pang,J.Zhao,Adaptive passification and stabilization for switched nonlinearly parameterized systems,Int.J.Robust Nonlin.Control,27:1147-1170,2017.
[25]Y.Y.Liu,G.S.Stojanovski,M.J.Stankovski,G.M.Dimirovski and J.Zhao,Feedback passification of switched nonlinear systems using storage-like functions,Int.J.Control,Autom.Syst.9(5):980-986,2011.
[26]H.B.Jiang,Hybrid adaptive and impulsive synchronisation of uncertain complex dynamical networks by the generalised Barbalat‘s lemma,IET Control Theory Appl.,3(10),1330-1340,2009.