Finite-Time Stabilization of Stochastic Nonlinear Systems in p-Normal Form
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- 英文论文题名：Finite-Time Stabilization of Stochastic Nonlinear Systems in p-Normal Form
- 论文作者：Fangzheng Gao ; Yuqiang Wu
- 英文论文作者：Fangzheng Gao ; Yuqiang Wu ; School of Mathematics and Statistics ; Anyang Normal University ; School of Automation ; Southeast University ; Institute of Automation ; Qufu Normal University
- 年：2017
- 作者机构：School of Mathematics and Statistics,Anyang Normal University;School of Automation,Southeast University;Institute of Automation,Qufu Normal University;
- 英文论文关键词：Stochastic Nonlinear Systems ; p-Normal Form ; State Feedback ; Finite-Time Stabilization
- 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：260k
- 原文格式：D
- 会议级别：全国
摘要
This paper investigates the problem of finite-time stabilization for a class of stochastic nonlinear systems in p-normal form. Different from the existing results, the considered systems are allowed to have the powers of both odd and even rational numbers. By delicately combining sign function with adding a power integrator technique, a continuous state feedback controller is presented to guarantee that the closed-loop system is finite-time stable in probability. Simulation results of a liquid-level system are provided to show the effectiveness and applicability of the proposed method.
This paper investigates the problem of finite-time stabilization for a class of stochastic nonlinear systems in p-normal form. Different from the existing results, the considered systems are allowed to have the powers of both odd and even rational numbers. By delicately combining sign function with adding a power integrator technique, a continuous state feedback controller is presented to guarantee that the closed-loop system is finite-time stable in probability. Simulation results of a liquid-level system are provided to show the effectiveness and applicability of the proposed method.
This paper investigates the problem of finite-time stabilization for a class of stochastic nonlinear systems in p-normal form. Different from the existing results, the considered systems are allowed to have the powers of both odd and even rational numbers. By delicately combining sign function with adding a power integrator technique, a continuous state feedback controller is presented to guarantee that the closed-loop system is finite-time stable in probability. Simulation results of a liquid-level system are provided to show the effectiveness and applicability of the proposed method.
引文
[1]P.Florchinger.Lyapunov-like techniques for stochastic stability[J].SIAM J.Control Optim.1995,33(4):1151-1169.
[2]H.Deng and M.Krsti.Stochastic nonlinear stabilization-I:A backstepping design[J].Syst.Control Lett.,1997,32(3):143-150.
[3]Z.Pan and T.Basar.Backstepping controller design for nonlinear stochastic systems under a risksensitive cost criterion[J].SIAM J.Control Optim.1999,37(3):97-995.
[4]H.Deng and M.Krsti,R.J.Williams.Stabilization of stochastic nonlinear driven by noise of unknown covariance[J].IEEE Trans.Autom.Control,2001,46(8):1237-1253.
[5]Y.Liu,Z.Pan,and S.Shi.Output feedback control design for strict-feedback stochastic nonlinear systems under a risksensitive cost[J].IEEE Trans.Autom.Control,2003,48:509-514.
[6]S.Liu,Z.Jiang,and J.Zhang.Global output-feedback stabilization for a class of stochastic non-minimum-phase nonlinear systems[J].Automatica,2008,44(8):1944-1957.
[7]X.Yu and X.Xie.Output feedback regulation of stochastic nonlinear systems with stochastic i ISS inverse dynamics[J].IEEE Trans.Autom.Control,2010,55(2):304-320.
[8]W.Li,X.Xie,and S.Zhang.Output feeback stabilization of stochastic high-order nonlinear systems under weaker conditions[J].SIAM J.Control Optim.,2011,49:1262-1282.
[9]L.Liu and X.Xie.Output-feedback stabilization for stochastic high-order nonlinear systems with time-varying delay[J].Automatica,2011,47(12):2772-2779.
[10]X.Xie,N.Duan,and C.Zhao.A combined homogeneous domination and sign function approach to output-feedback stabilization of stochastic high-order nonlinear systems[J].IEEE Trans.Autom.Control,2014,59(5):1303-1309.
[11]C.Zhao and X.Xie.Global stabilization of stochastic highorder feedforward nonlinear systems with time-varying delay[J].Automatica,2014,50(11):203-210.
[12]S.Bhat and D.Bernstein.Finite-time stability of continuous autonomous systems[J].SIAM J.Control Optim.,2000,38(3):751-766.
[13]X.Huang,W.Lin and B.Yang.Global finite-time stabilization of a class of uncertain nonlinear systems[J].Automatica,2005,41:881-888.
[14]Y.Hong and Z.Jiang.Finite-time stabilization of nonlinear systems with parametric and dynamic uncertainties[J].IEEE Trans.Autom.Control,2006,51(12):1950-1956..
[15]Z.Sun,L.Xue,and K.Zhang.A new approach to finitetime adaptive stabilization of high-order uncertain nonlinear system[J].Automatica,2015,58:60-66.
[16]J.Li,C.Qian,and S.Ding.Global finite-time stabilisation by output feedback for a class of uncertain nonlinear systems[J].Int.J.Control,2010,83(11):2241-2252.
[17]X.Zhang,G.Feng,and Y.Sun.Finite-time stabilization by state feedback control for a class of time-varying nonlinear systems[J].Automatica,2012,48(3):499-504.
[18]Y.Liu.Global finite-time stabilization via time-varying feedback for uncertain nonlinear systems[J].SIAM J.Control Optim.,2014,52(3):1886-1913.
[19]J.Fu,R.Ma,and T.Chai.Global finite-time stabilization of a class of switched nonlinear systems with the powers of positive odd rational numbers[J].Automatica,2015,54:360-373.
[20]F.Gao and Y.Wu.Global state feedback stabilisation for a class of more general high-order non-linear systems[J].IET Control Theory Appl.,2014,8(16):1648-1655.
[21]F.Gao,Y.Wu,and C.Zhang.Finite-time stabilization of uncertain nonholonomic systems in feedforward-like form by output feedback[J].ISA Trans.,2015,59:125-132.
[22]Y.Wu,F.Gao,and Z.Liu.Finite-time state feedback stabilization of nonholonomic systems with low-order nonlinearities[J].IET Control Theory Appl.,2015,9(10):1553-1560.
[23]J.Yin,S.Khoo,Z.Man,and X.Yu.Finite-time stability and instability of stochastic nonlinear systems[J].Automatica,2011,47:2671-2677.
[24]S.Khoo,J.Yin,Z.Man,and X.Yu.Finite-time stabilization of stochastic nonlinear systems in strict-feedback form[J].Automatica,2013,49(5):1403-1410.
[25]J.Yin and S.Khoo.Continuous finite-time state feedback stabilizers for some nonlinear stochastic systems[J].Int.J.Robust Nonlinear Control,2015,25(11):1581-1600.
[26]W.Zha,J.Zhai,S.Fei,and Y.Wang.Finite-time stabilization for a class of stochastic nonlinear systems via output feedback[J].ISA Trans.,2014,53(3):709-716.
[27]H.Wang and Q.Zhu.Finite-time stabilization of high-order stochastic nonlinear systems in strict-feedback form[J].Automatica,2015,54:284-291.
[28]W.Zha,J.Zhai,W.Ai,and S.Fei.Finite-time state-feedback control for a class of stochastic high-order nonlinear systems[J].Int.J.Comput.Math.,2015,92(3):643-660.
[29]Q.Lan,S.Li,S.Khoo,and P.Shi.Global finite-time stabilization for a class of stochastic nonlinear systems by output feedback[J].Int.J.Control,2015 88(3):494-506.
[30]F.Gao,Y.Wu,and X.Yu.Global state feedback stabilisation of stochastic high-order nonlinear systems with high-order and low-order nonlinearities[J].Int.J.Syst.Sci.,2016,47(16):3846-3856.
[31]F.Gao and Y.Wu.Global finite-time stabilisation for a class of stochastic high order time-varying nonlinear systems[J].Int.J.Control,2016,89(12):2453-2465.
[32]L.Liu,S.Xu,and Y.Zhang.Finite-time output feedback control for a class of stochastic low-order nonlinear systems[J].Int.J.Control,2016,DOI:10.1080/00207179.2016.1209563.
[33]C.Qian and W.Lin.A continuous feedback approach to global strong stabilization of nonlinear systems[J].IEEE Trans.Autom.Control,2001,46(7):1061-1079.
[34]S.Ding,S.Li,and X.Zheng.Nonsmooth stabilization of a class of nonlinear cascaded systems[J].Automatica,2012,48(10):2597-2606.
[35]H.K.Khalil.Nonlinear Systems[M].NJ:Prentice-Hall,2002.
[36]F.Gao,Y.Wu and Z.Zhang.Global fixed-time stabilization of a class of switched nonlinear systems in p-normal form[J].Automatica,2016,submitted.
[2]H.Deng and M.Krsti.Stochastic nonlinear stabilization-I:A backstepping design[J].Syst.Control Lett.,1997,32(3):143-150.
[3]Z.Pan and T.Basar.Backstepping controller design for nonlinear stochastic systems under a risksensitive cost criterion[J].SIAM J.Control Optim.1999,37(3):97-995.
[4]H.Deng and M.Krsti,R.J.Williams.Stabilization of stochastic nonlinear driven by noise of unknown covariance[J].IEEE Trans.Autom.Control,2001,46(8):1237-1253.
[5]Y.Liu,Z.Pan,and S.Shi.Output feedback control design for strict-feedback stochastic nonlinear systems under a risksensitive cost[J].IEEE Trans.Autom.Control,2003,48:509-514.
[6]S.Liu,Z.Jiang,and J.Zhang.Global output-feedback stabilization for a class of stochastic non-minimum-phase nonlinear systems[J].Automatica,2008,44(8):1944-1957.
[7]X.Yu and X.Xie.Output feedback regulation of stochastic nonlinear systems with stochastic i ISS inverse dynamics[J].IEEE Trans.Autom.Control,2010,55(2):304-320.
[8]W.Li,X.Xie,and S.Zhang.Output feeback stabilization of stochastic high-order nonlinear systems under weaker conditions[J].SIAM J.Control Optim.,2011,49:1262-1282.
[9]L.Liu and X.Xie.Output-feedback stabilization for stochastic high-order nonlinear systems with time-varying delay[J].Automatica,2011,47(12):2772-2779.
[10]X.Xie,N.Duan,and C.Zhao.A combined homogeneous domination and sign function approach to output-feedback stabilization of stochastic high-order nonlinear systems[J].IEEE Trans.Autom.Control,2014,59(5):1303-1309.
[11]C.Zhao and X.Xie.Global stabilization of stochastic highorder feedforward nonlinear systems with time-varying delay[J].Automatica,2014,50(11):203-210.
[12]S.Bhat and D.Bernstein.Finite-time stability of continuous autonomous systems[J].SIAM J.Control Optim.,2000,38(3):751-766.
[13]X.Huang,W.Lin and B.Yang.Global finite-time stabilization of a class of uncertain nonlinear systems[J].Automatica,2005,41:881-888.
[14]Y.Hong and Z.Jiang.Finite-time stabilization of nonlinear systems with parametric and dynamic uncertainties[J].IEEE Trans.Autom.Control,2006,51(12):1950-1956..
[15]Z.Sun,L.Xue,and K.Zhang.A new approach to finitetime adaptive stabilization of high-order uncertain nonlinear system[J].Automatica,2015,58:60-66.
[16]J.Li,C.Qian,and S.Ding.Global finite-time stabilisation by output feedback for a class of uncertain nonlinear systems[J].Int.J.Control,2010,83(11):2241-2252.
[17]X.Zhang,G.Feng,and Y.Sun.Finite-time stabilization by state feedback control for a class of time-varying nonlinear systems[J].Automatica,2012,48(3):499-504.
[18]Y.Liu.Global finite-time stabilization via time-varying feedback for uncertain nonlinear systems[J].SIAM J.Control Optim.,2014,52(3):1886-1913.
[19]J.Fu,R.Ma,and T.Chai.Global finite-time stabilization of a class of switched nonlinear systems with the powers of positive odd rational numbers[J].Automatica,2015,54:360-373.
[20]F.Gao and Y.Wu.Global state feedback stabilisation for a class of more general high-order non-linear systems[J].IET Control Theory Appl.,2014,8(16):1648-1655.
[21]F.Gao,Y.Wu,and C.Zhang.Finite-time stabilization of uncertain nonholonomic systems in feedforward-like form by output feedback[J].ISA Trans.,2015,59:125-132.
[22]Y.Wu,F.Gao,and Z.Liu.Finite-time state feedback stabilization of nonholonomic systems with low-order nonlinearities[J].IET Control Theory Appl.,2015,9(10):1553-1560.
[23]J.Yin,S.Khoo,Z.Man,and X.Yu.Finite-time stability and instability of stochastic nonlinear systems[J].Automatica,2011,47:2671-2677.
[24]S.Khoo,J.Yin,Z.Man,and X.Yu.Finite-time stabilization of stochastic nonlinear systems in strict-feedback form[J].Automatica,2013,49(5):1403-1410.
[25]J.Yin and S.Khoo.Continuous finite-time state feedback stabilizers for some nonlinear stochastic systems[J].Int.J.Robust Nonlinear Control,2015,25(11):1581-1600.
[26]W.Zha,J.Zhai,S.Fei,and Y.Wang.Finite-time stabilization for a class of stochastic nonlinear systems via output feedback[J].ISA Trans.,2014,53(3):709-716.
[27]H.Wang and Q.Zhu.Finite-time stabilization of high-order stochastic nonlinear systems in strict-feedback form[J].Automatica,2015,54:284-291.
[28]W.Zha,J.Zhai,W.Ai,and S.Fei.Finite-time state-feedback control for a class of stochastic high-order nonlinear systems[J].Int.J.Comput.Math.,2015,92(3):643-660.
[29]Q.Lan,S.Li,S.Khoo,and P.Shi.Global finite-time stabilization for a class of stochastic nonlinear systems by output feedback[J].Int.J.Control,2015 88(3):494-506.
[30]F.Gao,Y.Wu,and X.Yu.Global state feedback stabilisation of stochastic high-order nonlinear systems with high-order and low-order nonlinearities[J].Int.J.Syst.Sci.,2016,47(16):3846-3856.
[31]F.Gao and Y.Wu.Global finite-time stabilisation for a class of stochastic high order time-varying nonlinear systems[J].Int.J.Control,2016,89(12):2453-2465.
[32]L.Liu,S.Xu,and Y.Zhang.Finite-time output feedback control for a class of stochastic low-order nonlinear systems[J].Int.J.Control,2016,DOI:10.1080/00207179.2016.1209563.
[33]C.Qian and W.Lin.A continuous feedback approach to global strong stabilization of nonlinear systems[J].IEEE Trans.Autom.Control,2001,46(7):1061-1079.
[34]S.Ding,S.Li,and X.Zheng.Nonsmooth stabilization of a class of nonlinear cascaded systems[J].Automatica,2012,48(10):2597-2606.
[35]H.K.Khalil.Nonlinear Systems[M].NJ:Prentice-Hall,2002.
[36]F.Gao,Y.Wu and Z.Zhang.Global fixed-time stabilization of a class of switched nonlinear systems in p-normal form[J].Automatica,2016,submitted.