Multi-Rate Sampled-Data Control for a Class of Nonlinear Systems via Input-Lyapunov Matching
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- 英文论文题名：Multi-Rate Sampled-Data Control for a Class of Nonlinear Systems via Input-Lyapunov Matching
- 论文作者：Jinping Jia ; Weisheng Chen ; Hao Dai
- 英文论文作者：Jinping Jia ; Weisheng Chen ; Hao Dai ; School of Mathematics and Statistics ; Xidian University ; School of Aerospace Science and Technology ; Xidian University
- 年：2017
- 作者机构：School of Mathematics and Statistics,Xidian University;School of Aerospace Science and Technology,Xidian University;
- 英文论文关键词：Multi-Rate Sampling ; Nonlinear System ; Sampled-Data System ; Input-Lyapunov Matching
- 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：4
- 文件大小：196k
- 原文格式：D
- 会议级别：全国
摘要
This paper studies the sampled-data control problem for a class of nonlinear systems. A multi-rate digital controller is designed by combining the input-Lyapunov matching approach and the multi-rate approach. The proposed control scheme ensures the stability of the closed-loop sampled-data system. Compared with emulated strategies, our controller has the form of series in power of sampling period, and preserves the stabilization property of the continuous-time controller at the sampling instants. These advantages will produce better control performance.
This paper studies the sampled-data control problem for a class of nonlinear systems. A multi-rate digital controller is designed by combining the input-Lyapunov matching approach and the multi-rate approach. The proposed control scheme ensures the stability of the closed-loop sampled-data system. Compared with emulated strategies, our controller has the form of series in power of sampling period, and preserves the stabilization property of the continuous-time controller at the sampling instants. These advantages will produce better control performance.
This paper studies the sampled-data control problem for a class of nonlinear systems. A multi-rate digital controller is designed by combining the input-Lyapunov matching approach and the multi-rate approach. The proposed control scheme ensures the stability of the closed-loop sampled-data system. Compared with emulated strategies, our controller has the form of series in power of sampling period, and preserves the stabilization property of the continuous-time controller at the sampling instants. These advantages will produce better control performance.
引文
[1]W.Lin and C.J.Qian,Adding one power integrator:a tool for global stabilization of high-order lower-triangular systems,Systems Control Letters,39(5):39-351,2000.
[2]W.Lin and C.J.Qian,Robust regulation of a chain of power integrators perturbed by a lower-triangular vector field,Internat.J.Robust Nonlinear Control,10(5):397-421,2000.
[3]W.Lin and C.J.Qian,Adaptive regulation of high-order lower-triangular systems:an adding a power integrator technique,Systems Control Lett.,39(5):353-364,2000.
[4]W.Lin and C.J.Qian,Recursive observer design,homogeneous approximation,and nonsmooth output feedback stabilization of nonlinear systems,IEEE Transactions on Automatic Control,51:1457-1471:2006.
[5]J.Back,S.G.Cheong,H.Shim and J.H.Seo,Nonsmooth feedback stabilizer for strict-feedback nonlinear systems that may not be linearizable at the origin,Systems Control Letters,56(11-12):742-752,2007.
[6]X.J.Xie and J.Tian,Adaptive state-feedback stabilization of high-order stochastic systems with nonlinear parameterization,Automatica,45(1):126-133,2009.
[7]X.J.Xie,N.Duan and X.Yu,State-feedback control of highorder stochastic nonlinear systems with Si ISS inverse dynamics,IEEE Transactions on Automatic Control,56(8):1921-2011,2011.
[8]C.L.Wang and Y.Lin,Decentralized adaptive tracking control for a class of interconnected nonlinear time-varying systems,Automatica,54:16-24,2015.
[9]Z.Y.Sun,X.H.Zhang and X.J.Xie,Global continuous output-feedback stabilization for a class of high-order nonlinear systems with multiple time delays,Journal of the Franklin Institute,351,4334-4356.(2014).
[10]Z.Y.Sun,T.Li and S.H.Yang,A unified time-varying feedback approach and its applications in adaptive stabilization of high-order uncertain nonlinear systems,Automatica,70:249-257,2016.
[11]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,Automatica,54:360-373,2015.
[12]W.T.Zha,C.J.Qian,J.Y.Zhai and S.M.Fei,Robust control for a class of nonlinear systems with unknown measurement drifts,Automatica,71:33-37,2016.
[13]D.Neˇsi,A.R.Teel and D.Carnevale,Explicit computation of the sampling period in emulation of controllers for nonlinear sampled-data systems,IEEE Transactions on Automatic Control,54(3):619-624,2009.
[14]H.Omran,L.Hetel,M.Petreczky,J.P.Richard and F.Lamnabhi-Lagarrigue,Stability analysis of some classes of input-affine nonlinear systems with aperiodic sampled-data control,Automatica,70:266-274,2016.
[15]B.D.O.Anderson,Controller design:moving from theory to practice,IEEE Control Systems,13(4):16-25,1993.
[16]D.Neˇsi and A.R.Teel,Stabilization of sampled-data nonlinear systems via backstepping on their Euler approximate model,Automatica,42(10):1801-1808,2006.
[17]R.Postoyan,T.Ahmed-Ali and F.Lamnabhi-Lagarrigue,Robust backstepping for the Euler approximate model of sampled-data strict-feedback systems,Automatica,45(9):2164-2168,2009.
[18]S.Monaco and D.Normand-Cyrot,Issues on nonlinear digital systems,European Journal of Control,7(2):160-177,2001.
[19]D.Neˇsi,A.R.Teel and P.V.Kokotovic,Sufficient conditions for stabilization of sampled-data noninear systems via discrete-time approximations,Systems Control Letters,38(4-5):259-270,1999.
[20]D.Neˇsi and L.Grüne,Lyapunov based continuous-time controller redesign for sampled-data implementation,Automatica,41(7):1143-1156,2005.
[21]L.Burlion,T.Ahmed-Ali and F.Lamnabhi-Lagarrigue,On the stabilization of sampled-data non-linear systems by using backstepping on the higher order approximate models,Internat.J.Control,79(9):1087-1095,2006.
[22]V.Tanasa,S.Monaco and D.Normand-Cyrot,Backstepping control under multi-rate sampling,IEEE Transactions on Automatic Control,61(5):1208-1222,2016.
[23]W.Grobner and H.Knapp,Contributions to the method of lie series.Bibliographisches Insititut,1967.
[24]S.Monaco,D.Normand-Cyrot and C.Califano,From chronological calculus to exponential representations of continuous and discrete-time dynamics:a Lie-Algebraic approach,IEEE Transactions on Automatic Control,52(12):2227-2241,2007.
[25]D.Neˇsi,A.R.Teel and E.D.Sontag,Formulas relating KL stability estimates of discrete-time and sampled-data nonlinear sampled-data systems,IEEE Transactions on Automatic Control,54(3):619-624,1999.
[2]W.Lin and C.J.Qian,Robust regulation of a chain of power integrators perturbed by a lower-triangular vector field,Internat.J.Robust Nonlinear Control,10(5):397-421,2000.
[3]W.Lin and C.J.Qian,Adaptive regulation of high-order lower-triangular systems:an adding a power integrator technique,Systems Control Lett.,39(5):353-364,2000.
[4]W.Lin and C.J.Qian,Recursive observer design,homogeneous approximation,and nonsmooth output feedback stabilization of nonlinear systems,IEEE Transactions on Automatic Control,51:1457-1471:2006.
[5]J.Back,S.G.Cheong,H.Shim and J.H.Seo,Nonsmooth feedback stabilizer for strict-feedback nonlinear systems that may not be linearizable at the origin,Systems Control Letters,56(11-12):742-752,2007.
[6]X.J.Xie and J.Tian,Adaptive state-feedback stabilization of high-order stochastic systems with nonlinear parameterization,Automatica,45(1):126-133,2009.
[7]X.J.Xie,N.Duan and X.Yu,State-feedback control of highorder stochastic nonlinear systems with Si ISS inverse dynamics,IEEE Transactions on Automatic Control,56(8):1921-2011,2011.
[8]C.L.Wang and Y.Lin,Decentralized adaptive tracking control for a class of interconnected nonlinear time-varying systems,Automatica,54:16-24,2015.
[9]Z.Y.Sun,X.H.Zhang and X.J.Xie,Global continuous output-feedback stabilization for a class of high-order nonlinear systems with multiple time delays,Journal of the Franklin Institute,351,4334-4356.(2014).
[10]Z.Y.Sun,T.Li and S.H.Yang,A unified time-varying feedback approach and its applications in adaptive stabilization of high-order uncertain nonlinear systems,Automatica,70:249-257,2016.
[11]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,Automatica,54:360-373,2015.
[12]W.T.Zha,C.J.Qian,J.Y.Zhai and S.M.Fei,Robust control for a class of nonlinear systems with unknown measurement drifts,Automatica,71:33-37,2016.
[13]D.Neˇsi,A.R.Teel and D.Carnevale,Explicit computation of the sampling period in emulation of controllers for nonlinear sampled-data systems,IEEE Transactions on Automatic Control,54(3):619-624,2009.
[14]H.Omran,L.Hetel,M.Petreczky,J.P.Richard and F.Lamnabhi-Lagarrigue,Stability analysis of some classes of input-affine nonlinear systems with aperiodic sampled-data control,Automatica,70:266-274,2016.
[15]B.D.O.Anderson,Controller design:moving from theory to practice,IEEE Control Systems,13(4):16-25,1993.
[16]D.Neˇsi and A.R.Teel,Stabilization of sampled-data nonlinear systems via backstepping on their Euler approximate model,Automatica,42(10):1801-1808,2006.
[17]R.Postoyan,T.Ahmed-Ali and F.Lamnabhi-Lagarrigue,Robust backstepping for the Euler approximate model of sampled-data strict-feedback systems,Automatica,45(9):2164-2168,2009.
[18]S.Monaco and D.Normand-Cyrot,Issues on nonlinear digital systems,European Journal of Control,7(2):160-177,2001.
[19]D.Neˇsi,A.R.Teel and P.V.Kokotovic,Sufficient conditions for stabilization of sampled-data noninear systems via discrete-time approximations,Systems Control Letters,38(4-5):259-270,1999.
[20]D.Neˇsi and L.Grüne,Lyapunov based continuous-time controller redesign for sampled-data implementation,Automatica,41(7):1143-1156,2005.
[21]L.Burlion,T.Ahmed-Ali and F.Lamnabhi-Lagarrigue,On the stabilization of sampled-data non-linear systems by using backstepping on the higher order approximate models,Internat.J.Control,79(9):1087-1095,2006.
[22]V.Tanasa,S.Monaco and D.Normand-Cyrot,Backstepping control under multi-rate sampling,IEEE Transactions on Automatic Control,61(5):1208-1222,2016.
[23]W.Grobner and H.Knapp,Contributions to the method of lie series.Bibliographisches Insititut,1967.
[24]S.Monaco,D.Normand-Cyrot and C.Califano,From chronological calculus to exponential representations of continuous and discrete-time dynamics:a Lie-Algebraic approach,IEEE Transactions on Automatic Control,52(12):2227-2241,2007.
[25]D.Neˇsi,A.R.Teel and E.D.Sontag,Formulas relating KL stability estimates of discrete-time and sampled-data nonlinear sampled-data systems,IEEE Transactions on Automatic Control,54(3):619-624,1999.