Gain Scheduled Control for Linear Differential Inclusions Subject to Constraint Input
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- 英文论文题名：Gain Scheduled Control for Linear Differential Inclusions Subject to Constraint Input
- 论文作者：Pengyuan Li ; Yuhu Wu ; Xi-Ming Sun ; Wei Wang
- 英文论文作者：Pengyuan Li ; Yuhu Wu ; Xi-Ming Sun ; Wei Wang ; Dalian University of Technology
- 年：2017
- 作者机构：Dalian University of Technology;
- 英文论文关键词：Actuator Saturation ; Gain Scheduled Controller ; Linear Differential Inclusion ; Robust Control
- 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：347k
- 原文格式：D
- 会议级别：全国
摘要
This paper is concerned with the problem of robust stabilization of linear differential inclusions(LDIs) subject to actuator saturation. A family of continuous controllers based on a parameter-dependent quadratic Lyapunov function(LF)are designed for a given worst-case disturbance while complying the saturation bounds. Based on the closed-loop behavior,the controller is selected such that the system has the best performance at each time. The internal stability and guaranteed performance can be obtained simultaneously through the dynamic gain scheduled control law. The benefit of the proposed scheme is presented via a numerical example.
This paper is concerned with the problem of robust stabilization of linear differential inclusions(LDIs) subject to actuator saturation. A family of continuous controllers based on a parameter-dependent quadratic Lyapunov function(LF)are designed for a given worst-case disturbance while complying the saturation bounds. Based on the closed-loop behavior,the controller is selected such that the system has the best performance at each time. The internal stability and guaranteed performance can be obtained simultaneously through the dynamic gain scheduled control law. The benefit of the proposed scheme is presented via a numerical example.
This paper is concerned with the problem of robust stabilization of linear differential inclusions(LDIs) subject to actuator saturation. A family of continuous controllers based on a parameter-dependent quadratic Lyapunov function(LF)are designed for a given worst-case disturbance while complying the saturation bounds. Based on the closed-loop behavior,the controller is selected such that the system has the best performance at each time. The internal stability and guaranteed performance can be obtained simultaneously through the dynamic gain scheduled control law. The benefit of the proposed scheme is presented via a numerical example.
引文
[1]G.V.Smirnov,Introduction to the theory of differential inclusions.American Mathematical Soc.,2002,vol.41.
[2]R.Goebel,A.R.Teel,T.Hu,and Z.Lin,“Conjugate convex lyapunov functions for dual linear differential inclusions,”IEEE Transactions on Automatic Control,vol.51,no.4,pp.661–666,2006.
[3]Y.Wu and T.Shen,“Reach control problem for linear differential inclusion systems on simplices,”IEEE Transactions on Automatic Control,vol.61,no.5,pp.1403–1408,2016.
[4]S.P.Boyd,L.El Ghaoui,E.Feron,and V.Balakrishnan,Linear matrix inequalities in system and control theory.SIAM,1994,vol.15.
[5]A.R.Teel,“Semi-global stabilizability of linear null controllable systems with input nonlinearities,”IEEE Transactions on Automatic Control,vol.40,no.1,pp.96–100,1995.
[6]T.Hu,Z.Lin,and B.M.Chen,“An analysis and design method for linear systems subject to actuator saturation and disturbance,”Automatica,vol.38,no.2,pp.351–359,2002.
[7]B.M.Chen,T.H.Lee,K.Peng,and V.Venkataramanan,“Composite nonlinear feedback control for linear systems with input saturation:theory and an application,”IEEE Transactions on Automatic Control,vol.48,no.3,pp.427–439,2003.
[8]˙I.Kse and F.Jabbari,“Control of systems with actuator amplitude and rate constraints,”in Proceedings of the 2001American Control Conference,2001,vol.6.IEEE,2001,pp.4914–4919.
[9]S.Sajjadi-Kia and F.Jabbari,“Controllers for linear systems with bounded actuators:Slab scheduling and anti-windup,”Automatica,vol.49,no.3,pp.762–769,2013.
[10]B.Zhou,W.X.Zheng,and G.-R.Duan,“An improved treatment of saturation nonlinearity with its application to control of systems subject to nested saturation,”Automatica,vol.47,no.2,pp.306–315,2011.
[11]Y.-F.Gao,X.-M.Sun,C.Wen,and W.Wang,“Adaptive tracking control for a class of stochastic uncertain nonlinear systems with input saturation,”IEEE Transactions on Automatic Control,2016.
[12]B.Zhou,Q.Wang,Z.Lin,and G.-R.Duan,“Gain scheduled control of linear systems subject to actuator saturation with application to spacecraft rendezvous,”IEEE Transactions on Control Systems Technology,vol.22,no.5,pp.2031–2038,2014.
[13]I.E.K Se and F.Jabbari,“Scheduled controllers for linear systems with bounded actuators,”Automatica,vol.39,no.8,pp.1377–1387,2003.
[14]S.Sajjadi-Kia and F.Jabbari,“Multi-stage anti-windup compensation for open-loop stable plants,”IEEE Transactions on Automatic Control,vol.56,no.9,pp.2166–2172,2011.
[15]A.Megretski,“L2 bibo output feedback stabilization with saturated control,”in Proc.13th IFAC world congress,vol.500.Citeseer,1996,pp.435–440.
[16]Z.Lin and A.Saberi,“Semi-global exponential stabilization of linear systems subject to input saturation via linear feedbacks,”Systems&Control Letters,vol.21,no.3,pp.225–239,1993.
[17]Z.Lin,Low gain feedback.springer London,1999.
[18]B.Zhou,G.Duan,and Z.Lin,“A parametric lyapunov equation approach to the design of low gain feedback,”IEEE Transactions on Automatic Control,vol.53,no.6,pp.1548–1554,2008.
[19]Z.Lin,A.A.Stoorvogel,and A.A.Saberi,“Output regulation for linear systems subject to input saturation,”Automatica,vol.32,no.1,p.29,1996.
[20]X.Cai,L.Liu,and W.Zhang,“Saturated control design for linear differential inclusions subject to disturbance,”Nonlinear Dynamics,vol.58,no.3,pp.487–496,2009.
[21]I.Masubuchi,A.Kume,and E.Shimemura,“Spline-type solution to parameter-dependent lmis,”in Proceedings of the37th IEEE Conference on Decision and Control,1998,vol.2.IEEE,1998,pp.1753–1758.
[2]R.Goebel,A.R.Teel,T.Hu,and Z.Lin,“Conjugate convex lyapunov functions for dual linear differential inclusions,”IEEE Transactions on Automatic Control,vol.51,no.4,pp.661–666,2006.
[3]Y.Wu and T.Shen,“Reach control problem for linear differential inclusion systems on simplices,”IEEE Transactions on Automatic Control,vol.61,no.5,pp.1403–1408,2016.
[4]S.P.Boyd,L.El Ghaoui,E.Feron,and V.Balakrishnan,Linear matrix inequalities in system and control theory.SIAM,1994,vol.15.
[5]A.R.Teel,“Semi-global stabilizability of linear null controllable systems with input nonlinearities,”IEEE Transactions on Automatic Control,vol.40,no.1,pp.96–100,1995.
[6]T.Hu,Z.Lin,and B.M.Chen,“An analysis and design method for linear systems subject to actuator saturation and disturbance,”Automatica,vol.38,no.2,pp.351–359,2002.
[7]B.M.Chen,T.H.Lee,K.Peng,and V.Venkataramanan,“Composite nonlinear feedback control for linear systems with input saturation:theory and an application,”IEEE Transactions on Automatic Control,vol.48,no.3,pp.427–439,2003.
[8]˙I.Kse and F.Jabbari,“Control of systems with actuator amplitude and rate constraints,”in Proceedings of the 2001American Control Conference,2001,vol.6.IEEE,2001,pp.4914–4919.
[9]S.Sajjadi-Kia and F.Jabbari,“Controllers for linear systems with bounded actuators:Slab scheduling and anti-windup,”Automatica,vol.49,no.3,pp.762–769,2013.
[10]B.Zhou,W.X.Zheng,and G.-R.Duan,“An improved treatment of saturation nonlinearity with its application to control of systems subject to nested saturation,”Automatica,vol.47,no.2,pp.306–315,2011.
[11]Y.-F.Gao,X.-M.Sun,C.Wen,and W.Wang,“Adaptive tracking control for a class of stochastic uncertain nonlinear systems with input saturation,”IEEE Transactions on Automatic Control,2016.
[12]B.Zhou,Q.Wang,Z.Lin,and G.-R.Duan,“Gain scheduled control of linear systems subject to actuator saturation with application to spacecraft rendezvous,”IEEE Transactions on Control Systems Technology,vol.22,no.5,pp.2031–2038,2014.
[13]I.E.K Se and F.Jabbari,“Scheduled controllers for linear systems with bounded actuators,”Automatica,vol.39,no.8,pp.1377–1387,2003.
[14]S.Sajjadi-Kia and F.Jabbari,“Multi-stage anti-windup compensation for open-loop stable plants,”IEEE Transactions on Automatic Control,vol.56,no.9,pp.2166–2172,2011.
[15]A.Megretski,“L2 bibo output feedback stabilization with saturated control,”in Proc.13th IFAC world congress,vol.500.Citeseer,1996,pp.435–440.
[16]Z.Lin and A.Saberi,“Semi-global exponential stabilization of linear systems subject to input saturation via linear feedbacks,”Systems&Control Letters,vol.21,no.3,pp.225–239,1993.
[17]Z.Lin,Low gain feedback.springer London,1999.
[18]B.Zhou,G.Duan,and Z.Lin,“A parametric lyapunov equation approach to the design of low gain feedback,”IEEE Transactions on Automatic Control,vol.53,no.6,pp.1548–1554,2008.
[19]Z.Lin,A.A.Stoorvogel,and A.A.Saberi,“Output regulation for linear systems subject to input saturation,”Automatica,vol.32,no.1,p.29,1996.
[20]X.Cai,L.Liu,and W.Zhang,“Saturated control design for linear differential inclusions subject to disturbance,”Nonlinear Dynamics,vol.58,no.3,pp.487–496,2009.
[21]I.Masubuchi,A.Kume,and E.Shimemura,“Spline-type solution to parameter-dependent lmis,”in Proceedings of the37th IEEE Conference on Decision and Control,1998,vol.2.IEEE,1998,pp.1753–1758.