Linear quadratic output feedback for LTI system with new LMI formulation
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- 英文论文题名：Linear quadratic output feedback for LTI system with new LMI formulation
- 论文作者：Wei He ; Bo Li ; Wei Xie ; Weilin Wu
- 英文论文作者：Wei He ; Bo Li ; Wei Xie ; Weilin Wu ; College of Automation Science and Technology ; South China University of Technology ; Guangdong Dowstone Technology Co. ; Ltd
- 年：2017
- 作者机构：College of Automation Science and Technology,South China University of Technology;Guangdong Dowstone Technology Co.,Ltd;
- 英文论文关键词：LTI systems ; Linear quadratic control ; output feedback ; Linear matrix inequalities
- 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：TP13
- 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：222k
- 原文格式：D
- 会议级别：全国
摘要
In this paper,linear quadratic control is considered for linear time invariant(LTI) systems with dynamic output feedback.Firstly,a new matrix inequality is presented for LTI systems with quadratic criterion and Lyapunov function.Secondly,nonlinear matrix inequality is transformed into linear matrix inequalities(LMIs) with the ideas of elimination.Consequently,the synthesis of linear quadratic output feedback is transformed into solving LMIs optimization problem.Finally,a numerical example is included to illustrate the effectiveness of the proposed approach.
In this paper,linear quadratic control is considered for linear time invariant(LTI) systems with dynamic output feedback.Firstly,a new matrix inequality is presented for LTI systems with quadratic criterion and Lyapunov function.Secondly,nonlinear matrix inequality is transformed into linear matrix inequalities(LMIs) with the ideas of elimination.Consequently,the synthesis of linear quadratic output feedback is transformed into solving LMIs optimization problem.Finally,a numerical example is included to illustrate the effectiveness of the proposed approach.
In this paper,linear quadratic control is considered for linear time invariant(LTI) systems with dynamic output feedback.Firstly,a new matrix inequality is presented for LTI systems with quadratic criterion and Lyapunov function.Secondly,nonlinear matrix inequality is transformed into linear matrix inequalities(LMIs) with the ideas of elimination.Consequently,the synthesis of linear quadratic output feedback is transformed into solving LMIs optimization problem.Finally,a numerical example is included to illustrate the effectiveness of the proposed approach.
引文
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[12]Duan G R,Yu H H.LMIs in Control Systems:Analysis,Design and Applications[M].CRC Press,2013.
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[17]Chen W,Zheng J,Qiu L.Linear quadratic optimal control of continuous-time LTI systems with random input gains[C]//Information and Automation(ICIA),2012International Conference on.IEEE,2012:241-246.
[18]Rotondo D,Puig V,Nejjari F.Linear quadratic control of LPV systems using static and shifting specifications[C].Control Conference(ECC),2015 European.IEEE,2015:3085-3090.
[19]Zhou X Y,Li D.Continuous-time mean-variance portfolio selection:A stochastic LQ framework[J].Applied Mathematics and Optimization,2000,42(1):19-33.
[20]Huang Y,Zhang W.Study on stochastic linear quadratic optimal control with constraint[J],Acta Automatica Sinica,2006,32(2):246.
[21]Schur J.(U|¨)ber Potenzreihen,die im Innern des Einheitskreises beschrankt sind[J].Journal f(u|¨)r die reine und angewandte Mathematik,1917,147:205-232.
[22]Chilali M,Gahinet P,Apkarian P.Robust pole placement in LMI regions[J].IEEE Transactions on Automatic Control,1999,44(12):2257-2270.
[23]Yu L,Chu J.An LMI approach to guaranteed cost control of linear uncertain time-delay systems[J].Automatica,1999,35(6):1155-1159.
[24]Apkarian P,Gahinet P,Becker G.Self-scheduled H∞control of linear parameter-varying systems:a design example[J].Automatica,1995,31(9):1251-1261.
[2]B.D.O.Anderson,J.B.Moore,Optimal Control Linear Quadratic Methods,Prentice-Hall,New York,1989.
[3]F.L.Lewis,Optimal Control,John Wiley and Sons,New York,1986.
[4]M.Aoki,Optimization of stochastic systems.New York:Academic Press,1967.
[5]R.E.Kalman and R.W.Koepcke,"Optimal synthesis of linear sampling control systems using generalized performance indices,"Transactions of the American Society of Mechanical Engineers,vol.80,pp.1820-1826,1958.
[6]Duncan T E,Pasik-Duncan B.Discrete time linear quadratic control with arbitrary correlated noise[J].IEEE Transactions on Automatic Control,2013,58(5):1290-1293.
[7]Chen S,Li X,Zhou X Y.Stochastic linear quadratic regulators with indefinite control weight costs[J].SIAM Journal on Control and Optimization,1998,36(5):1685-1702.
[8]Yaz E.Infinite horizon quadratic optimal control of a class of nonlinear stochastic systems[J].IEEE Transactions on Automatic Control,1989,34(11):1176-1180.
[9]Rami M A,Chen X,Moore J B,et al.Solvability and asymptotic behavior of generalized Riccati equations arising in indefinite stochastic LQ controls[J].IEEE Transactions on Automatic Control,2001,46(3):428-440.
[10]Rami M A,Zhou X Y.Linear matrix inequalities,Riccati equations,and indefinite stochastic linear quadratic controls[J].IEEE Transactions on Automatic Control,2000,45(6):1131-1143.
[11]Ostertag E.Mono-and multivariable control and estimation:Linear,quadratic and LMI methods[M].Springer Science&Business Media,2011.
[12]Duan G R,Yu H H.LMIs in Control Systems:Analysis,Design and Applications[M].CRC Press,2013.
[13]Antunes D J,Khashooei B A.Consistent event-triggered methods for linear quadratic control[C]//Decision and Control(CDC),2016 IEEE 55th Conference on.IEEE,2016:1358-1363.
[14]Ni Y H,Li X,Zhang J F.Indefinite mean-field stochastic linear-quadratic optimal control:from finite horizon to infinite horizon[J].2014.
[15]Wang J,Hou T,Ma H.Stochastic linear quadratic control with regional pole placement[C]//Intelligent Control and Automation(WCICA),2016 12th World Congress on.IEEE,2016:3361-3366.
[16]Zhang R,Lu R,Xue A,et al.New Minmax Linear Quadratic Fault-tolerant Tracking Control for Batch Processes[J].2016.
[17]Chen W,Zheng J,Qiu L.Linear quadratic optimal control of continuous-time LTI systems with random input gains[C]//Information and Automation(ICIA),2012International Conference on.IEEE,2012:241-246.
[18]Rotondo D,Puig V,Nejjari F.Linear quadratic control of LPV systems using static and shifting specifications[C].Control Conference(ECC),2015 European.IEEE,2015:3085-3090.
[19]Zhou X Y,Li D.Continuous-time mean-variance portfolio selection:A stochastic LQ framework[J].Applied Mathematics and Optimization,2000,42(1):19-33.
[20]Huang Y,Zhang W.Study on stochastic linear quadratic optimal control with constraint[J],Acta Automatica Sinica,2006,32(2):246.
[21]Schur J.(U|¨)ber Potenzreihen,die im Innern des Einheitskreises beschrankt sind[J].Journal f(u|¨)r die reine und angewandte Mathematik,1917,147:205-232.
[22]Chilali M,Gahinet P,Apkarian P.Robust pole placement in LMI regions[J].IEEE Transactions on Automatic Control,1999,44(12):2257-2270.
[23]Yu L,Chu J.An LMI approach to guaranteed cost control of linear uncertain time-delay systems[J].Automatica,1999,35(6):1155-1159.
[24]Apkarian P,Gahinet P,Becker G.Self-scheduled H∞control of linear parameter-varying systems:a design example[J].Automatica,1995,31(9):1251-1261.