Properties of solution of linear controlled systems with impulses at variable times
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- 英文论文题名：Properties of solution of linear controlled systems with impulses at variable times
- 论文作者：Yunfei Peng ; Kuilin Wu ; Shulin Qin ; Ying Kang
- 英文论文作者：Yunfei Peng ; Kuilin Wu ; Shulin Qin ; Ying Kang ; Department of Mathematics ; Guizhou University
- 年：2017
- 作者机构：Department of Mathematics,Guizhou University;
- 英文论文关键词：Impulses at variable times ; Controlled systems ; Qualitative theory
- 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：6
- 文件大小：211k
- 原文格式：D
- 会议级别：全国
摘要
The focus of this paper is the study of qualitative theory of the linear controlled systems with impulses at variable times.We prove some results on the existence and uniqueness, continuous dependence, G?ateaux differentiability of weak solution with respect to control function. These results are fundamental properties to study optimal control problems of differential equations with impulses at variable times.
The focus of this paper is the study of qualitative theory of the linear controlled systems with impulses at variable times.We prove some results on the existence and uniqueness, continuous dependence, G?ateaux differentiability of weak solution with respect to control function. These results are fundamental properties to study optimal control problems of differential equations with impulses at variable times.
The focus of this paper is the study of qualitative theory of the linear controlled systems with impulses at variable times.We prove some results on the existence and uniqueness, continuous dependence, G?ateaux differentiability of weak solution with respect to control function. These results are fundamental properties to study optimal control problems of differential equations with impulses at variable times.
引文
[1]N.U.Ahmed,Existence of optimal controls for a general class of impulsive systems on Banach space,SIAM J.Control Optim.,42:669-685,2003.
[2]N.U.Ahmed,Measure solutions for impulsive evolution equations with measurable vector fields,J.Math.Anal.Appl.,319,74-93,2006.
[3]J.P.Aubin,Optimal impulse control problems and quasivariational inequalities thirty years later:a viability approach,In Contrle optimal et EDP:Innovations et Applications,IOS Press,2000.
[4]Marat Akhmet and Enes Ylmaz,Neural networks with discontinuous/impact activations:impulsive differential equations,Nonlinear Systems and Complexity,9,67-83,2014.
[5]D.D.Bainov and A.B.Dishliev,Sutlicient conditions for absence of beating in systems of differential equations with impulses,Appl.Anal.,18,67-73,1984.
[6]D.D.Bainov and P.S.Simeonov,Impulsive Differential Equations:Asymptotic Properties of the Solutions,World Scientific,Singapore,1995.
[7]M.Benchohra,J.Henderson and S.Ntouyas,Impulsive Differential Equations and Inclusions,Hindawi Publishing Corporation,New York,2006.
[8]Anne J.Catll,David G.Schaeffer,Thomas P.Witelski,Eric E.Monson and Anna L.Lin,On spiking models for synaptic activity and impulsive differential equations,SIAM Review,50,553-569,2008.
[9]S.G.Hristova AND D.D Bainov,Periodic solutions of quasilinear nonautonomous systems with impulses,Bull.Austral.Math.,31,185-197,1985.
[10]Shouchuan Hu and V.Lakshmikantham,Periodic boundary value problem for second order impulsive differential systems,Nonlinear Anal.TMA,13,75-85,1989.
[11]Shouchuan Hu and V.Lakshmikantham,Impulsive differential systems and the pulse phenomena,J.Math.Anal.Appl.,137,605-612,1989.
[12]MM Krylov and NN Bogolyubov,Introduction to non-linear mechanics,Academiya Nauk Ukrin.SSR,Kiev,1937(in Russian).
[13]V.Lakshmikantham,D.D.Bainov and P.S.Simenonov,Theory of Impulsive Differential Equences,Wold Scientific,1989.
[14]P.L.Lions and B.Perthame,Quasi-variational inequaities and ergodic impulse control,SIAM J.Control Optim.,24,604-615,1986.
[15]S.Migorsky and Anna Ochal,Nonlinear impulsive evolution inclusions of second order,Dynam.Systems Apll.,16,155-173,2007.
[16]A.D.Milman and A.D.Myshkis,On the stability of motion in nonlinear mechanics,Siberian Mathematical Journal,1,233-237,1960.
[17]Y.Peng,X.Xiang and W.Wei,Optimal feedback control for a class of strongly nonlinear impulsive evolution equation,Comput.Math.Appl.,52,759-768,2006.
[18]Y.Peng,X.X iang and W.Wei,Nonlinear impulsive integrodifferential equations of mixed type with time-varying generating operators and optimal control,Dynam.Systems Appl.,16,481-496,2007.
[19]Y.Peng,X.Xiang,W.Wei,Second-order nonlinear impulsive integro-differential equations of mixed type with time-varying generating operators and optimal controls,Comput.Math.Appl.,57,42-53,2009.
[20]A.M.Samoilenko,Application of the method of averaging for the investigation of vibrations excited by instantaneous impulses in self-vibrating systems of the second order with a small parameter,Ukrainian Mathematical Journal,13,103-108,1961.
[21]A.M.Samoilenko and N.A.Perestyuk,The method of averaging in systems with an impulsive action,Ukrainian mathematical Journal,26,342-347,1974.
[22]A.M.Samoilenko and N.A.Perestyuk,On stability of solutions of impulsive systems,Differentsial’nye Uravneniya,17,1995-2002,1981.
[23]A.M.Samoilenko,N.A.Perestyuk and Y.Chapovsky,Impusive Differential Equations,World Scientific,1995.
[24]S.H.Smith,On the impulsive flow of a viscous liquid past a semi-infinite flat plate,SIAM J.Appl.Math,22(2),148-154,1972.
[2]N.U.Ahmed,Measure solutions for impulsive evolution equations with measurable vector fields,J.Math.Anal.Appl.,319,74-93,2006.
[3]J.P.Aubin,Optimal impulse control problems and quasivariational inequalities thirty years later:a viability approach,In Contrle optimal et EDP:Innovations et Applications,IOS Press,2000.
[4]Marat Akhmet and Enes Ylmaz,Neural networks with discontinuous/impact activations:impulsive differential equations,Nonlinear Systems and Complexity,9,67-83,2014.
[5]D.D.Bainov and A.B.Dishliev,Sutlicient conditions for absence of beating in systems of differential equations with impulses,Appl.Anal.,18,67-73,1984.
[6]D.D.Bainov and P.S.Simeonov,Impulsive Differential Equations:Asymptotic Properties of the Solutions,World Scientific,Singapore,1995.
[7]M.Benchohra,J.Henderson and S.Ntouyas,Impulsive Differential Equations and Inclusions,Hindawi Publishing Corporation,New York,2006.
[8]Anne J.Catll,David G.Schaeffer,Thomas P.Witelski,Eric E.Monson and Anna L.Lin,On spiking models for synaptic activity and impulsive differential equations,SIAM Review,50,553-569,2008.
[9]S.G.Hristova AND D.D Bainov,Periodic solutions of quasilinear nonautonomous systems with impulses,Bull.Austral.Math.,31,185-197,1985.
[10]Shouchuan Hu and V.Lakshmikantham,Periodic boundary value problem for second order impulsive differential systems,Nonlinear Anal.TMA,13,75-85,1989.
[11]Shouchuan Hu and V.Lakshmikantham,Impulsive differential systems and the pulse phenomena,J.Math.Anal.Appl.,137,605-612,1989.
[12]MM Krylov and NN Bogolyubov,Introduction to non-linear mechanics,Academiya Nauk Ukrin.SSR,Kiev,1937(in Russian).
[13]V.Lakshmikantham,D.D.Bainov and P.S.Simenonov,Theory of Impulsive Differential Equences,Wold Scientific,1989.
[14]P.L.Lions and B.Perthame,Quasi-variational inequaities and ergodic impulse control,SIAM J.Control Optim.,24,604-615,1986.
[15]S.Migorsky and Anna Ochal,Nonlinear impulsive evolution inclusions of second order,Dynam.Systems Apll.,16,155-173,2007.
[16]A.D.Milman and A.D.Myshkis,On the stability of motion in nonlinear mechanics,Siberian Mathematical Journal,1,233-237,1960.
[17]Y.Peng,X.Xiang and W.Wei,Optimal feedback control for a class of strongly nonlinear impulsive evolution equation,Comput.Math.Appl.,52,759-768,2006.
[18]Y.Peng,X.X iang and W.Wei,Nonlinear impulsive integrodifferential equations of mixed type with time-varying generating operators and optimal control,Dynam.Systems Appl.,16,481-496,2007.
[19]Y.Peng,X.Xiang,W.Wei,Second-order nonlinear impulsive integro-differential equations of mixed type with time-varying generating operators and optimal controls,Comput.Math.Appl.,57,42-53,2009.
[20]A.M.Samoilenko,Application of the method of averaging for the investigation of vibrations excited by instantaneous impulses in self-vibrating systems of the second order with a small parameter,Ukrainian Mathematical Journal,13,103-108,1961.
[21]A.M.Samoilenko and N.A.Perestyuk,The method of averaging in systems with an impulsive action,Ukrainian mathematical Journal,26,342-347,1974.
[22]A.M.Samoilenko and N.A.Perestyuk,On stability of solutions of impulsive systems,Differentsial’nye Uravneniya,17,1995-2002,1981.
[23]A.M.Samoilenko,N.A.Perestyuk and Y.Chapovsky,Impusive Differential Equations,World Scientific,1995.
[24]S.H.Smith,On the impulsive flow of a viscous liquid past a semi-infinite flat plate,SIAM J.Appl.Math,22(2),148-154,1972.