非齐次Schrödinger方程的精确内部能控性

2022-09-06 02:32白忠玉
高师理科学刊 2022年8期
关键词:宝珠科学出版社系统控制

白忠玉

非齐次Schrödinger方程的精确内部能控性

白忠玉

(海口经济学院 网络学院,海南 海口 571127)

Schrödinger方程;精确能控;边界控制

1 引言及预备知识

考虑非齐次Schrödinger方程

考虑方程

成立.

2 主要结果及证明

显然

结合式(2)(16)(18),得

由式(16)(21),得

证明 利用HUM方法[12]证明精确内部能控性.

3 实例分析

[1] Zheng C,Zhou Z C.Exact controllability for the fourth order Schrödinger equation[J].Chinese Annals of Mathematics,Series B,2012,33(3):395-404.

[2] Wen R L,Chai S G,Guo B Z.Well-posedness and exact controllability of fourth order Schrodinger equation with boundary control and collocated observation[J].SIAM J CONTROL OPTIM,2014,52(1):365-396.

[3] Wen R L,Chai S G,Guo B Z.Well-posedness and exact controllability of fourth order Schrödinger equation with hinged boundary control and collocated observation[J].Math Control Signals Syst,2016,28(3):1-28.

[4] Martin P,Rosier L,Rouchon P.Controllability of the 1D Schrdinger equation using flatness[J].Automatica,2018,91:208-216.

[5] Caponigro M,Sigalotti M.Exact controllability in projections of the bilinear Schrödinger equation[J].SIAM J Control Optim,2018,56(4):2901-2920.

[6] Duca A.Global Exact Controllability of Bilinear Quantum Systems on Compact Graphs and Energetic Controllability[J].SIAM Journal on Control and Optimization,2020,58(6):3092-3129.

[7] Cazenave T.An introduction to nonlinear Schrödinger equations[M].Rio de Janeiro:Instituto de Matemática-UFRJ,1989.

[8] 郭宝珠,柴树根.无穷维线性系统控制理论[M].北京:科学出版社,2012.

[9] Hörmander L.Analysis of Linear Partial Differential Operators[M].New York:Springer-Verlag,1983.

[10] Ouahra M A.Interpolation spaces:An introduction[J].Ann Math Blaise Pascal,2004,1(1):1-17.

[11] Lions J L,Magenes E.Problèmes aux Limites Non Homogènes et Applications[M].Paris:Dunod,1969.

[12] Lions J L.Exact Controllability,Stabilization and Perturbations for Distributed Systems[J].SIAM Review,1988,30(1):1-68.

Exact intetrior controllability of the nonhomogeneous Schrödinger equation

BAI Zhongyu

(School of Network Science,Haikou University of Economics,Haikou 571127,China)

Schrödinger equation;exact controllability;boundary control

1007-9831(2022)08-0013-05

O231.4

A

10.3969/j.issn.1007-9831.2022.08.004

2022-03-31

海南省自然科学基金项目(120RC663)

白忠玉(1980-),男,山东日照人,副教授,硕士,从事分布参数系统控制理论研究.E-mail:610977231@qq.com

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