On Exact Controllability of Networks of Nonlinear Elastic Strings in 3-Dimensional Space

作     者：Gnter R.LEUGERING *** SCHMIDT 

作者机构：Department of MathematicsFriedrich-Alexander University Department of Mathematics and StatisticsMcGill University 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2012年第33卷第1期

页      面：33-60页

核心收录：

学科分类：0711[理学-系统科学] 07[理学] 08[工学] 070104[理学-应用数学] 070105[理学-运筹学与控制论] 081101[工学-控制理论与控制工程] 071101[理学-系统理论] 0811[工学-控制科学与工程] 0701[理学-数学] 

基　　金：supported by the DFG SPP1253:Optimization with PDE-Constaints the DFG-CE315 Cluster of Excellence:Engineering of Advanced Materials 

主　　题：Nonlinear strings Network Quasilinear system of hyperbolic equations Controllability 

摘      要：This paper concerns a system of nonlinear wave equations describing the vibra- tions of a 3-dimensional network of elastic strings. The authors derive the equations and appropriate nodal conditions, determine equilibrium solutions, and, by using the methods of quasilinear hyperbolic systems, prove that for tree networks the natural initial, boundary value problem has classical solutions existing in neighborhoods of the ＂stretched＂ equilibrium solutions. Then the local controllability of such networks near such equilib- rium configurations in a certain specified time interval is proved. Finally, it is proved that, given two different equilibrium states satisfying certain conditions, it is possible to control the network from states in a small enough neighborhood of one equilibrium to any state in a suitable neighborhood of the second equilibrium over a sufficiently large time interval.