Sensitivity analysis of hyperbolic optimal control problems

被引：13
作者：
Kowalewski, Adam [2 ]
Lasiecka, Irena [3 ,4 ]
Sokolowski, Jan [1 ,4 ]
机构：
[1] Univ Nancy 1, Inst Elie Cartan, UMR Nancy Univ CNRS INRIA 7502, Math Lab, F-54506 Vandoeuvre Les Nancy, France
[2] AGH Univ Sci & Technol, Inst Automat, PL-30059 Krakow, Poland
[3] Univ Virginia, Dept Math, Charlottesville, VA 22904 USA
[4] Polish Acad Sci, Syst Res Inst, PL-01447 Warsaw, Poland
来源：
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS | 2012年 / 52卷 / 01期
关键词：
Sensitivity analysis; Optimal control problems; Hyperbolic boundary value problems; Linear partial differential operators; Steklov-Poincare operator; Kondratiev weighted spaces; DISTRIBUTED PARAMETER-SYSTEMS; SELF-ADJOINT EXTENSIONS; BOUNDARY-VALUE-PROBLEMS; TOPOLOGICAL DERIVATIVES; SHAPE OPTIMIZATION; POLARIZATION MATRICES; ASYMPTOTIC ANALYSIS; WAVE-EQUATIONS; OPERATORS;
D O I：
10.1007/s10589-010-9375-x
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
The aim of this paper is to perform sensitivity analysis of optimal control problems defined for the wave equation. The small parameter describes the size of an imperfection in the form of a small hole or cavity in the geometrical domain of integration. The initial state equation in the singularly perturbed domain is replaced by the equation in a smooth domain. The imperfection is replaced by its approximation defined by a suitable Steklov's type differential operator. For approximate optimal control problems the well-posedness is shown. One term asymptotics of optimal control are derived and justified for the approximate model. The key role in the arguments is played by the so called "hidden regularity" of boundary traces generated by hyperbolic solutions.
引用
收藏
页码：147 / 179
页数：33
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