SECOND-ORDER ANALYSIS AND NUMERICAL APPROXIMATION FOR BANG-BANG BILINEAR CONTROL PROBLEMS

被引：22

作者：

Casas, Eduardo ^{[1
]}

Wachsmuth, Daniel ^{[2
]}

Wachsmuth, Gerd ^{[3
]}

机构：

[1] Univ Cantabria, Dept Matemat Aplicada & Ciencias Comp, ETSI Ind & Telecomunicac, E-39005 Santander, Spain

[2] Univ Wurzburg, Inst Math, D-97074 Wurzburg, Germany

[3] Brandenburg Tech Univ Cottbus Senftenberg, Inst Math, D-03046 Cottbus, Germany

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2018年 / 56卷 / 06期

关键词：

bang-bang control; bilinear controls; second-order conditions; sufficient optimality conditions; error analysis; SEMILINEAR ELLIPTIC-EQUATIONS; OPTIMALITY CONDITIONS; BOUNDARY CONTROL; CONVERGENCE; EQUIVALENCE;

D O I：

10.1137/17M1139953

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We consider bilinear optimal control problems whose objective functionals do not depend on the controls. Hence, bang-bang solutions will appear. We investigate sufficient second-order conditions for bang-bang controls, which guarantee local quadratic growth of the objective functional in L-1. In addition, we prove that for controls that are not bang-bang, no such growth can be expected. Finally, we study the finite-element discretization and prove error estimates of bang-bang controls in L-1-norms.

引用

页码：4203 / 4227

页数：25

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