期刊
RUSSIAN MATHEMATICAL SURVEYS
卷 68, 期 3, 页码 401-433出版社
Steklov Mathematical Inst, Russian Acad Sciences
DOI: 10.1070/RM2013v068n03ABEH004838
关键词
extremum problem; optimal control; phase constraints; mix; controllability; abnormality
类别
资金
- Russian Foundation for Basic Research [10-01-00188, 11-01-00529]
In this paper a general result concerning Lagrange's principle for so-called smoothly approximately convex problems is proved which encompasses necessary extremum conditions for mathematical and convex programming, the calculus of variations, Lyapunov problems, and optimal control problems with phase constraints. The problem of local controllability for a dynamical system with phase constraints is also considered. In an appendix, results are presented that relate to the development of a 'Lagrangian approach' to problems where regularity is absent and classical approaches are meaningless.
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