Calculus of variations and optimal control
著者
書誌事項
Calculus of variations and optimal control
（Translations of mathematical monographs, v. 180）
American Mathematical Society, c1998
- タイトル別名
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Variat︠s︡ionnoe ischislenie i optimalʹnoe upravlenie
Вариационное исчисление и оптимальное управление
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注記
Bibliography: p. 371-372
内容説明・目次
内容説明
The theory of a Pontryagin minimum is developed for problems in the calculus of variations. The application of the notion of a Pontryagin minimum to the calculus of variations is a distinctive feature of this book. A new theory of quadratic conditions for a Pontryagin minimum, which covers broken extremals, is developed, and corresponding sufficient conditions for a strong minimum are obtained. Some classical theorems of the calculus of variations are generalized.
目次
First order conditions: First order conditions Theory of a weak minimum for the problem on a fixed time interval Theory of the maximum principle Extremals and the Hamiltonian of a control system Hamilton-Jacobi equation and field theory Transformations of problems and invariance of extremals Quadratic conditions: Quadratic conditions and conjugate points for broken extremals Quadratic conditions for a Pontryagin minimum and sufficient conditions for a strong minimum: Proofs Quadratic conditions in the general problem of the calculus of variations and related optimal control problems Investigation of extremals by quadratic conditions: Examples Bibliography.
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