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.
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Für höhere Schule und Studium
Für Beruf und Forschung
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ISBN-13
978-0-8218-0753-8 (9780821807538)
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Schweitzer Klassifikation
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.
