Titlebook: Optimal Control Theory; Leonard D. Berkovitz Book 1974 Springer Science+Business Media New York 1974 Control.Kontrolle (Math.).Planungsrec

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Examples of Control Problems,led control problems. Despite their present day origins these problems, from a mathematical point of view, are variants of a class of problems that has been studied for several hundred years; namely, the problems of the calculus of variations.

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Formulation of the Control Problem,inary formulation of the mathematical problem of optimal control. It should, however, motivate the precise and more general formulation of the mathematical problem of optimal control which is given in Section 3. In Section 4 we discuss various equivalent formulations of the problem, and in Section 5

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Existence without Convexity,..(t,x) be convex. In the case of non- compact constraints it was also required that the trajectories be equi-absolutely continuous, and reasonable growth conditions to ensure this were formulated. All of the conditions placed on the problem can be justified except, perhaps, the requirement that the

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Proof of the Maximum Principle,principle and shall obtain the maximum principle as a special case of this theorem. An essential property of an optimal trajectory is used to motivate the introduction of a concept called .-. extremality. A necessary condition for .-. extremality is then stated (Theorem 3.1 of this chapter), and it

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