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A Note on Nonsmooth Optimal Control Problems

In: From Nano to Space

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  • Hans Joachim Oberle

    (University of Hamburg, Department of Mathematics)

Abstract

The paper is concerned with general optimal control problems (OCP) which are characterized by a nonsmooth ordinary state differential equation. More precisely, we assume that the right-hand side of the state equation is piecewise smooth and that the switching points, which separate these pieces, are determined as roots of a state- and control dependent (smooth) switching function. For this kind of optimal control problems necessary conditions are developed. Special attention is payed to the situation that the switching function vanishes identically along a nontrivial subarc. Such subarcs, which are called singular state subarcs, are investigated with respect to the necessary conditions and to the junction conditions. In extension to earlier results, cf. [5], in this paper the case of a zero-order switching function is considered.

Suggested Citation

  • Hans Joachim Oberle, 2008. "A Note on Nonsmooth Optimal Control Problems," Springer Books, in: Michael H. Breitner & Georg Denk & Peter Rentrop (ed.), From Nano to Space, pages 309-321, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-74238-8_22
    DOI: 10.1007/978-3-540-74238-8_22
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