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Differential inclusions and abstract control problems

Published online by Cambridge University Press:  17 April 2009

Mieczyław Cichoń
Mieczyław Cichoń
Affiliation:
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Matejki 48/4960–769 PoznańPoland e-mail: mcichon@math.amu.edu.plmcichon@plpuam11.bitnet
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We prove an existence theorem for differential inclusions in Banach spaces. Here {A (t): t ∈ [0,T]} is a family of linear operators generating a continuous evolution operator K (t, s). We concentrate on maps F with F (t,·) weakly sequentially hemi-continuous.

Moreover, we show a compactness of the set of all integral solutions of the above problem. These results are also applied to a semilinear optimal control problem. Some corollaries, important in the theory of optimal control, are given too. We extend in several ways theorems existing in the literature.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 53 , Issue 1 , February 1996 , pp. 109 - 122
Copyright
Copyright © Australian Mathematical Society 1996

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