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Lempio, Frank:
Minimumnormprobleme und Zeitoptimale Steuerungen.
In: Collatz, Lothar ; Werner, H. ; Meinardus, Günter
(Hrsg.):
Numerische Methoden der Approximationstheorie : Numerical Methods of Approximation Theory; Vortragsauszüge der Tagung über numerische Methoden der Approximationstheorie vom 25. bis 31. Mai 1975 im Mathematischen Forschungsinstitut Oberwolfach (Schwarzwald). -
Basel
: Birkhäuser
,
1976
. - S. 277-298
. - (International Series of Numerical Mathematics
; 30
)
(Numerische Methoden der Approximationstheorie ; 3)
ISBN 978-3-7643-0824-7
DOI: https://doi.org/10.1007/978-3-0348-7692-6_14
| Rez.: |
Abstract
We consider special boundary control systems for parabolic differential equations where the target set is described by a convex body of continuous functions. In this paper we are mainly interested in time-optimal control problems.
Our first approach to these problems is the usual one which allows us to sharpen a bang-bang-principle recently proved by WECK. Here we make use of the same analyticity arguments used already by GLASHOFF for control problems with fixed time interval.
Our second approach consists in embedding the time-optimal control problem into a family of minimum norm problems with general operator restrictions. We investigate these minimum norm problems by means of a characterization theorem for abstract approximation problems, and we believe that this approach will be useful not only for the special problems treated in this paper but also for more general situations.