ISSN:
1573-2878
Keywords:
Differential inclusions
;
Banach spaces having Radon-Nikodym property
;
mild solutions
;
Polish spaces
;
relaxed controls
;
measure-valued controls
;
Cesari property
;
distributed controls
;
boundary controls
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Using Cesari's approach, we prove the existence of optimal controls for a class of systems governed by differential inclusions on a Banach space having the Radon-Nikodym property. Theorem 3.1 gives the existence result for optimal relaxed controls under fairly general assumptions on the system and the admissible controls. This result depends on a fundamental result (Theorem 2.1) that proves the existence of mild solutions of differential inclusions on a Banach space, which has also independent interest. Further, the preparatory results, such as Lemma 3.1 and Lemma 3.2, are also useful in the study of time-optimal and terminal control problems. For illustration of the results, we present two examples, one on distributed controls for a class of systems governed by nonlinear parabolic equations and the other on boundary controls with discontinuous boundary operator.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00939270
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