Existence of optimal controls for a class of systems governed by differential inclusions on a Banach space |
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Authors: | N U Ahmed |
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Institution: | (1) Department of Electrical Engineering, University of Ottawa, Ottawa, Ontario, Canada |
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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.This work is supported in part by the National Science and Engineering Council of Canada under Grant No. 7109. |
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Keywords: | Differential inclusions Banach spaces having Radon-Nikodym property mild solutions Polish spaces relaxed controls measure-valued controls Cesari property distributed controls boundary controls |
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