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.
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Communicated by L. Cesari
This work is supported in part by the National Science and Engineering Council of Canada under Grant No. 7109.
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Ahmed, N.U. Existence of optimal controls for a class of systems governed by differential inclusions on a Banach space. J Optim Theory Appl 50, 213–237 (1986). https://doi.org/10.1007/BF00939270
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DOI: https://doi.org/10.1007/BF00939270