Semi-linear optimal control problem on a smooth oscillating domain

Aiyappan, S and Nandakumaran, AK and Prakash, R (2020) Semi-linear optimal control problem on a smooth oscillating domain. In: Communications in Contemporary Mathematics, 22 (4).

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Abstract

We demonstrate the asymptotic analysis of a semi-linear optimal control problem posed on a smooth oscillating boundary domain in the present paper. We have considered a more general oscillating domain than the usual "pillar-type" domains. Consideration of such general domains will be useful in more realistic applications like circular domain with rugose boundary. We study the asymptotic behavior of the problem under consideration using a new generalized periodic unfolding operator. Further, we are studying the homogenization of a non-linear optimal control problem and such non-linear problems are limited in the literature despite the fact that they have enormous real-life applications. Among several other technical difficulties, the absence of a sufficient criteria for the optimal control is one of the most attention-grabbing issues in the current setting. We also obtain corrector results in this paper.

Item Type:	Journal Article
Publication:	Communications in Contemporary Mathematics
Publisher:	World Scientific Publishing Co. Pte Ltd
Additional Information:	The copyright for this article belongs to World Scientific Publishing Co. Pte Ltd
Keywords:	asymptotic analysis; homogenization; Optimal control; oscillating boundary; unfolding operator
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	06 Feb 2023 08:44
Last Modified:	06 Feb 2023 08:44
URI:	https://eprints.iisc.ac.in/id/eprint/79892

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