Optimal Control for Allen-Cahn Equations Enhanced by Model Predictive Control
نویسندگان
چکیده
منابع مشابه
Optimal Control for Allen-Cahn Equations Enhanced by Model Predictive Control
The Allen-Cahn equation is a simple model of a nonlinear reaction-diffusion process. It is often used to model interface motion in time, e.g. phase separation in alloys. It has applications in many areas including material sciences, biology, geology, as well as image processing. We will consider a simple scalar Allen-Cahn equation subject to distributed control. Here, the nonlinear reaction ter...
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Optimization problems governed by Allen-Cahn systems including elastic effects are formulated and first-order necessary optimality conditions are presented. Smooth as well as obstacle potentials are considered, where the latter leads to an MPEC. Numerically, for smooth potential the problem is solved efficiently by the Trust-Region-NewtonSteihaug-cg method. In case of an obstacle potential firs...
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In this paper we consider a elastic vector-valued Allen-Cahn MPCC (Mathematical Programs with Complementarity Constraints) problem. We use a regularization approach to get the optimality system for the subproblems. By passing to the limit in the optimality conditions for the regularized subproblems, we derive certain generalized first-order necessary optimality conditions for the original problem.
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ژورنال
عنوان ژورنال: IFAC Proceedings Volumes
سال: 2013
ISSN: 1474-6670
DOI: 10.3182/20130925-3-fr-4043.00062