Optimal switching for hybrid semilinear evolutions
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Publication:313360
DOI10.1016/J.NAHS.2016.05.001zbMATH Open1346.49033arXiv1605.05153OpenAlexW2963026767MaRDI QIDQ313360
Author name not available (Why is that?)
Publication date: 9 September 2016
Published in: (Search for Journal in Brave)
Abstract: We consider the optimization of a dynamical system by switching at discrete time points between abstract evolution equations composed by nonlinearly perturbed strongly continuous semigroups, nonlinear state reset maps at mode transition times and Lagrange-type cost functions including switching costs. In particular, for a fixed sequence of modes, we derive necessary optimality conditions using an adjoint equation based representation for the gradient of the costs with respect to the switching times. For optimization with respect to the mode sequence, we discuss a mode-insertion gradient. The theory unifies and generalizes similar approaches for evolutions governed by ordinary and delay differential equations. More importantly, it also applies to systems governed by semilinear partial differential equations including switching the principle part. Examples from each of these system classes are discussed.
Full work available at URL: https://arxiv.org/abs/1605.05153
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