Singular controls and chattering arcs in optimal control problems arising in biomedicine
Urszula Ledzewicz, Heinz Schättler (2009)
Control and Cybernetics
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Urszula Ledzewicz, Heinz Schättler (2009)
Control and Cybernetics
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Jorge Antonio Torres-Muñoz, Irandi Gutierrez-Carmona, Alma Rosa Dominguez-Bocanegra (2016)
Kybernetika
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The present work is centred on the problem of biomass productivity optimization of a culture of microalgae Spirulina maxima. The mathematical tools consisted of necessary and sufficient conditions for optimal control coming from the celebrated Pontryagin's Maximum Principle (PMP) as well as the Bellman's Principle of Optimality, respectively. It is shown that the optimal dilution rate turns to be a bang-singular-bang control. It turns out that, the experimental results are in accordance...
Heinz Schättler, Miroslava Jankovic (1993)
Forum mathematicum
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Sophie Jan (2013)
ESAIM: Control, Optimisation and Calculus of Variations
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We apply four different methods to study an intrinsically bang-bang optimal control problem. We study first a relaxed problem that we solve with a naive nonlinear programming approach. Since these preliminary results reveal singular arcs, we then use Pontryagin’s Minimum Principle and apply multiple indirect shooting methods combined with homotopy approach to obtain an accurate solution of the relaxed problem. Finally, in order to recover a purely bang-bang solution for the original...
Hans Oberle, Ricki Rosendahl (2008)
Control and Cybernetics
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Serovajskij, S.Ya. (2003)
Sibirskij Matematicheskij Zhurnal
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Barbara Bily (2002)
Applicationes Mathematicae
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Necessary conditions for some optimal control problem for a nonlinear 2-D system are considered. These conditions can be obtained in the form of a quasimaximum principle.
B. Bonnard, G. Launay (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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In this article we consider a control system modelling a batch reactor in which three species X, X, X are reacting according to the scheme X → X → X, each reaction being irreversible. The control is the temperature T of the reactions or the derivative of this temperature with respect to time. The terminal constraint is to obtain a given concentration of the product X2 at the end of the batch. The objective of our study is to introduce and to apply all the mathematical tools to compute...
J. Warschat (1985)
RAIRO - Operations Research - Recherche Opérationnelle
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Noriaki Yamazaki (2009)
Banach Center Publications
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In this paper we consider optimal control problems for abstract nonlinear evolution equations associated with time-dependent subdifferentials in a real Hilbert space. We prove the existence of an optimal control that minimizes the nonlinear cost functional. Also, we study approximating control problems of our equations. Then, we show the relationship between the original optimal control problem and the approximating ones. Moreover, we give some applications of our abstract results. ...
B. Bonnard, G. Launay (1998)
ESAIM: Control, Optimisation and Calculus of Variations
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