Minimal time sequential batch reactors with bounded and impulse controls for one or more species

Pedro Gajardo 1, 2 Hector Ramirez 3 Alain Rapaport 4
4 MERE - Water Resource Modeling
CRISAM - Inria Sophia Antipolis - Méditerranée , INRA - Institut National de la Recherche Agronomique : UMR0729
Abstract : We consider the optimal control problem of feeding in minimal time a tank where several species compete for a single resource, with the objective being to reach a given level of the resource. We allow controls to be bounded measurable functions of time plus possible impulses. For the one-species case, we show that the immediate one-impulse strategy (filling the whole reactor with one single impulse at the initial time) is optimal when the growth function is monotonic. For nonmonotonic growth functions with one maximum, we show that a particular singular arc strategy (precisely defined in section 3) is optimal. These results extend and improve former ones obtained for the class of measurable controls only. For the two-species case with monotonic growth functions, we give conditions under which the immediate one-impulse strategy is optimal. We also give optimality conditions for the singular arc strategy (at a level that depends on the initial condition) to be optimal. The possibility for the immediate one-impulse strategy to be nonoptimal while both growth functions are monotonic is a surprising result and is illustrated with the help of numerical simulations.
Type de document :
Article dans une revue
SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2008, 47 (6), pp.2827-2856. 〈10.1137/070695204〉
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Contributeur : Alain Rapaport <>
Soumis le : mercredi 4 septembre 2013 - 10:03:14
Dernière modification le : samedi 27 janvier 2018 - 01:31:49

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Pedro Gajardo, Hector Ramirez, Alain Rapaport. Minimal time sequential batch reactors with bounded and impulse controls for one or more species. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2008, 47 (6), pp.2827-2856. 〈10.1137/070695204〉. 〈hal-00857823〉

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