Minimal time control of the two tanks gradostat model under a cascade Input constraint

Abstract : We study the minimum time control problem of a series of two interconnected chemostats under the input constraint $u_{2}\leq u_{1}$, where $u_{i}$ are the respective dilution rates in the tanks. This constraint brings controllability issues in the study of the optimal strategies. We overcome this difficulty by splitting the state domain into two subdomains, one with no lack of controllability of the target, and its complement where any optimal trajectory satisfies $u_{1}=u_{2}$. We explicitly compute the complete optimal synthesis that depends on the position of the target with respect to a semipermeable curve that passes through a steady-state singular point.
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Journal articles
SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2014, 52 (4), pp.2568-2594. 〈10.1137/130950379〉
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Contributor : Alain Rapaport <>
Submitted on : Saturday, November 22, 2014 - 5:38:08 PM
Last modification on : Thursday, July 26, 2018 - 12:16:02 PM

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Terence Bayen, Alain Rapaport, Matthieu Sebbah. Minimal time control of the two tanks gradostat model under a cascade Input constraint. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2014, 52 (4), pp.2568-2594. 〈10.1137/130950379〉. 〈hal-01086153〉

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