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Pré-Publication, Document De Travail Année : 2013

Optimal synthesis for a minimum time problem in the plane with a triangle control set

Résumé

This work is devoted to the study of a minimum time control problem where the state is governed by a two-dimensional affine system with two inputs taking values within a triangle, and describing a series of two interconnected chemostats. We show the existence of a subset of the invariant domain D associated to the system such that if the target is in this set, then it can be reached by any initial condition in D. For every target point in this subset, we provide an optimal synthesis of the problem by decomposing D into two subsets. In the first one, we give an explicit expression of the value function, and we show that there exist infinitely many optimal solutions whereas in the second one, we show that the optimal strategy is of singular type.
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Dates et versions

hal-00798651 , version 1 (09-03-2013)
hal-00798651 , version 2 (03-10-2013)
hal-00798651 , version 3 (02-06-2014)

Identifiants

  • HAL Id : hal-00798651 , version 1

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Térence Bayen, Alain Rapaport, Matthieu Sebbah. Optimal synthesis for a minimum time problem in the plane with a triangle control set. 2013. ⟨hal-00798651v1⟩
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