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Pré-Publication, Document De Travail Année : 2022

On the controllability of nonlinear systems with a periodic drift

Résumé

Sufficient conditions are established for controllability of affine control systems with a drift all of whose solutions are periodic. In contrast with previously known results, these conditions encompass the case of a control set whose convex hull is not a neighbourhood of the origin. The condition is expressed by means of pushforwards along the flow of the drift, rather than in terms of Lie brackets. It turns out that this also amounts to local controllability of a time-varying linear approximation with constrained controls. Global and local results are given, as well as a few illustrative examples.
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Dates et versions

hal-03779482 , version 1 (16-09-2022)
hal-03779482 , version 2 (15-12-2022)
hal-03779482 , version 3 (07-03-2024)

Identifiants

  • HAL Id : hal-03779482 , version 2

Citer

Jean-Baptiste Caillau, Lamberto Dell'Elce, Alesia Herasimenka, Jean-Baptiste Pomet. On the controllability of nonlinear systems with a periodic drift. 2022. ⟨hal-03779482v2⟩
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