Extension of the bang-bang principle for piecewise affine dynamics under constraints
Résumé
As an extension of the classical bang-bang principle for linear systems, we show that for non-autonomous regional optimal control problems with state constraints, the bang-bang principle does not hold globally even when the dynamics is continuous with respect to the state variable. However, we show that there exist minimal time trajectories to reach a target with extreme controls at the loci where the dynamics is differentiable. We give two examples which exhibit singular arcs exactly at the loci of non-differentiability, i.e. at the boundaries of the regions.
Domaines
Mathématiques [math]| Origine | Fichiers produits par l'(les) auteur(s) |
|---|