The controllability behavior of nonlinear control systems is described by associating semigroups to locally maximal subsets of complete controllability, i.e., local control sets. Periodic trajectories are called equivalent if there is a `homotopy' between them involving only trajectories. The resulting object is a semigroup, which we call the dynamic index of the local control set. It measures the dierent ways the system can go through the local control set.
On the classification of control sets / F. COLONIUS; M. SPADINI. - STAMPA. - 273:(2002), pp. 217-231. (Intervento presentato al convegno Dynamics, bifurcations, and control tenutosi a Kloster Irsee (Germania) nel 2001).
On the classification of control sets
SPADINI, MARCO
2002
Abstract
The controllability behavior of nonlinear control systems is described by associating semigroups to locally maximal subsets of complete controllability, i.e., local control sets. Periodic trajectories are called equivalent if there is a `homotopy' between them involving only trajectories. The resulting object is a semigroup, which we call the dynamic index of the local control set. It measures the dierent ways the system can go through the local control set.
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