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 different ways the system can go through the local control set.
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Colonius, F., Spadini, M. (2002). On the Classification of Control Sets. In: Colonius, F., Grüne, L. (eds) Dynamics, Bifurcations, and Control. Lecture Notes in Control and Information Sciences, vol 273. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45606-6_15
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DOI: https://doi.org/10.1007/3-540-45606-6_15
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