In this paper we associate a semigroup to a locally maximal subset of complete controllability, i.e., a local control set. This fundamental semigroup is based on equivalence classes under homotopies in the set of trajectories. It reflects the structure of the set of closed (trajectory) loops in the local control set. We discuss the relations between different local control sets and prove a Van Kampen-type theorem for their unions and intersections.
Fundamental semigroups for local control sets / F. COLONIUS; L. SAN MARTIN; M. SPADINI. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - STAMPA. - 185 (suppl.):(2006), pp. S69-S91. [10.1007/s10231-004-0137-1]
Fundamental semigroups for local control sets
SPADINI, MARCO
2006
Abstract
In this paper we associate a semigroup to a locally maximal subset of complete controllability, i.e., a local control set. This fundamental semigroup is based on equivalence classes under homotopies in the set of trajectories. It reflects the structure of the set of closed (trajectory) loops in the local control set. We discuss the relations between different local control sets and prove a Van Kampen-type theorem for their unions and intersections.
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