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On the structure of uniformly hyperbolic chain control sets

Kawan, Christoph
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 07/10/2015
Relevância na Pesquisa
16.57%
We prove the following theorem: Let Q be an isolated chain control set of a control-affine system on a smooth compact manifold M. If Q is uniformly hyperbolic without center bundle, then the lift of Q to the extended state space U x M, where U is the space of control functions, is a graph over U. In other words, for every control u in U there is a unique x in Q such that the corresponding state trajectory phi(t,x,u) evolves in Q.; Comment: 11 pages

Uniformly hyperbolic control theory

Kawan, Christoph
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 25/11/2015
Relevância na Pesquisa
36.57%
This paper gives a summary of a body of work at the intersection of control theory and smooth nonlinear dynamics. The main idea is to transfer the concept of uniform hyperbolicity, central to the theory of smooth dynamical systems, to control-affine systems. Combining the strength of geometric control theory and the hyperbolic theory of dynamical systems, it is possible to deduce control-theoretic results of non-local nature that reveal remarkable analogies to the classical hyperbolic theory of dynamical systems.