INVARIANCE ENTROPY OF HYPERBOLIC CONTROL SETS

Autor(es)

Da Silva, Adriano ^[1] ; Kawan, Christoph ^[2]

Afiliação do(s) autor(es)

^[1] IMECC UNICAMP, Dept Matemat, BR-13083859 Campinas, SP - Brazil

^[2] Univ Passau, Fak Informat & Math, D-94032 Passau - Germany

• Tipo de documento: Artigo Científico
• Fonte: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS; v. 36, n. 1, p. 97-136, JAN 2016.
• Citações Web of Science: 15

Resumo

In this paper, we improve the known estimates for the invariance entropy of a nonlinear control system. For sets of complete approximate controllability we derive an upper bound in terms of Lyapunov exponents and for uniformly hyperbolic sets we obtain a similar lower bound. Both estimates can be applied to hyperbolic chain control sets, and we prove that under mild assumptions they can be merged into a formula. The proof of our result reveals the interesting qualitative statement that there exists no control strategy to make a uniformly hyperbolic chain control set invariant that cannot be beaten or at least approached (in the sense of lowering the necessary data rate) by the strategy to stabilize the system at a periodic orbit in the interior of this set. (AU)

• Processo FAPESP: 13/19756-8 - Entropia invariante para a ação de semigrupos em espaços homogêneos
• Beneficiário: Adriano João da Silva
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado