Invariance entropy for a class of partially hyperbolic sets

Autor(es)

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

Afiliação do(s) autor(es)

^[1] Univ Passau, Fac Comp Sci & Math, D-94032 Passau - Germany

^[2] Imecc Unicamp, Dept Matemat, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Mathematics of Control, Signals, and Systems (MCSS); v. 30, n. 4 DEC 2018.
• Citações Web of Science: 1

Resumo

Invariance entropy is a measure for the smallest data rate in a noiseless digital channel above which a controller that only receives state information through this channel is able to render a given subset of the state space invariant. In this paper, we derive a lower bound on the invariance entropy for a class of partially hyperbolic sets. More precisely, we assume that Q is a compact controlled invariant set of a control- affine system whose extended tangent bundle decomposes into two invariant subbundles E + and E0- with uniform expansion on E + and at most subexponential expansion on E0-. Under the additional assumptions that Q is isolated and that the u- fibers of Q vary lower semicontinuously with the control u, we derive a lower bound on the invariance entropy of Q in terms of relative topological pressure with respect to the unstable determinant. Under the assumption that this bound is tight, our result provides a first quantitative explanation for the fact that the invariance entropy does not only depend on the dynamical complexity on the set of interest. (AU)

• Processo FAPESP: 16/11135-2 - Sistemas lineares em grupos de Lie e estruturas quase-Riemannianas
• Beneficiário: Adriano João da Silva
• Modalidade de apoio: Auxílio à Pesquisa - Regular