| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [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
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | Mathematics of Control, Signals, and Systems (MCSS); v. 30, n. 4 DEC 2018. |
| Web of Science Citations: | 1 |
| Abstract | |
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) | |
| FAPESP's process: | 16/11135-2 - Linear systems on Lie groups and almost-Riemannian structures |
| Grantee: | Adriano João da Silva |
| Support Opportunities: | Regular Research Grants |