Invariance entropy of hyperbolic control sets

Hyperbolic Chain Control Sets on Flag Manifolds

“…To provide a formula for the invariance entropy of the hyperbolic chain control sets on F , we use the following result from [12].…”

“…Invariance entropy, in the spirit of the preceding paragraph, measures the smallest rate of information about the state, above which a controller is able to prevent trajectories from leaving a given set (cf. [6,9,12,15]). In [12], we proved a result that is very much in the spirit of Bowen's results about entropy on uniformly hyperbolic sets of dynamical systems.…”

“…[6,9,12,15]). In [12], we proved a result that is very much in the spirit of Bowen's results about entropy on uniformly hyperbolic sets of dynamical systems. We showed that in order to keep a system inside a uniformly hyperbolic set of complete controllability with an information rate as small as possible, no strategies have to be conceived more complicated than stabilization at periodic trajectories.…”

Minimal data rates and entropy in digitally networked systems

“…The paper at hand reports on the most recent developments in the theory of feedback and invariance entropy. Section 2 presents a result, proven in [3], which gives an explicit formula for the IE of a uniformly hyperbolic chain control set of a control-affine system. In Section 3, a brief summary of the paper [5] is given, which extends the concept of IE from single feedback loops to networks of physically uncoupled systems.…”

Bounds for invariance pressure

“…A basic reference for invariance entropy is Kawan's monograph [18]; here also the relation to minimal data rates is explained which gives the main motivation from applications. Further references include the seminal paper Nair, Evans, Mareels and Moran [19] as well as Colonius and Kawan [9] and da Silva and Kawan [13], [14]. In the latter paper, robustness properties in the hyperbolic case are proved.…”