Upper and lower estimates for invariance entropy
The invariance entropy of a control system is a quantity that measures the smallest data rate necessary for keeping the system by feedback control in a given compact invariant set of the state space. The authors provide upper and lower bounds on this invariance entropy in the case of systems defined on arbitrary smooth manifolds, thereby extending results available in the case of Euclidean space. Tools from differential geometry are used to derive an upper bound depending on a Riemannian metric, and a lower bound depending on a volume form. Applications are described to the study of bilinear control systems through their projection on the unit sphere, and control-affine systems in dimension one.
scientific article; zbMATH DE number 5888334