Dynamical Systems and Nonlinear Control Theory
Mohr, Ryan and Mezi'c, Igor (2010), "The use of ergodic theory in designing dynamics for search problems", Decision and Control (CDC), 2010 49th IEEE Conference on: 7300 -- 7307.
In this paper, we use tools from ergodic theory to design dynamics for searching for a target of unknown size. We show that the expected time to find a target is controlled by the local dimension of the invariant measure. The expected time to find the target behaves as -C log δ where δ is the minimum volume of the target. This relation holds in any dimension for a large class of systems. Sampling non-uniform target priors and continuous time search are discussed.