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The use of ergodic theory in designing dynamics for search problems

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2 Author(s)
Mohr, R. ; Dept. of Mech. Eng., Univ. of California, Santa Barbara, CA, USA ; Mezic, I.

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.

Published in:

Decision and Control (CDC), 2010 49th IEEE Conference on

Date of Conference:

15-17 Dec. 2010