
Accession Number : ADA194534
Title : Minimizing Escape Probabilities: A Large Deviations Approach,
Corporate Author : BROWN UNIV PROVIDENCE RI LEFSCHETZ CENTER FOR DYNAMICAL SYSTEMS
Personal Author(s) : Dupuis, Paul ; Kushner, Harold
PDF Url : ADA194534
Report Date : Oct 1987
Pagination or Media Count : 33
Abstract : This document considers the problem of controlling a possibly degenerate diffusion process so as to minimize the probability of escape over a given time interval. It is assumed that the control acts on the process through the drift coefficient, and that the noise coefficient is small. By developing a large deviations type theory for the controlled diffusion, the authors obtain several results. The limit of the normalized log of the minimum exit probability is identified as the value I of an associated (deterministic) differential game. Furthermore, the authors identify a deterministic (and epsilon independent) mapping g from the sample values epsilon w (s), 0 or = S or = t, into the control space such that if we define the control used at time t by u(t) = g(epsilon w(s), 0 or = S , or = t), then the resulting control process is progressively measurable and delta optimal (in the sense that the limit of the normalized log of the exit probability is within delta of I).
Descriptors : *CONTROL THEORY, COEFFICIENTS, CONTROL, DIFFERENTIAL EQUATIONS, DIFFUSION, DRIFT, EXITS, MEASUREMENT, NOISE, PROBABILITY, TIME INTERVALS, APPLIED MATHEMATICS, WHITE NOISE, PROBLEM SOLVING
Subject Categories : Cybernetics
Distribution Statement : APPROVED FOR PUBLIC RELEASE