Accession Number:

ADA046449

Title:

Stochastically Perturbed Limit Cycles,

Descriptive Note:

Corporate Author:

PURDUE UNIV LAFAYETTE IND DEPT OF MATHEMATICS

Personal Author(s):

Report Date:

1977-08-01

Pagination or Media Count:

20.0

Abstract:

An important question in the stability and control of stochastic systems is the determination of the limiting long time behavior of the system using a fixed control. This paper answers that question in the case of a stochastic system perturbed by a small additive noise term where the control is such that the corresponding deterministic system has a stable limit cycle. It is shown that in the limit of large time the stochastic system is near the limit cycle. This is a stability result. Moreover, one can compute approximately at which portion of the limit cycle one is most likely to be found. Further various stationary averages can be computed. These results will be of use in designing approximate controls for stationary stochastic control systems. As a by-product, the above work allows one to deduce some additional results on singular perturbation problems in partial differential equations. Author

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE