Control of Exits From a Safe Region: A Stochastic Melnikov Approach.
Control of Exits From a Safe Region: A Stochastic
Franaszek, M.; Frey, M. R. R.; Simiu, E.
Control of Oscillations and Chaos (COC'97).
International Conference, First (1st). Volume 3 of 3.
97TH8329. Proceedings. Institute of Electrical and
Electronics Engineers (IEEE). August 27-29, 1997, St.
Petersburg, Russia, Chernousko, F. L.; Fradkov, A. L.,
Editor(s)(s), 569-572 pp, 1997.
exits; chaos; control; dynamical systems; stochastic
process; structural engineering
For a wide class of stochastically excited multistable
systems the Melnikov necessary condition for chaos
contains information on the effectiveness of the various
frequency components of the excitation in inducing exits
from a potential well. This information can be used to
develop an open-loop control procedure aimed at reducing
the system's exit rate. The Melnikov approach is based
on a first-order approximation and is in principle
applicable only for small perturbations. Nevertheless,
results of simulations show that it is valid
qualitatively even if the excitations are relatively
large. We test the effectiveness of the proposed
control procedure, and briefly review the use of the
phase space flux factor to assess or design the control