Efficient Open-Loop Control for a Class of Stochastic Multistable Systems.
Efficient Open-Loop Control for a Class of Stochastic
Simiu, E.; Franaszek, M.
University of Victoria. CANCAM 95. Canadian Congress
of Applied Mechanics, 15th. Proceedings. Volume 2.
May 28-June 1, 1995, Victoria, British Columbia,
Tabarrok, B.; Dost, S., Editor(s)(s), 780-781 pp, 1995.
Sponsor:Office of Naval Research, Washington, DC
building technology; chaos; control; dynamical systems;
exit rate; Melnikov processes; stochastic dynamics
The performance of certain nonlinear stochastic systems
is deemed acceptable if, during a specified time
interval, the systems have sufficiently low
probabilities of escape from a preferred region of phase
space. These probabilities can be reduced by using an
appropriate control system. We propose a Melnikov-based
approach to achieving an efficient open-loop control.
The approach is applicable to the wide class of
multistable systems that have dissipation- and
excitation-free counterparts possessing homoclinic or
heteroclinic orbits. That class includes, e.g., the rf
Josephson junction and the Duffing equation, and higher-
and infinitely-dimensional systems. We review the
theoretical basis of our approach, use numerical
simulations to test its effectiveness for the
paradigmatic case of the stochastically excited Duffing
equation, and discuss our results.