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Efficient Open-Loop Control for a Class of Stochastic Multistable Systems.

pdf icon Efficient Open-Loop Control for a Class of Stochastic Multistable Systems. (227 K)
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.


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.