Melnikov-Based Open-Loop Control of Escape for a Class of Nonlinear Systems.
Melnikov-Based Open-Loop Control of Escape for a Class
of Nonlinear Systems.
Simiu, E.; Franaszek, M.
American Society of Mechanical Engineers. Design
Engineering Technical Conferences. Proceedings.
DE-Vol. 84-1. Book No. H1000A. 1995, Cudney, H. H.;
Sinha, S. C.; Cusumano, J. P.; Pfeiffer, F.,
Editor(s)(s), 897-902 pp, 1995.
Journal of Dynamic Systems, Measurement, and Control,
Vol. 119, 590-594, September 1997.
Sponsor:Office of Naval Research, Washington, DC
building technology; control; dynamical systems;
nonlinear dynamics; random vibration; stochastic
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. We propose an open-loop control method for
reducing these probabilities. The method is applicable
to stochastic systems whose dissipation- and
excitation-free counterparts have homoclinic or
heteroclinic orbits. The Melnikov relative scale
factors are system properties containing information on
the frequencies of the random forcing spectral
components that are most effective in inducing escapes.
This information is useful in practice even if the
dissipation and excitation terms are relatively large.
An ideal open-loop control force applied to the system
would be equal to the negative of a fraction of the
exciting force from which the ineffective components
have been filtered out. Limitations inherent in any
practical control system make it impossible to achieve
such an ideal control. Nevertheless, numerical
simulations show that substantial advantages can be
achieved in some cases by designing control systems that
take into account the information contained in the
Melnikov scale factors.