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Melnikov-Based Open-Loop Control of Escape for a Class of Nonlinear Systems.

pdf icon Melnikov-Based Open-Loop Control of Escape for a Class of Nonlinear Systems. (552 K)
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.


Office of Naval Research, Washington, DC


building technology; control; dynamical systems; nonlinear dynamics; random vibration; 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. 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.