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Phase Space Transport and Control of Escape From a Potential Well.


pdf icon Phase Space Transport and Control of Escape From a Potential Well. (710 K)
Frey, M. R. R.; Simiu, E.

Physica D, Vol. 95, 128-143, 1996.

Keywords:

building technology; escape; control systems; dynamical systems; Melnikov function; stochastic differential equations; stability; chaos

Abstract:

A framework for controlling a nonlinear dynamical system against escape from a potential well is presented based on reducing the phase space transport across the separatrix associated with the potential well. A bandlimited open-loop control with finite lag is considered for systems with weak additive stationary forcing including, specifically, the colored Gaussian case. The related multiplicative, closed-loop control problem is shown to reduce to an open-loop problem. A numerical example based on the Duffing oscillator is presented to illustrate the theory.