Phase Space Transport and Control of Escape From a Potential Well.
Phase Space Transport and Control of Escape From a
Frey, M. R. R.; Simiu, E.
Physica D, Vol. 95, 128-143, 1996.
building technology; escape; control systems; dynamical
systems; Melnikov function; stochastic differential
equations; stability; chaos
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.