In this study we examine the complex and chaotic oscillations of a dyn
amical system with nonlinear excitation and restoring forces for the p
urpose of controlling these oscillatory states. The physical system, m
odeled as a system of first-order nonlinear ordinary differential equa
tions, takes into account a geometric nonlinearity in the restoring fo
rce, a quadratic viscous drag, and a harmonic excitation force. It is
controlled using small perturbations about a selected unstable cycle a
nd control is instigated for periodic cycles of varying periodicities
The controller, when applied on the dynamical system with additive ran
dom noise in the excitation, successfully controls the system with noi
se levels in excess of 5% of the total energy, giving the first eviden
ce that (stochastic) control of these systems is possible. (C) 1997 Am
erican Institute of Physics.