CONTROL OF NOISY CHAOTIC MOTION IN A SYSTEM WITH NONLINEAR EXCITATIONAND RESTORING FORCES

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.