Control of chaos in noisy flows

A nonlinear dynamical system in a chaotic state is very sensitive to errors. Inherent noise in physical systems gives rise to difficulties for stabilizing chaotic systems onto desired unstable periodic orbits, particularly with large eigenvalues. The idea of adjusting the system state more frequently to eliminate error deviations from a desired orbit is utilized and given in variational form for flows. This control scheme acting on multiple sections can cope with relatively large noise levels. A Duffing oscillator and a parametrically excited pendulum are used in numerical studies. The relationship between controllable noise levels and the number of control sections is discussed. {} 1996 The American Physical Society.