A clown sits precariously atop his unicycle, stopping at the viewing stand to get a few more laughs with his antics. The discerning observer notices, however, that the clown never actually stops. Rather, he moves slightly ahead and then back and then ahead again in a seemingly uncoordinated, jerky fashion. In fact, these motions are precise corrections the clown makes to stabilize his otherwise unstable vertical perch. Many examples of this type of action-reaction behavior come to mind in everyday experience, from the tightrope walker in the same circus to a waiter one-handedly whisking away a wobbling tray loaded with dishes. The clown's balancing act provides a good analogy for newly developed methods for controlling a class of system behavior, called chaos, which was previously assumed to be beyond control. Contrary to the traditional view of chaos as totally random activity, the chaotic systems now under study, called deterministic chaotic systems, have been found to exhibit an underlying order that is not apparent to the casual observer. Yet despite their underlying order, these deterministic chaotic systems are so sensitive to initial conditions that predicting their long-term behavior is essentially impossible. Deterministic chaotic systems are as diverse as chaotic lasers, arrhythmically beating hearts, and oscillatory chemical reactions.
A new phase in the study of chaotic behavior is now unfolding as researchers have learned how to control chaos in a wide range of physical and biological systems. It is possible to stabilize otherwise unstable states in chaotic systems by applying a feedback algorithm that is analogous to the clown's balancing act. Unstable periodic states of chaotic systems can be stabilized with small, controlled perturbations to a system parameter, transforming irregular chaotic behavior into regular periodic oscillations.
Like the clown maintaining his perch, a system in a particular periodic state can be stabilized by making precise corrections in position. However, the correction is not made in Euclidean space but in a mathematical space defined by dynamical variables that characterize a given system. These techniques have been used to stabilize steady beams in high-powered lasers, and current work offers the possibility of extending the regime of stable burning in combustion--with potential applications ranging from power plant burners to the business end of a rocket.
One of the most attractive features of the new control algorithms is that they can be applied without knowing the governing equations of a system. Although control methods had been developed earlier, these required an accurate model of the system so that the corresponding mathematical equations could be suitably
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