DYNAMICS OF ADAPTIVE SYSTEMS

In this paper we introduce a simple adaptive control mechanism into nonlinear systems which are capable of complicated oscillatory states and chaotic dynamics. We show that it provides efficient regulation while displaying novel behavior. Sudden perturbations in the system's parameters can degenerate into chaotic bursts with no precursors. When such bursts occur, the system first reverberates wildly and then recovers in times that are inversely proportional to the stiffness of the control. We also exhibit a general control principle which provides a quantitative relation between the maximum amplitude of a perturbation from which a system can recover, and the speed at which it does so. © 1990 IEEE