Abstract

The problem of finding nonlinear resonances is closely related to the problem of optimal control of nonlinear dynamical systems. Among modern control methods, the nonfeedback methods are being developed intensively for controlling dynamics in nonautonomous systems. It is common for these methods to add parametric perturbations at a frequency resonant to the driving force. Recently, a new approach to the nonfeedback control has been applied [1]. It has been shown that a slow modulation of the control parameter can also stabilize unstable periodic orbits. But this can been achieved only in an inertial system, for example, in a laser with small relaxation rates.

© 1998 IEEE