Controlling Chaos in a Temporally Irregular Environment and its Application to Engineering Systems

Abstract

Responses of many man-made systems (e.g., ships or oil-drilling platforms), when subject to irregularly time varying environments, can be described by irregularly driven dynamical systems. Consequently, failures of such systems (e.g., capsize of a ship or collapse of a platform), under increasingly severe environmental conditions, come about when the system state escapes from a destroyed chaotic attractor located in some favorable region of the phase space. In this paper we review a control strategy [see Ding et al. (1994) for more details], based on a previous method of chaos control, which can prevent such failures from taking place. The key feature of the new method is the incorporation of prediction of the evolution of the environment. This makes effective operation of the control possible even when the temporal behavior of the environment has substantial irregularity. We illustrate the ideas using ship capsizing as an example. We then apply the technique to a nonlinear oscillator model of a ship-borne crane. The purpose here is to eliminate uncertainties associated with sudden changes (crises) in attractor structures as a result of environmental drift.