Chaos Control by Nonfeedback Methods in the Presence of Noise

Nonfeedback methods of chaos control are suited for practical applications because of their speed, flexibility, no online monitoring and processing requirements. For applications where none, no real-time, or only highly restricted measurements of the system are available, or where the system behavior is to be altered more drastically, these schemes are quite useful. These methods convert the chaotic motion to any arbitrary fixed point or periodic orbit or quasiperiodic orbit. These attributes make them promising for controlling chaotic circuits, fast electro-optical systems, systems in which no parameter is accessible for control, and so on. For possible practical applications of the control methods, the robustness of the methods in the presence of noise is of special interest. The noise can be in the form of external disturbances to the system or in the form of uncertainties due to inexact modelling of the system. In this paper, we make an analysis of the control performance of various nonfeedback methods in controlling the chaotic behavior in the presence of noise in the chaotic system. The various nonfeedback methods considered for the analysis are: addition of (i) constant force, (ii) weak periodic force, (iii) periodic delta-pulses, (iv) rectangular-pulses. The examples considered for this study are the Murali–Lakshmanan–Chua Circuit, and Duffing–Ueda oscillator.