Chaos Control by Nonfeedback Methods in the Presence of Noise |
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| Institution: | 1. Machine Dynamics Laboratory, Department of Applied Mechanics, Indian Institute of Technology, Madras 600 036, India;1. Universidad Diego Portales, UDP, Facultad de Ingeniería y Ciencias, Av. Ejército Libertador 441, Casilla 298-V, Santiago, Chile;2. Universidad de Santiago de Chile, USACH, Departamento de Matemática, Casilla 307, Correo 2, Santiago, Chile;3. Universidade de Brasília, Departamento de Matemática, Campus Universitário Darcy Ribeiro, Asa Norte 70910-900, Brasília-DF, Brazil;1. Organization for the Strategic Coordination of Research and Intellectual Property, Meiji University, Kawasaki 214-8571, Japan;2. Department of Electronics and Bioinformatics, Meiji University, Kawasaki 214-8571, Japan;3. Department of Mechanical and Energy System Engineering, Oita University, Oita 870–1192, Japan;1. Department of Applied Mathematics, VŠB - Technical University of Ostrava, 17. listopadu 15/2172, 708 33 Ostrava, Czech Republic;2. IT4Innovations, VŠB - Technical University of Ostrava, 17. listopadu 15/2172, 708 33 Ostrava, Czech Republic;3. AGH University of Science and Technology, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30-059 Kraków, Poland |
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| Abstract: | 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. |
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