Control of Chua's Circuit

Abstract

This paper considers the control of a polynomial variant of the original Chua's circuit. Both state space techniques and input-output techniques are presented. It is shown that standard control theory approaches can easily accommodate a chaotic system. Furthermore, it is shown that a harmonic balance approach could predict the period doubling phenomenon and onset of the double scroll chaos, as well as providing a control approach.

Model Reduction Methods for Chaotic Systems

“…With this in mind it is suggested that the linear nonlinear decoupling approach discussed above will probably be the most fruitful area for stabilizing higher dimensional attractors. In particular, the methods used in [9] and [12], which are based on harmonic balance, are probably a good place to begin considering robustness of chaotic attractors to modelling errors in the control design. The purpose of this paper has been to lay some framework for the development of model reduction methods for chaotic systems.…”

“…This will be called preservation of frequency response, and will only be applicable to systems that can be separated into a dynamic linear forward path with a single static nonlinearity in the feedback path. The idea is to reduce the order of the linear forward path while maintaining its frequency response characteristic with respect to the describing function of the static nonlinearity [11,12,9]. The problem is that all systems cannot be easily decomposed into this form.…”

“…This approach is most applicable to stabilizing a chaotic system to some predefined unstable operating point and thus allowing standard linear small perturbation control design [12]. Although it can be applied to any system, many standard linear model reduction methods are known to have difficulty in reducing unstable systems.…”

Computer Simulations of Chua’s Circuits with Small-World Connection

“…So, the spiral waves have initiated progressive research in all kinds of nonlinear systems [7], [8]. On the other hand, Chua's circuits have been applied in many aspects, such as controlling chaos [9], secure communication via Chua's circuit [10], trajectory recognition via array of Chua's circuits [11]. Therefore, it has significant meaning to study the properties of Chua's circuits with small-world connection.…”

Output feedback form of Chua’s circuit and modular adaptive control of chaos using single measurement

“…doi:10.1016/j.chaos.2005.08.139 using a unified canonical feedback control strategy. Hartley and Mossayebi [12] used both state space techniques and input-output techniques to control polynomial variant of the original ChuaÕs circuit. A feedback controller to suppress chaotic states of a modified ChuaÕs circuit system is given in [13].…”