Fuzzy Control of Chaos

Chaos control exploits the sensitivity to initial conditions and to perturbations that is inherent in chaos as a means to stabilize unstable periodic orbits within a chaotic attractor. The control can operate by altering system variables or system parameters, and either by discrete corrections or by continuous feedback. Many methods of chaos control have been derived and tested [Chen & Dong, 1993; Lindner & Ditto, 1995; Ogorzałek, 1993]. Why then consider fuzzy control of chaos? A fuzzy controller works by controlling a conventional control method. We propose that fuzzy control can become useful together with one of these other methods — as an extra layer of control — in order to improve the effectiveness of the control in terms of the size of the region over which control is possible, the robustness to noise, and the ability to control long period orbits. In this paper, we put forward the idea of fuzzy control of chaos, and we provide an example showing how a fuzzy controller applying occasional proportional feedback to one of the system parameters can control chaos in Chua’s circuit.