Introduction to Chaos Control and Anti-Control

Bifurcation Control: Theories, Methods, and Applications

“…Bifurcation control refers to the task of designing a controller to modify the bifurcation properties of a given nonlinear system, thereby achieving some desirable dynamical behaviors. Typical bifurcation control objectives include delaying the onset of an inherent bifurcation [Tesi et al, 1996;, introducing a new bifurcation at a preferable parameter value [Abed, 1995;Chen et al, 1998b], changing the parameter value of an existing bifurcation point [Chen & Dong, 1998;Moiola & Chen, 1996], modifying the shape or type of a bifurcation chain , stabilizing a bifurcated solution or branch [Abed & Fu, 1986, 1987Abed et al, 1994;Kang, 1998aKang, , 1998bLaufenberg et al, 1997;Littleboy & Smith, 1998;Nayfeh et al, 1996;Senjyu & Uezato, 1995], monitoring the multiplicity [Calandrini et al, 1999;Moiola & Chen, 1998], amplitude [Berns et al, 1998a;Moiola et al, 1997a], and/or frequency of some limit cycles emerging from bifurcation [Cam & Kuntman, 1998;Chen & Moiola, 1994;Chen & Dong, 1998b], optimizing the system performance near a bifurcation point [Basso et al, 1998], or a combination of some of these objectives Chen 1998Chen , 1999aChen , 1999b. Bifurcation control with various of objectives have been implemented in experimental systems or tested by using numerical simulations in a great number of engineering, biological, and physicochemical systems; examples can be named in chemical engineering [Alhumaizi & Elnashaie, 1997;Moiola et al, 1991], mechanical engineering [Liaw & Abed, 1996;Wang et al, 1994b;Cheng, 1990;Gu et al, 1997, Hackl et al, 1993…”

Controlling chaos and voltage collapse using an ANFIS-based composite controller-static var compensator in power systems

“…Computation of the k 1 was done by using Eq. (12), the results are summarized in Table 6. Table 6 shows that the k 1 for V ref = 0.98 pu was obtained at the value of j0.2 pu.…”

“…Furthermore, the modeling of chaotic behavior using recurrent neural networks in power systems was previously studied in [10]. Practical techniques for recognizing and classifying chaotic behavior were identified by Parker and Chua [11], while control and anti-control chaos were developed by Chen [12]. One scheme of chaos utility was used on electrical systems for smelting based on chaos control.…”

The Appliance of Duffing Chaotic Detection system in displacement measurement of capacitance sensor

“…The chaotic system is sensitive to sine signals of specific frequency. So it is used as a detection system face to weak signal [3,4]. Various parameters of the weak signal can be detected from the dynamic behavior of chaotic system through some appropriate signal processing methods [5].…”