title: Series-nonuniform rational B-spline signal feedback: From chaos to any embedded periodic orbit or target point.
abstract: The self-controlling feedback control method requires an external periodic oscillator with special design, which is technically challenging. This paper proposes a chaos control method based on time series non-uniform rational B-splines (SNURBS for short) signal feedback. It first builds the chaos phase diagram or chaotic attractor with the sampled chaotic time series and any target orbit can then be explicitly chosen according to the actual demand. Second, we use the discrete timing sequence selected from the specific target orbit to build the corresponding external SNURBS chaos periodic signal, whose difference from the system current output is used as the feedback control signal. Finally, by properly adjusting the feedback weight, we can quickly lead the system to an expected status. We demonstrate both the effectiveness and efficiency of our method by applying it to two classic chaotic systems, i.e., the Van der Pol oscillator and the Lorenz chaotic system. Further, our experimental results show that compared with delayed feedback control, our method takes less time to obtain the target point or periodic orbit (from the starting point) and that its parameters can be fine-tuned more easily.
authors.affiliation: Department of Computer Science and Technology, University of Science and Technology of China, Hefei 230027, People's Republic of China.
authors.forename: Chenxi
authors.initials: C
authors.lastname: Shao
authors.affiliation: Department of Computer Science and Technology, University of Science and Technology of China, Hefei 230027, People's Republic of China.
authors.forename: Yong
authors.initials: Y
authors.lastname: Xue
authors.affiliation: Department of Computer Science and Technology, University of Science and Technology of China, Hefei 230027, People's Republic of China.
authors.forename: Fang
authors.initials: F
authors.lastname: Fang
authors.affiliation: Department of Computer Science and Technology, University of Science and Technology of China, Hefei 230027, People's Republic of China.
authors.forename: Fangzhou
authors.initials: F
authors.lastname: Bai
authors.affiliation: Department of Computer Science and Engineering, Pennsylvania State University, State College, Pennsylvania 16801, USA.
authors.forename: Peifeng
authors.initials: P
authors.lastname: Yin
authors.affiliation: Department of Modern Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China.
authors.forename: Binghong
authors.initials: B
authors.lastname: Wang