A general method to stabilize unstable periodic orbits for switched dynamical systems with a periodically moving threshold. (14th October 2018)

• Record Type: Journal Article
• Authors: Miino, Yuu; Ito, Daisuke; Asahara, Hiroyuki; Kousaka, Takuji; Ueta, Tetsushi
• Is Part Of: International journal of circuit theory and applications. Volume 46:Number 12(2018)
• Page Start: 2380
• Page End: 2393
• Publication Date: 2018-10-14
• Subjects: circuit implementation -- controlling chaos -- numerical simulation -- switched dynamical system; Electric circuit analysis -- Periodicals; 621.319205
• DOI: 10.1002/cta.2573
• Languages: English
• ISSNs: 0098-9886

Abstract

Summary: In the previous study, a method to control chaos for switched dynamical systems with constant threshold value has been proposed. In this paper, we extend this method to the systems including a periodically moving threshold. The main control scheme is based on the pole placement; then, a small control perturbation added to the moving threshold value can stabilize an unstable periodic orbit embedded within a chaotic attractor. For an arbitrary periodic function of the threshold movement, we mathematically derive the variational equations, the state feedback parameters, and a control gain by composing a suitable Poincaré map. As examples, we illustrate control implementations for systems with thresholds whose movement waveforms are sinusoidal and sawtooth‐shape, and unstable one and two periodic orbits in each circuit are stabilized in numerical and circuit experiments. In these experiments, we confirm enough convergence of the control input. Abstract : In the previous study, a method to control chaos for switched dynamical systems with constant threshold value has been proposed. In this paper, we extend this method to the systems including a periodically moving threshold. As examples, we illustrate control implementations for systems with thresholds whose movement waveforms are sinusoidal and sawtooth‐shape, and unstable one and two periodic orbits in each circuit are stabilized in numerical and circuit experiments.