A general method to stabilize unstable periodic orbits for switched dynamical systems with a periodically moving threshold

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 Poincare 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.

This is the peer reviewed version of the following article: Miino Y, Ito D, Asahara H, Kousaka T, Ueta T. A general method to stabilize unstable periodic orbits for switched dynamical systems with a periodically moving threshold. Int J Circ Theor Appl. 2018;46:2380‐2393., which has been published in final form at https://doi.org/10.1002/cta.2573. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.