Yuu Miino, Daisuke Ito, Hiroyuki Asahara, Takuji Kousaka, Tetsushi Ueta, A general method to stabilize unstable periodic orbits for switched dynamical systems with a periodically moving threshold, John Wiley & Sons, Inc., International Journal of Circuit Theory and Applications, 1-14, Oct. 2018.
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. 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.