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A general method to stabilize unstable periodic orbits for switched dynamical systems with a periodically moving threshold
Author(s) -
Miino Yuu,
Ito Daisuke,
Asahara Hiroyuki,
Kousaka Takuji,
Ueta Tetsushi
Publication year - 2018
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.2573
Subject(s) - sawtooth wave , control theory (sociology) , attractor , perturbation (astronomy) , periodic orbits , chaotic , mathematics , control of chaos , dynamical systems theory , mathematical analysis , computer science , physics , control (management) , synchronization of chaos , quantum mechanics , artificial intelligence , computer vision
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.