title: Adaptive time-delayed stabilization of steady states and periodic orbits.
abstract: We derive adaptive time-delayed feedback controllers that stabilize fixed points and periodic orbits. First, we develop an adaptive controller for stabilization of a steady state by applying the speed-gradient method to an appropriate goal function and prove global asymptotic stability of the resulting system. For an example we show that the advantage of the adaptive controller over the nonadaptive one is in a smaller controller gain. Second, we propose adaptive time-delayed algorithms for stabilization of periodic orbits. Their efficiency is confirmed by local stability analysis. Numerical examples demonstrate the applicability of the proposed controllers.
authors: School of Electrical Engineering, Tel Aviv University, Tel Aviv 69978, Israel.
authors: Anton
authors: A
authors: Selivanov
authors: Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany.
authors: Judith
authors: J
authors: Lehnert
authors: Department of Theoretical Cybernetics, Saint-Petersburg State University, St. Petersburg 199034, Russia and Institute for Problems of Mechanical Engineering, Russian Academy of Sciences, Bolshoy Avenue, 61, Vasilievsky Ostrov, St. Petersburg 199178, Russia.
authors: Alexander
authors: A
authors: Fradkov
authors: Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany.
authors: Eckehard
authors: E
authors: Schöll