International Symposium on Nonlinear Theory and its Applications
Adaptive Control of Steady States and Slowly Varying States in the Duffing-Holmes Type System with Unstable High-Pass Filter
Elena Tama?evi?i?t?e, Ar?nas Tama?evi?ius, Gytis Mykolaitis, Skaidra Bumelien?e,
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We describe a very simple feedback controller for stabilizing unknown unstable steady states of dynamical systems. The feedback loop contains an unstable first order high-pass filter. The controller is reference-free. It does not require knowledge of the location of the states in the phase space and is suitable not only for fixed steady states but for slowly varying states as well. As a specific example we consider the damped Duffing-Holmes type oscillator and investigate it analytically, numerically and experimentally. Experiments have been performed using a simplified version of the electronic Young-Silva circuit imitating dynamical behavior of the Duffing-Holmes system.