Tracking and controlling unstable steady states of dynamical systems |
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| Affiliation: | 1. Nonlinear Electronics Laboratory, Center for Physical Sciences and Technology, LT-01108 Vilnius, Lithuania;2. Department of Physics, Vilnius Gediminas Technical University, LT-10223 Vilnius, Lithuania;1. School of Mathematical Sciences, Shandong Normal University, Ji’nan 250014, PR China;2. Research Center on Logistics optimization and Prediction of Engineering Technology, Ji’nan, Shandong 250014, PR China;1. Department of Instrumentation and Applied Physics, Indian Institute of Science, Bangalore, India;2. Computational Mechanics Lab, Department of Civil Engineering, Indian Institute of Science, Bangalore, India;1. School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, PR China;2. School of Mathematics Science, University of Electronic Science and Technology of China, Chengdu 610054, PR China;3. School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 610054, PR China;4. School of Mathematics and Computer Science, Yunnan University of Nationalities, Kunming 650031, PR China |
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| Abstract: | An adaptive controller for stabilization of unknown unstable steady states (spirals, nodes and saddles) of nonlinear dynamical systems is considered and its robustness under the changes of the location of the fixed point in the phase space is demonstrated. An analog electronic controller, based on a low-pass filter technique, is described. It can be easily switched between a stable and an unstable mode of operation for stabilizing either spirals/nodes or saddles, respectively. Numerical and experimental results for two autonomous systems, the damped Duffing–Holmes oscillator and the chaotic Lorenz system, are presented. |
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| Keywords: | Dynamical systems Unstable steady states Control |
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