In this paper we consider three di®erent synchronization problems consisting in designing a nonlinear feedback unidirectional coupling term for two (possibly chaotic) dynamical systems in order to drive the trajectories of one of them, the slave system, to a reference trajectory or to a prescribed neighborhood of the reference trajectory of the second dynamical system: the master system. If the slave system is chaotic then synchronization can be viewed as the control of chaos; namely the coupling term allows to suppress the chaotic motion by driving the chaotic system to a prescribed reference trajectory. Assuming that the entire vector field representing the velocity of the state can be modified, three different methods to define the nonlinear feedback synchronizing controller are proposed: one for each of the treated problems. These methods are based on results from the small parameter perturbation theory of autonomous systems having a limit cycle, from nonsmooth analysis and from the singular perturbation theory respectively. Simulations to illustrate the effectiveness of the obtained results are also presented.
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|Titolo:||Synchronization problems for unidirectional feedback coupled nonlinear systems|
|Rivista:||DYNAMICS OF CONTINUOUS, DISCRETE AND IMPULSIVE SYSTEMS. SERIES A: MATHEMATICAL ANALYSIS|
|Citazione:||Makarenkov, O., Nistri, P., & Papini, D. (2008). Synchronization problems for unidirectional feedback coupled nonlinear systems. DYNAMICS OF CONTINUOUS, DISCRETE AND IMPULSIVE SYSTEMS. SERIES A: MATHEMATICAL ANALYSIS, 15, 453-468.|
|Appare nelle tipologie:||1.1 Articolo in rivista|