| Abstract [eng] |
Stabilization of unstable equilibrium (UEQ) of dynamical systems is an important problem in basic science and engineering applications, if periodic or chaotic oscillations are unacceptable behaviours. There is a need for adaptive, i.e. model-independent and reference-free methods, automatically tracing and stabilizing unknown UEQ. Therefore fast feedback methods using unstable filter control, stable filter control and proportional feedback control techniques, as well as synergetic methods, based on combined unstable feedback control and stable filter control techniques also with an auxiliary differentiator in the feedback loop for stabilizing equilibrium with a priori unknown coordinates of both weakly and strongly damped dynamical systems, were developed. Synchronization is a universal and very common phenomenon. Though in the most cases synchronization plays a positive role, sometimes it has a negative impact. Strong synchronization in the human brain is an example. It is widely believed that synchrony of spiking neurons in a neuronal population causes the symptoms of the Parkinson’s disease. Therefore, the development of the methods and practical techniques for controlling, more specifically, for suppressing synchrony of coupled oscillators, in general, and particularly with possible application to neuronal arrays, is of great importance. Methods for destroying synchrony or suppressing oscillations in mean-field coupled oscillators were developed. |
