Identification of van der Pol oscillator network parameters

Abstract

The problem of state observation and parameters identification of an oscillatory system consisting of coupled van der Pol oscillators is considered. The unknowns are: velocity of oscillations and parameters that characterize the threshold values for displacements of network's oscillators at which the damping forces change sign. An invariant relations method for simultaneous of the state and parameters estimation is used. Such approach is based on dynamical extension of original system and synthesis of appropriate invariant relations, from which the unknowns can be expressed as a function of the known quantities on the trajectories of extended system during the observed motion. The stability property is formally checked considering the oscillatory behavior of the system. On the first step the corresponding observation and identification problems are solved for one of autonomous van der Pol oscillator, further, the results obtained are extended to a system of interconnected oscillators. The simulation results confirm efficiency of the proposed scheme of nonlinear observer and identifier design for network of oscillators.