Nonlinear observer for system of the Van der Pol oscillators
Journal Title: Дослідження в математиці і механіці - Year 2016, Vol 21, Issue 1
Abstract
The problem of velocities determination for interconnected Van der Pole oscillators by known data is considered as observation problem. Such systems arise on modelling of many cyclical biological or physical processes. A new method — a synthesis of invariant relations is used to design nonlinear observer. The method allows us to represent unknowns as a function of known quantities. The scheme of the construction of invariant relations consists in the expansion of the original dynamical system by equations of some controlled subsystem (integrator). Control in the additional system is used for the synthesis of some relations that are invariant for the extended system and have the attraction property for all of its trajectories. Such relations are considered in observation problems as additional equations for unknown state vector of initial oscillators ensemble. To design the observer, first we introduce a observer for unique Van der Pole oscillator and prove its exponential convergence. This observer is then extended on several coupled Van der Pole oscillators. The performance of the proposed method is investigated by numerical simulations.
Authors and Affiliations
N. V. Zhogoleva
Keywords
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