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Automatica, Vol.45, No.4, 1097-1099, 2009
A Kushner approach for small random perturbations of the Duffing-van der Pol system
The stochastic version of the Duffing-van der Pol system (SDvdP), which assumes the structure of a non-linear stochastic differential equation, is an appealing and a standard case from the stochastic systems' point of view, since it involves linear and non-linear vector fields, i.e. system non-linearities state, independent and state-dependent stochastic accelerations. This paper discusses and explores the efficacy of three non-linear filters, which are developed using the Kushner equation, for the stochastic differential system of concern here. This paper introduces the notion of a qualitative analysis to decide a structure of the observation equation for non-linear stochastic filtering as well. (C) 2009 Elsevier Ltd. All rights reserved.