Chattering phenomenon in the sliding control of manipulators. Analysis via a stochastic modelling

In order to get some new results on the chattering phenomenon which appears in the sliding control of manipulators, it is suggested to use a sliding equation in the form of a stochastic differential equation excited by a Gaussian white noise. The problem so refers to the stochastic Hamilton principle and the dynamic programming, but here, in an engineering mathematics approach, one proposes an alternative via the dynamical equations of the state moments. One applies Hamilton's principle expressed in terms of small deviations from the nominal reference trajectory, and the point of importance is that one refers to Taylor's expansions up to the third order. The main conclusion of this analysis is an improvement of the control and the introduction of new constraints on the selection of the coefficients of the sliding equation.