On the parameter convergence properties of a combined VS/adaptive control scheme during sliding motion

The effects of the use of a variable structure control component within an adaptive control scheme, previously proposed by the authors (1992, 1995), are investigated in this paper. The discontinuous control action does not allow the explicit identification of the coefficients of the filters, but only the identification of the so-called equivalent control coinciding with the ideal control. By coupling the variable structure control strategy with a continuous parameter adjustment mechanism it is instead possible to obtain an equivalent control which, during the sliding motion, turns out to be equal to a suitably constructed prediction error. As long as the parameter adaptation is driven by both the tracking error (which vanishes in finite time) and the prediction error, then the controller parameters prove to be exponentially convergent to the ideal values, provided that the reference signal is sufficiently persistently exciting.