Indirect adaptive non-linear control of discrete time systems containing a dead-zone

In this paper an indirect adaptive output feedback control result which applies to discrete time systems containing a dead-zone nonlinearity and linear dynamics is presented. A plant parametrization that is linear in a set of unknown parameters is first developed. This is accomplished by forcing the regional descriptions of the dead-zone to be entirely contained in the definition of a regressor. This is convenient for estimation, since adaptation for the parameters of the separate regions of the non-linearities is implicitly accommodated by the regressor. Unfortunately, this parametrization necessitates multiple estimates of the zeros of the plant. To overcome the difficulty of designing a feedback/feedforward controller given multiple estimates of the zeros, we implement a non-linear ‘zero-resolving’ prefilter. This prefilter to the plant allows one to design a feedback/feedforward controller based on one set of zeros.