MODEL-REFERENCE ADAPTIVE-CONTROL FOR PLANTS WITH UNKNOWN RELATIVE DEGREE

One of the basic assumptions in stable model reference adaptive contro l (MRAC) that the relative degree n of the modeled part of the plant is known exactly and matches that of the reference model is relaxed by the development of a new MRAC scheme which requires only an upper bou nd n(u) for n*. This is done at the expense of updating additional pa rameters and projecting some of the estimated parameters onto appropri ate convex sets in the parameter space These convex sets can be develo ped without using any a priori knowledge about the plant parameters. F urthermore, when a lower bound n(l) in addition to an upper bound for n is known, the number of the estimated parameters can be reduced co nsiderably. The new MRAC scheme guarantees signal boundedness and zero residual tracking error. In addition, it is robust with respect to pl ant uncertainties provided a modified adaptive law is used to update t he controller parameters.