Reference tracking control and attenuation of unknown periodic disturbances in the presence of noise for unknown minimum-phase LTI plants

The rejection of unknown periodic disturbances in the plant output through adaptive feedback has been an active area of research. In most successful efforts, it is assumed that the plant model is a known LTI stable system. In this paper, we relax the assumption of stable known plant and consider the case where the plant model can be unstable with unknown parameters. We do assume, however, that the plant model is minimum phase and use the model reference adaptive control structure to meet the objectives of reference tracking and unknown periodic disturbance rejection without amplifying the effect of broadband noises. The cost of achieving these objectives is the use of overparameterization that adds to the number of computations. The main contribution of this paper is that it shows that the problem of rejecting unknown periodic disturbances can be solved for unstable plants with unknown parameters as long as they are minimum phase. Numerical examples illustrate the effectiveness of the proposed control methodology.