Overparameterized robust MRAC for rejection of unknown periodic disturbances acting on unknown plants in the presence of noise

The problem of rejecting unknown sinusoidal disturbances in the output of an unknown LTI system which is also corrupted by wide-band noise has received a lot of interest in the recent years. Most of the successful efforts proposed up to now assume that the model of the LTI system is stable and is known exactly. This paper shows how an overparameterized classical robust model-reference adaptive control (MRAC) scheme can handle the problem of simultaneous reference-model tracking and unknown disturbance suppression. The results are applicable to a plant whose dominant modeled part is unknown and possibly unstable, yet has stable zeros and a known relative degree. Some considerations are taken to avoid boosting broadband noise effects on the plant output and to improve robustness with respect to plant unstructured unmodeled dynamics. The architecture of the classical MRAC is employed together with overparameterization of the controller and an auxiliary control input for performance improvement. The performance and robustness properties of the scheme are discussed and numerical simulations are given to demonstrate the efficacy of the scheme.