Optimal robust tracking for discrete-time minimum-phase plant under unknown bias and norms of external disturbance and uncertainties

This paper addresses a problem of the optimal robust tracking of a given bounded reference signal for a discrete-time minimum-phase plant with a known approximate nominal model under a bounded and biased external disturbance and coprime factor perturbations. The bias and norm of the external disturbance and the gains of the perturbations are assumed to be unknown. The control criterion is the worst-case asymptotic tracking error in the class of the disturbances and perturbations under consideration, which depends on the above unknown parameters and the reference signal. A solution of the optimal tracking problem with a given accuracy is based on optimal errors quantification within the 1-theory of robust control, polyhedral estimation of the unknown parameters, and treating the control criterion as the identification criterion.