ℓ-Step ahead optimal robust controller for uncertain auto-regressive systems

In this article, an ℓ-step ahead optimal robust controller for uncertain linear discrete Auto-Regressive (AR) systems is presented. The novelty in the suggested scheme stems from the utilization of a lattice filter for: a) the system's identification, b) calculation of the output uncertainty interval and the computation of the optimal robust control effort. The utilized controller comprises of two parts. The first part, based on the a priori bounds of the lattice filter's reflection coefficients and the operating limits of the reference signal, calculates the set of all feasible predicted output values. The second part consists of an optimal robust controller that minimizes a properly adopted cost function, based on the predicted uncertainty intervals. The scope of the controller is to penalize the variance of the tracking error and the control effort. This computation is recursive over the length of the ℓ-step ahead time window and the number of stages of the lattice filter. Simulation studies are used to prove the efficacy of the proposed controller.