Linear finite fractional difference predictors for model predictive control

In this paper, a Grünwald-Letnikov-originated fractional-order difference (FD) is modeled with finite-length approximators called a finite fractional difference (FFD) and a normalized finite fractional difference (NFFD), whose time-domain structure enables their effective employment in the prediction process for linear discrete-time fractional-order state-space systems. The main, original contribution is the analytical derivation of a bank of long-range predictors for FFD/NFFD-based state-space systems. The predictors can constitute a basis for the synthesis of any linear model(-based) predictive control (MPC) strategy. We illustrate the usefulness of the predictors in the EHPC design, admitting open-loop stable nonminimum phase plants.