Robust model predictive control of uncertain fractional systems: a thermal application

In this study, a robust model predictive control of fractional‐order systems with real uncertain parameters is presented. The Grünwald–Letnikov's method is used as an internal model to predict the plant future dynamic behaviour. This method consists in replacing the non‐integer derivation operator of the adopted system representation by a discrete approximation. Therefore a robust fractional model predictive control is developed based on an uncertain fractional model. Moreover, the output deviation approach is adopted to design the j ‐step ahead output predictor, and the corresponding control law is obtained by the resolution of a min–max optimisation problem that takes into account the uncertainties of the fractional‐order model parameters and under input constraints. The efficiency and the performances of the proposed predictive controller are illustrated with practical results of a thermal system.