Fuzzy generalised predictive control for a class of fractional-order non-linear systems

Abstract

Fractional-order fuzzy generalised predictive control (FFGPC) for a class of non-linear systems is studied. Based on the Grünwald-Letnikov fractional calculus, Laplace transform, and discretisation, a class of fractional-order non-linear systems are transformed to fit the standard controlled autoregressive integrating moving average (CARMA) model. With the help of the Takagi-Sugeno fuzzy linearisation theory, a linear CARMA model for the non-linear systems is represented. Then, a new FFGPC method is proposed for the fractional-order non-linear systems based on the obtained CARMA predictive model and generalised predictive control theory. Numerical simulations are implemented to verify the effectiveness and superiority of the new method. This work also provides a reference for the control of relevant fractional-order systems.