Stabilising model predictive control for discrete-time fractional-order systems

In this paper, a model predictive control scheme is proposed for constrained fractional-order discrete-time systems. We prove that constraints are satisfied and we prescribe conditions for the origin to be an asymptotically stable equilibrium point of the controlled system. A finite-dimensional approximation of the original infinite-dimensional dynamics is employed for which the approximation error can become arbitrarily small. The approximate dynamics is used to design a tube-based model predictive controller which steers the system state to a neighbourhood of the origin of controlled size. Stability conditions are finally derived for the MPC-controlled system which are computationally tractable and account for the infinite dimensional nature of the fractional-order system and the state and input constraints. The proposed control methodology guarantees asymptotic stability of the discrete-time fractional order system, satisfaction of the prescribed constraints and recursive feasibility.