Stabilising Model Predictive Control for Discrete-time Fractional-order Systems

TL;DR

This paper introduces a stabilising model predictive control approach for constrained discrete-time fractional-order systems, ensuring stability, constraint satisfaction, and recursive feasibility by using finite-dimensional approximations.

Contribution

It develops a novel MPC scheme for fractional-order systems with stability guarantees and practical computational conditions, addressing the challenges of infinite-dimensional dynamics.

Findings

Guarantees asymptotic stability of the controlled system

Ensures all constraints are satisfied at all times

Provides computationally tractable stability conditions

Abstract

In this paper we propose a model predictive control scheme for constrained fractional-order discrete-time systems. We prove that all constraints are satisfied at all time instants and we prescribe conditions for the origin to be an asymptotically stable equilibrium point of the controlled system. We employ a finite-dimensional approximation of the original infinite-dimensional dynamics for which the approximation error can become arbitrarily small. We use the approximate dynamics to design a tube-based model predictive controller which steers the system state to a neighbourhood of the origin of controlled size. We finally derive stability conditions 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.