# Model predictive control for offset-free reference tracking of fractional order systems

## TL;DR

This paper introduces an offset-free model predictive control method for fractional-order systems, utilizing a finite-dimensional approximation and disturbance observer to achieve accurate reference tracking and disturbance rejection.

## Contribution

It presents a novel offset-free MPC scheme for fractional-order systems using the Grünwald-Letnikov derivative with a disturbance observer for steady-state error correction.

## Key findings

- Effective disturbance reconstruction at steady state
- Improved reference tracking in fractional pharmacokinetic models
- Demonstrated success in controlling anti-arrhythmic medication

## Abstract

In this paper an offset-free model predictive control scheme is presented for fractional-order systems using the Gr\"unwald-Letnikov derivative. The infinite-history fractional-order system is approximated by a finite-dimensional state-space system and the modeling error is cast as a bounded disturbance term. Using a state observer, it is shown that the unknown disturbance at steady state can be reconstructed and modeling errors and other persistent disturbances can be attenuated. The effectiveness of the proposed controller-observer ensemble is demonstrated in the optimal administration of an anti-arrhythmic medicine with fractional-order pharmacokinetics.