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

摘要

AbstractIn this paper an offset-free model predictive control scheme is presented for fractional-order systems using the Grünwald–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.Highlights•An offset-free MPC formulation is proposed for fractional-order systems.•Takes into account input/state constraints.•Rejects modeling errors due to the approximation of the dynamics and uncertainties on parameters.•Can be applied to real-world problems such as drug administration in fractional pharmacokinetics.