Estimating unknown parameters in fractional-order dynamical systems

Develop and analyze methods to estimate the unknown parameters of fractional-order dynamical systems—including the state-transition matrix A, input matrix B, and fractional-order vector a—for discrete-time fractional-order linear time-invariant systems governed by the Grünwald–Letnikov difference operator, directly from observed trajectories, even under linear fractional operators.

Background

The paper highlights that fractional-order systems exhibit non-Markovian dynamics with long-range memory, making standard system identification approaches ineffective. The Grünwald–Letnikov fractional derivative introduces combinatorial complexity that further complicates parameter estimation.

Prior work has addressed aspects of fractional-order system identification under restrictive assumptions, and the authors frame robust identification of parameters (A, B, a) in fractional-order models as an unresolved challenge. Their proposed framework offers partial progress but explicitly notes the broader estimation problem remains open.