Intrinsic fractional LQ theory without augmented embeddings

Establish a native fractional-order linear–quadratic control theory that yields Riccati-type differential or algebraic equations directly in the original Caputo/Riemann–Liouville coordinates, eliminating reliance on high-order diffusive or Oustaloup augmented realizations.

Background

Throughout the paper, LQ/LQR for fractional systems is implemented either via diffusive state augmentation (Prony) or frequency-domain Oustaloup approximations, after which classical Riccati equations apply in an augmented ODE.

The authors highlight the lack of an intrinsic Riccati framework stated directly in fractional coordinates, including desired links to Matignon-type stability sectors and extensions to differential games.