Stability under constraints for fractional-order control

Establish stability guarantees and viability/invariance conditions for constrained optimal control of systems governed by Caputo or Riemann–Liouville fractional dynamics, including rigorous handling of pointwise state and input constraints under memory.

Background

The survey emphasizes that memory fundamentally changes feasibility and stability analysis, especially when hard constraints are present.

While MPC and LQR can be implemented via augmented realizations, the underlying theoretical guarantees for stability with nonlocal dynamics under constraints are not yet consolidated.

References

Open problems: We identify gaps in (i) existence and uniqueness of equilibria with memory and refined Isaacs-type conditions; (ii) controllability and observability notions aligned with OC and games; (iii) stability under constraints; (iv) scalable FO--MPC and multi-agent solvers; and (v) integrated data-driven identification and learning with FO control and game design.

— Fractional Calculus in Optimal Control and Game Theory: Theory, Numerics, and Applications -- A Survey (2512.12111 - Mojahed et al., 13 Dec 2025) in Section 1 (Introduction), Positioning and scope, bullet list “Open problems”