Integrated data-driven identification and learning with fractional control and games

Develop integrated frameworks that couple data-driven identification and learning of fractional-order models with optimal control and differential game design, including uncertainty quantification and stability/robustness guarantees for memory-dependent dynamics.

Background

The survey summarizes modeling options (Caputo/RL, diffusive, Oustaloup) and notes the need for identification approaches that preserve physical interpretability and stability/passivity in the presence of memory.

An end-to-end integration with controller or game-theoretic synthesis—together with certification—remains to be developed.

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”