Fractional order distributed optimization algorithm for double-fractional-integrator dynamics grounded on proportional-integral feedback

This paper endeavors to tackle the dynamic convex optimization problem over undirected topological networks, which is solved through the collaboration between interlinked agents operating in the form of double-fractional-integrator dynamics. The proposed algorithm employs nabla fractional difference and proportional-integral feedback, which distinguishes it from existing algorithms in the literature and allows for a better characterization of the non-locality and non-Markovianity of the dynamic system. Moreover, the developed algorithm achieves asymptotic convergence and offers the potential to reduce communication costs, enhance robustness against disturbance, accelerate convergence rates, and facilitate parameter selection. Notably, the effectiveness of the developed algorithm is validated through the presented comprehensive simulation results.