A Gradient Tracking Protocol for Optimization Over Nabla Fractional Multi-Agent Systems

This paper investigates the distributed consensus optimization over a class of nabla fractional multi-agent systems (nFMASs). The proposed approach, built upon conventional gradient tracking techniques, addresses the specificity of the studied system by introducing a fractional gradient tracking protocol based on globally differential information of optimization variables. This protocol is applicable to nabla fractional systems of any order less than 1 and can be extended to integer discrete-time systems. The distributed optimization algorithms derived from this protocol ensure globally precise convergence under fixed step-sizes, thereby guaranteeing the feasibility of consensus optimization over nFMASs. Simulation results are presented to validate and substantiate the effectiveness of the proposed algorithms.