Fractional order distributed optimization algorithm based on proportional-integral protocol

In this paper, a distributed algorithm based on fractional proportional-integral protocol is proposed to solve convex optimization problems with an additive objective function composed of individual objective functions. Unlike traditional distributed algorithms, the traditional calculus is generalized to nabla fractional calculus, which allows the algorithm to describe the dynamic properties of the system more comprehensively and accurately. The integral state does not share with neighbours, which reduces the communication burden and enhances the robustness against disturbance. The algorithm could achieve Mittag–Leffler convergence under undirected graph with the plain assumption. Simulation results are provided to substantiate the effectiveness of the developed algorithm.