Finite-Time Distributed Optimization in Unbalanced Multiagent Networks: Fractional-Order Dynamics, Disturbance Rejection, and Chatter Avoidance

Abstract

This study focuses on solving the finite-time distributed optimization issue of fractional-order multiagent systems (FOMASs) over unbalanced directed graphs (digraphs) that are subject to disturbances. Each agent in the FOMASs has a local cost function that is only available to itself, which may or may not be convex and quadratic. To address this challenge, the study proposes a fully distributed gradient-sum-estimation (GSE) optimization algorithm as a continuous control law, which comprises three parts. In the first part, a disturbance estimator term is proposed for each agent to estimate its disturbance within a finite time. In the second part, a sliding-mode control (SMC) term is presented to ensure that all agents reach the sliding surface within a finite time. In the last part, a novel GSE-based optimization term is constructed to capture the global optimal solution within a finite time. The GSE is fully distributed and used for estimating the sum of all gradients within a finite time. This fully distributed GSE optimization algorithm has zero-error finite-time convergence, disturbance rejection, and chatter avoidance properties. Finally, the study verifies the validity and superiority of the proposed GSE optimization algorithm by comparing some graphical simulation results.Note to Practitioners—Due to the presence of disturbances in actual industrial systems, the distributed optimization problem of disturbed FOMASs is studied in this study, which can be applied to energy consumption optimization, parameter estimation and scheduling, economic dispatch, and distributed energy resources optimal in power systems. Our study proposes a novel completely distributed fractional-order controller that is endowed with the properties of disturbance rejection, zero-error finite-time optimal convergence, and chatter avoidance. The commonly existing limitation that each local cost function is convex or quadratic hinders its implementation in real-world scenarios. We address this limitation and broaden the scope of local cost functions to include nonconvex and nonquadratic functions. In addition, by comparing the simulation results, the fractional-order controller of FOMASs has superior steady-state and transient performance over the conventional first-order MASs controller, such as faster convergence and lower energy consumption. As a result, the proposed fractional-order controller is more in line with practical engineering applications.