Distributed Constrained Consensus of Utilities via a Self Evaluation Approach

Xiaochu Wang,Ting Sun,Changhao Sun

doi:10.1109/access.2019.2939018

Abstract

This paper investigates the problem of distributed constrained consensus of utilities for multiple networked nodes, which is essentially challenging in view of the fact that local constraints may hinder the global optimization across the network. Focusing on this problem, a generalized framework is developed via a self evaluation approach, in which each node uses utility evaluations to update individual states by interacting with neighbors only. Following the framework, the distributed constrained consensus algorithms is derived, with theoretical analyses presented to show the convergence and stability. In addition, an approximation method is proposed as well for ease of engineering implementation. Finally, illustrative examples are provided and analyzed to substantiate the efficacy of the proposed algorithm.

Highlights

Networked distributed systems have been attracting great interests due to the advantage that a group of simple networked nodes working cooperatively can perform the same applications as a complex mono system
Earlier research mainly concentrates on unconstrained consensus problems, where states of nodes are allowed to be processed arbitrarily without any constraints, to study fundamental rules for guaranteeing information among nodes to achieve a consensus in a distributed manner [1], [12]–[14]
Excellent work has been presented to solve constrained consensus problems, these algorithms cannot be used to solve Problem Eq (1) because their asymmetric formed equations will cause the nonconservation of the state summation

Summary

INTRODUCTION

Networked distributed systems have been attracting great interests due to the advantage that a group of simple networked nodes working cooperatively can perform the same applications as a complex mono system. Excellent work has been presented to solve constrained consensus problems, these algorithms cannot be used to solve Problem Eq (1) because their asymmetric formed equations will cause the nonconservation of the state summation They often require an elaboratedly-designed sequence of stepsizes to guarantee convergence. 1) A novel principle following ‘‘the law of connected vessels’’ in Physics is developed to help design distributed algorithms, where no Lagrange functions or dual methods are needed to reformulate the primal problem, and where a self evaluation approach is proposed to guide nodes to interact. This principle has great potential to inspire and simplify the algorithm designs for similar problems.

PRELIMINARIES

CONSTRAINED CONSENSUS ALGORITHM

EXAMPLE 1

EXAMPLE 2

EXAMPLE 3

CONCLUSION