Augmented Cucker-Smale Model for Distributed Optimization

Qiao Zhang,Hongyue He,Minyang Liu,Bing Xu,Ming He

doi:10.1109/access.2021.3110514

Qiao Zhang, Hongyue He + Show 3 more

Open Access

https://doi.org/10.1109/access.2021.3110514

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Abstract

The Cucker-Smale (C-S) model describes an interacting particle system in which the connection weights decrease with increasing distance. This model features emergent behaviors by which the velocities of the particles converge to a common value without a central command. However, the consensus value of the original C-S flocking model is restricted to the leader-following consensus or average consensus. Moreover, for the short-range communication-based C-S model, consensus can only be obtained for specific initial configurations. In this paper, the short-range communication-based C-S model is extended to achieve distributed optimization, where the consensus value optimizes the objective function of the group for any bounded initial configuration. Simulation examples are provided to demonstrate the effectiveness of our approach.

Highlights

Inspired by the observation that remote neighbors have less influence than closer neighbors in flocks of birds or schools of fish, Cucker and Smale proposed the Cucker-Smale (C-S) model, which illustrates autonomous interacting agents with connectivity intensity that fades as the pairwise distance increases [1], [2]
The emergent behaviors of the C-S flocking model lie in the fact that the velocities of all agents converge to a common consensus value without a central command
Model, asymptotic flocking occurs independently of the initial configurations; when the communication weight has a short range, asymptotic flocking can only be achieved for specific initial configurations

Summary

INTRODUCTION

Inspired by the observation that remote neighbors have less influence than closer neighbors in flocks of birds or schools of fish, Cucker and Smale proposed the Cucker-Smale (C-S) model, which illustrates autonomous interacting agents with connectivity intensity that fades as the pairwise distance increases [1], [2]. According to whether a leader is present, the consensus of the C-S flocking model either obeys leader-following consensus or average consensus For the former, the velocities of the particles converge to the velocity of the leader [1]–[3]; for the latter, the velocities of the particles converge to the average value of the initial velocities of the agents [4], [5]. In this paper, inspired by [21], we add optimization terms on top of the original C-S flock term to extend the short-range communication-based C-S model and achieve. For the short-range communication-based C-S model, optimal consensus is achieved for any bounded initial configuration. The augmented C-S model for the timevarying distributed optimization problem is presented. ; define sign vi sign vi1 ,sign vi2 , . . . ,sign vin T , where sign (·) is the sign function; and let R, R+ , Rn represent the sets of real numbers, one-dimensional positive real vectors, and n-dimensional real vectors, respectively, where denotes the Euclidean norm, denotes the 1-norm, and 1

PRELIMINARIES AND PROBLEM FORMULATION

PROBLEM FORMULATION

NUMERICAL SIMULATION

CONCLUSION