Event-Triggered Discrete-Time Distributed Consensus Optimization over Time-Varying Graphs

Qingguo Lü,Huaqing Li

doi:10.1155/2017/5385708

Abstract

This paper focuses on a class of event-triggered discrete-time distributed consensus optimization algorithms, with a set of agents whose communication topology is depicted by a sequence of time-varying networks. The communication process is steered by independent trigger conditions observed by agents and is decentralized and just rests with each agent’s own state. At each time, each agent only has access to its privately local Lipschitz convex objective function. At the next time step, every agent updates its state by applying its own objective function and the information sent from its neighboring agents. Under the assumption that the network topology is uniformly strongly connected and weight-balanced, the novel event-triggered distributed subgradient algorithm is capable of steering the whole network of agents asymptotically converging to an optimal solution of the convex optimization problem. Finally, a simulation example is given to validate effectiveness of the introduced algorithm and demonstrate feasibility of the theoretical analysis.

Highlights

In the last decade, multiagent systems have obtained some achievements in theory and application, like consensus problem [1,2,3,4,5,6,7], flocking problem [8,9,10], resource allocation control [11,12,13], and so on [14,15,16,17]
This paper focuses on a class of event-triggered discrete-time distributed consensus optimization algorithms, with a set of agents whose communication topology is depicted by a sequence of time-varying networks
Multiagent systems have obtained some achievements in theory and application, like consensus problem [1,2,3,4,5,6,7], flocking problem [8,9,10], resource allocation control [11,12,13], and so on [14,15,16,17]

Summary

Introduction

Multiagent systems have obtained some achievements in theory and application, like consensus problem [1,2,3,4,5,6,7], flocking problem [8,9,10], resource allocation control [11,12,13], and so on [14,15,16,17]. Recent works [40,41,42,43,44,45] have coordinately put their efforts on the consensus of multiagent systems by designing the control protocols based on event-triggered sampling schemes. Inspired by the previous works, this paper proposes a novel distributed subgradient algorithm for multiagent convex optimization with event-triggered sampling scheme. Previous works did not perform well on the applications of the distributed algorithms in multiagent network; for example, they may just study discrete-time distributed consensus optimization over time-varying graphs without trigger condition or they only consider event-based distributed consensus of multiagent systems with general networks. We study the convex optimization problem of discrete-time multiagent systems by a distributed event-triggered sampling control scheme, where the event-triggered control strategy in this paper can eliminate unnecessary communications among neighboring agents, leading to the reduction of computation costs and energy consumption in practice.

Preliminaries and Concepts

Main Results

Numerical Example

Conclusion and Future Work