A Supermodular Optimization Framework for Leader Selection under Link Noise in Linear Multi-Agent Systems

TL;DR

This paper presents a supermodular optimization framework for selecting leaders in multi-agent systems to minimize steady-state error under noisy links, offering efficient algorithms with theoretical guarantees.

Contribution

It introduces a novel supermodular optimization approach for leader selection in MAS, applicable to various dynamic and static network scenarios, with provable performance bounds.

Findings

Outperforms degree-based and random leader selection methods.

Provides bounds for static, failure-prone, and dynamic topologies.

Achieves performance comparable to state-of-the-art algorithms.

Abstract

In many applications of multi-agent systems (MAS), a set of leader agents acts as a control input to the remaining follower agents. In this paper, we introduce an analytical approach to selecting leader agents in order to minimize the total mean-square error of the follower agent states from their desired value in steady-state in the presence of noisy communication links. We show that the problem of choosing leaders in order to minimize this error can be solved using supermodular optimization techniques, leading to efficient algorithms that are within a provable bound of the optimum. We formulate two leader selection problems within our framework, namely the problem of choosing a fixed number of leaders to minimize the error, as well as the problem of choosing the minimum number of leaders to achieve a tolerated level of error. We study both leader selection criteria for different scenarios, including MAS with static topologies, topologies experiencing random link or node failures, switching topologies, and topologies that vary arbitrarily in time due to node mobility. In addition to providing provable bounds for all these cases, simulation results demonstrate that our approach outperforms other leader selection methods, such as node degree-based and random selection methods, and provides comparable performance to current state of the art algorithms.