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

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