Optimal topology selection for leader-following multi-agent systems with opposite leaders

In this paper, we consider two optimal topology selection problems of multi-agent systems with two leaders — a tracking target and its opponent. First, we study how to select a given number of guided informed-agents (the followers who receive the tracking target's information) in order to minimize the tracking error. Second, we consider the problem of selecting the minimal number of guided informed-agents under an upper bound constraint of the tracking error. Two algorithms are established to approximately solve them. Finally, numerical examples are worked out on two different networks to illustrate the effectiveness of our theoretical results.