Topology selection for multi-agent systems with opposite leaders

For the multi-agent system with a navigational leader and its opponent, the followers cannot converge to the state of the navigational leader. In this paper, we consider the topology selection problem to minimize the opponent’s influence which is measured by the tracking error of the system. Firstly, two combinatorial optimization problems are formulated. One is to minimize the tracking error by selecting guided informed-agents (the followers who can obtain the navigational leader’s information). The other is to choose minimal number of guided informed-agents under an upper bound constraint of the tracking error. Secondly, for the scenario where the guided informed-agents are preset, we consider the problem of assigning the weights of edges to minimize the tracking error. Three convex optimization problems are proposed to evaluate the upper and lower bounds of the tracking error. Finally, numerical examples are provided to illustrate the effectiveness of the theoretical results.