Formation Containment for Multi-Agent Networks With Cooperative-Competitive Interactions in Two-Dimensional Space

Cooperation and competition relationships are ubiquitous in multi-agent networks. A good cooperative relationship is likely to prompt neighboring agents to draw close each other, while a competitive relationship can easily lead to neighboring agents moving away from each other. This paper aims to investigate how to implement formation containment for multi-agent networks with both cooperative and competitive interactions in two-dimensional space, where the followers are unaware of the topology information and the expected formation information, but the leaders are. The leaders form a connection matrix based on the expected formation information, and then utilize it to build interaction relationships with the group of followers. The followers design asynchronous distributed control protocols based on the interaction information of local neighbors and adjust their own states. By establishing topological and algebraic conditions for cooperative and competitive relationships, it is theoretically confirmed that followers can still gather into the convex hull formed by the leaders and form the expected formation, even if the network contains both cooperative and competitive relationships. At last, the theoretical results of this paper are validated through numerical simulations.