Cluster–bipartite output consensus of singular heterogeneous multi–agent systems under cooperation–competition networks

This paper investigates the distributed cluster-bipartite output consensus problem for singular heterogeneous linear multi-agent systems under cooperative-competitive communication networks. Different from conventional state consensus tracking, a consensus control framework that consists of multiple clusters and multiple leaders modeled as exosystems is introduced to accomplish more complex collaborative tasks. However, when agents exhibit heterogeneous and singular dynamics, the cooperative-competitive interactions both within and between subgroups pose a challenge to the design of distributed control protocols. To address this issue, a new cluster-bipartite output consensus control protocol based on output regulation theory is proposed, which enables agents in different subgroups to respectively achieve bipartite consensus. For bipartite tracking of leaders within their own subgroups, a distributed observer relying on Riccati inequality and a topological matrix is developed. By solving the singular regulation equations, this paper presents both state-feedback and output-feedback cluster-bipartite control protocols. Finally, simulation results validate the effectiveness of the proposed algorithm with the designed controllers.