Prescribed-time Bipartite Consensus Formation Control for General Linear Multi-agent Systems

The prescribed-time bipartite consensus formation problem for multi-agent systems with general linear dynamics is analyzed in this paper, where the underlying directed topologies both contain cooperative and antagonistic interaction. Firstly, by leveraging Pontryagin's maximum principle, the distributed bipartite consensus formation controllers are developed. In particular, the settling time can be arbitrarily prescribed according to practical demand. Then, under the application of proposed controllers, the bipartite consensus formation is achieved by multi-step motion planning. Here, the bipartite consensus formation means that the agents among each group achieve own desired formation configuration and move in an opposite direction with their rival group. Moreover, the formation problem degenerates into consensus problem when formation configuration vectors are appointed as 0. Besides, while solving formation problems, a performance indicator with respect to control input we select is optimal, which is meaningful for formation with limited energy in actual application. Compared with existing works on this issue, a main contribution of this paper lies in that the distributed bipartite consensus formation controllers with a prescribed settling time are raised, which solve the two major problems of achieving formation configurations at a prescribed time and limitation of the energy supply in formation flying, simultaneously. Finally, numerical prescribed-time bipartite consensus formation examples are formulated to illustrate the effectiveness of controllers.