Distributed Finite-time Bipartite Consensus Control for Constrained Nonlinear MASs: A Switched Function Approach Based on Prioritized Strategy

The distributed finite-time bipartite consensus control problem for nonlinear multi-agent systems (MASs) is discussed in this work. This paper proposes the prioritized strategy that utilizes a more relaxed criteria, i.e., a signed digraph containing one spanning tree, to achieve bipartition among all agents in the system. To improve the scheme's applicability, a non-strict feedback structure is adopted for the agent model. Different from some existing finite-time control schemes, a novel $C^{1}$ finite-time fuzzy adaptive controller is proposed utilizing the smooth switched function. The singularity problem that arises from the differential virtual control law is effectively solved by constructing the switched function. With aid of the distributed backstepping technique, as well as barrier Lyapunov functions and finite-time control approach, all agents successfully attain bipartite consensus while maintaining bounded errors. Simulation results certify the validity of the scheme.