Practical bipartite consensus for multi-agent systems: A barrier function-based adaptive sliding-mode control approach

This paper is concerned with bipartite consensus tracking for multi-agent systems with unknown disturbances. A barrier function-based adaptive sliding-mode control (SMC) approach is proposed such that the bipartite steady-state error is converged to a predefined region of zero in finite time. Specifically, based on an error auxiliary taking neighboring antagonistic interactions into account, an SMC law is designed with an adaptive gain. The gain can switch to a positive semi-definite barrier function to ensure that the error auxiliary is constrained to a predefined neighborhood of zero, which in turn guarantees practical bipartite consensus tracking. A distinguished feature of the proposed controller is its independence on the bound of disturbances, while the input chattering phenomenon is alleviated. Finally, a numerical example is provided to verify the effectiveness of the proposed controller.