Finite-time consensus for single-integrator kinematics with unknown inherent nonlinear dynamics under a directed interaction graph

This paper deals with the finite-time consensus for single-integrator kinematics with unknown inherent nonlinear dynamics under a directed interaction graph. A distributed nonlinear algorithm is proposed to solve the problem given that some sufficient conditions are satisfied. Due to the existence of the unknown inherent nonlinear dynamics and the desired finite-time convergence property, the stability analysis is challenging because the traditional stability tools frequently used in solving the consensus problem cannot be applied here. For this purpose, we propose a novel comparison based stability tool, which plays an important role in the stability analysis of the proposed algorithm.