Adaptive finite-time consensus for multiple mechanical systems with unknown backlash nonlinearity and uncertain dynamics

This paper studies the problem of finite-time consensus (FTC) for uncertain multiple mechanical systems with unknown backlash nonlinearity and external disturbance. Combining finite-time control technique and graph theory, a distributed adaptive FTC protocol is proposed. Radial basis function neural networks are employed to approximate the unknown functions. If the designed parameters of control algorithms and adaptive laws are appropriately chosen, then it can be proved that the position errors between arbitrary two mechanical systems will converge to a small region of zero in finite time as well as the velocity errors. Finally, the effectiveness of the proposed control scheme is verified by numerical simulation.