Practical finite-time consensus of multi-agent systems with unknown nonlinear dynamics and the asymmetric input dead zone

This paper investigates the practical finite-time consensus problem for heterogeneous multi-agent systems with unknown nonlinear dynamics, the asymmetric input dead zone, and external disturbances under directed topology. The model of heterogeneous multi-agent systems is composed of first-order and second-order dynamics. First, we show that under the proposed protocol, the sliding mode surface converges to a compact set in finite time. Then, we prove that the position errors and the velocity errors (for second-order agents) between any two agents reach a small desired neighborhood of the origin in finite time. In this approach, adaptive neural networks are employed to compensate for the nonlinear dynamics of agents. By applying sliding mode control, the external disturbances and the imperfect approximation of neural networks are rejected. The approach of the adaptive compensator plus dead zone is applied to overcome the asymmetric input dead zone. Besides, our proposed protocol is fully distributed, which means that the global graph information is not required beforehand by adaptive control gains. The effectiveness of our proposed protocol is finally validated through numerical simulations.