Adaptive consensus of nonlinear multi-agent systems with unknown backlash-like hysteresis

• Unknown backlash-like hysteresis and unknown control direction are considered.
• Dynamics of the systems are high-order with unknown nonlinear dynamics.
• A modified robust strategy is employed to deal with approximation error.

In this brief, we consider the consensus problem of high-order nonlinear multi-agent systems with unknown backlash-like hysteresis and unknown control direction. By using backstepping technique, a distributed adaptive control scheme, with the adoption of Nussbaum-type function, is developed to solve this consensus problem. Radial basis function neural network is employed to neutralize the uncertain nonlinear dynamics. The approximation error of the neural networks, together with external disturbance and a bounded term from the hysteresis model, is adaptively estimated and counteracted by a robust term. Under undirected connected communication topology, it is proved that the consensus can be achieved asymptotically with the proposed control protocol. Finally, a numerical example is presented to illustrate the performance of the proposed protocol.