Fixed-time consensus for multiple mechanical systems with input dead-zone and quantization under directed graphs

This paper is concerned with the fixed-time consensus tracking control for uncertain multiple mechanical systems under general directed communication graphs. The considered systems are governed by mechanical dynamics that contain not only input quantization, but also asymmetric dead-zone nonlinearity as well as unknown external disturbances. By employing a nonlinear decomposition between the system input and the control signal, the major difficulty for the coupling between the quantized input and dead-zone nonlinearity is resolved. On the basis of this, an adaptive fixed-time control strategy is designed by utilizing the technique of adding a power integrator. Rigorous proofs show that the consensus errors can converge to an arbitrarily small range centered at zero in a preassigned time, where the settling time has no connection with the initial conditions. Therefore, we can preassign the convergence time according to the requirement of the task. In the end, a simulation example is presented to validate the efficiency of the designed methodology.