Fixed-time consensus tracking control of multiple nonholonomic dynamics under disturbance

Abstract

In this paper, the fixed-time consensus tracking problem is investigated for a multi-agent system with nonholonomic dynamics under the disturbances with unknown upper bounds. For an undirected communication graph, fixed-time distributed state observers and input observers are respectively proposed to estimate state and input of leader system. To deal with the unknown upper-bound disturbance, a second-order sliding mode super-twisting structure adaptive disturbance observer is developed to estimate disturbance in fixed time. Then, by resorting to the estimated information and adding a power integrator method, a novel nonlinear controller is designed for tracking the leader state in fixed-time under disturbance. Moreover, the fixed-time consensus analysis is showed, and the upper bound of settling time is calculated without dependence on initial states even in the presence of disturbance. Finally, numerical examples are included to demonstrate the effectiveness of the proposed procedure.