Prescribed finite-time consensus with severe unknown nonlinearities and mismatched disturbances

This paper considers the problem of prescribed finite-time leader-following consensus for a class of second-order multi-agent systems (MAS). Compared to the existing methods, the dynamics of the followers in the proposed method is rather general, containing some severe unknown nonlinearities and mismatched disturbances. First, a time-varying distributed observer is proposed to estimate the leader information in prescribed finite time. The leader is driven by a control input that is unknown to all the followers. Then, a new composite controller with a time-varying disturbance observer is presented. By gracefully combining the barrier Lyapunov functions and logic-based switching rules, we show that the unknown nonlinearities and mismatched disturbances can be well handled. Thus, the prescribed finite-time consensus problem can be solved. Finally, by the properties of Lyapunov functions and time-varying gains, we present a new method to show that the control signals are bounded. A simulation example is provided to verify the effectiveness of the proposed method.