Adaptive fault-tolerant fixed-time tracking consensus control for high-order unknown nonlinear multi-agent systems with performance constraint

Abstract This paper investigates fixed-time tracking consensus problem for high-order nonlinear multi-agent systems (MASs) with actuator faults and performance constraint. Different from existing results that focus on first/second/high-order MASs with integral structure, the investigated MASs involve complex nonlinear dynamics with each agent being modeled as high-order non-strict-feedback form. That is, unknown nonlinear function appears in every state component equation of each subsystem, and contains all the states of the corresponding subsystem. Due to the adverse effects from complex nonlinear dynamics, the previous methods may be unavailable, which motivates the work. To address the problems arising from unknown nonlinear dynamics and actuator faults, fuzzy systems and robust technique are employed. Meanwhile, the performance constraints on the tracking errors can be ensured by appropriately utilizing barrier Lyapunov functions and graph theory. Furthermore, power integrator technique incorporated with Lyapunov functions is used to guarantee the property of fixed time convergence. It is shown that, by using the proposed control strategy, despite the presence of high-order complex nonlinear dynamics and actuator faults, the tracking consensus errors can converge into a neighborhood around zero within fixed time. In addition, the tracking consensus performance can be guaranteed during the whole operation, and all the signals in MASs are bounded. Finally, the effectiveness of the proposed control strategy has been proved by rigorous stability analysis and two simulation examples.