Observer-based finite-time consensus control for multiagent systems with nonlinear faults.

• In the framework of finite-time command filter control, this paper constructs a quadratic function in the controller. Compared with [23, 24, 25], the presented adaptive finite-time control algorithm not only solves the "explosion of complexity" problem effectively, but also circumvents the singularity problem. • In contrast to the literatures on finite-time control [43, 44, 45], the cases of faults happening during transmission phase of system are rarely considered. Moreover, nonlinear faults may exist in many real systems, which necessitates the design of fault-tolerant controllers to enhance the system reliability and guarantee consistent control performance. In this paper, nonaffine nonlinear faults are taken into account, which is more complex than linear faults studied in [37, 39, 46]. • Different from the results [28, 29, 47] which used the trial-and-error method to validate the observation gain matrix, this paper skillfully introduces the differential mean value theorem and the convex combination theorem to transform the acquisition of the observation gain matrix from solving a nonlinear matrix inequality to solving a set of LMIs. Meanwhile, the solvability of LMIs guarantees the stability of the observer and simplifies the algorithm. The present work deals with the consensus issue for nonlinear multiagent systems (MASs) subject to nonaffine nonlinear faults and unmeasurable states. First, the Butterworth low-pass filter (BLPF) is exploited to eliminate the algebraic loop problem arising from nonaffine nonlinear faults. In light of the convex combination theory, a neural observer is established to estimate the unmeasured states, which improves the efficiency of solving the observer gain. Then, with the help of the adaptive backstepping algorithm, an observer-based neural finite-time control protocol is proposed in which a quadratic function is constructed to circumvent the singularity problem. The finite-time stability criterion and Lyapunov stability theorem are utilized to demonstrate that all signals of the closed-loop system are bounded in finite time. Finally, a simulation experiment is applied to show the effectiveness of the present method. [ABSTRACT FROM AUTHOR]