Fully Distributed Fault-Tolerant Finite-Time Consensus Control for Nonlinear Second-Order Multi-Agent Systems

This paper studies the finite-time consensus control for nonlinear second-order multi-agent systems in the presence of the actuator failures and disturbances. The efficiency factor of the control input and the disturbances term are considered to be unknown and time-varying. To approximate the unknown nonlinearities, Gaussian radial basis function neural networks (RBFNNs) are employed. Adaptive mechanisms are introduced to estimate the weights of the radial basis functions, the unknown upper bounds of disturbances, and the weights of the relative states among neighboring agents. With the help of the adaptive schemes, for multi-agent systems with actuator failures, nonlinearities and disturbances, the fault-tolerant finite-time consensus can be achieved without using the information of the upper bounds of the disturbances, the lower bounds of the control efficiency factor, and the eigenvalues of the Laplacian matrix. Thereby the proposed controller is fully distributed. The proof is based on the finite-time Lyapunov theory. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed method.