Fault-tolerant finite time consensus for multiple uncertain nonlinear mechanical systems under single-way directed communication interactions and actuation failures

This paper investigates the problem of finite time consensus for a group of uncertain nonlinear mechanical systems under single-way directed communication topology and actuation failures. Due to the existence of the unknown inherent nonlinear dynamics and the undetectable actuation faults, the resultant control gain of the system becomes unknown and time-varying, making the control impact on the system uncertain and the finite time control synthesis nontrivial. The underlying problem becomes further complex as the communication among the agents is not only local but also one-way directed. In this work, three major steps are employed to circumvent the aforementioned difficulties, leading to a robust adaptive fault-tolerant finite time consensus solution. Firstly, by deriving a useful property on the newly constructed Laplacian matrix, the technical difficulty in finite time control design and stability analysis is circumvented; Secondly, to deal with the time-varying and uncertain control gain, the concept of virtual parameter estimation error is introduced and incorporated into a skillfully chosen Lyapunov function; Thirdly, to facilitate the global stability analysis of the proposed adaptive fault-tolerant finite time consensus scheme for multiple nonlinear systems, an important lemma (Lemma 7) containing a useful inequality is derived. In addition, the finite convergence time for each agent to reach the required consensus configuration is explicitly established and recipes for control parameter selection to make the residual errors as small as desired are provided. The effectiveness of the proposed control scheme is confirmed by numerical simulation. (C) 2015 Elsevier Ltd. All rights reserved.