Robust Fault Detection for Second-order Multi-agent Systems on Directed Graph

In this paper, we propose a robust fault detection scheme for second-order multi-agent systems with external disturbance on directed graph. As the open-loop system of the multi-agent system contains disturbance term, there doesn't exist an observer whose error dynamics won't be influenced by the disturbance term. Hence we design observer for the augmented closed-loop system of multi-agent system based on the idea of unknown input observer, which is formed by adding an active disturbance rejection term to the control law. Then utilize above observers to generate residuals corresponding to all the agents of the MAS, the generators are only sensitive to the agents which the fault doesn't occur, which means that there exists one residual generator different from others. Through further residual dynamics analysis, the residual corresponding to the faulty agent will be zero after the fault occurs, the others will fluctuate. Then we prove the existence of above observers that we design. Finally, the efficiency of the proposed scheme is illustrated by some simulation examples. The rest of this paper is organized as follows. In section 2, some basic knowledge of graph theory and reduced-order UIO are introduced, then the problem formulation is given. Section 3 gives the main results of this paper.