Pivotal decomposition for reliability analysis of fault tolerant control systems on unmanned aerial vehicles

In this paper, we describe a framework to efficiently assess the reliability of fault tolerant control systems on low-cost unmanned aerial vehicles. The analysis is developed for a system consisting of a fixed number of actuators. In addition, the system includes a scheme to detect failures in individual actuators and, as a consequence, switch between different control algorithms for automatic operation of the actuators. Existing dynamic reliability analysis methods are insufficient for this class of systems because the coverage parameters for different actuator failures can be time-varying, correlated, and difficult to obtain in practice. We address these issues by combining new fault detection performance metrics with pivotal decomposition. These new metrics capture the interactions in different fault detection channels, and can be computed from stochastic models of fault detection algorithms. Our approach also decouples the high dimensional analysis problem into low dimensional sub-problems, yielding a computationally efficient analysis. Finally, we demonstrate the proposed method on a numerical example. The analysis results are also verified by Monte Carlo simulations.