## Fault Detection and Identification

Apart from ATC operations and Air Traffic Management systems, many practical systems, such as embedded systems, multi-agent systems, and cooperative systems, are also best described by hybrid systems. The continuous dynamics of the hybrid systems could model the physical system dynamics and the discrete dynamics could represent the logical decision components. To enhance the reliability or safety of these systems, fault detection methods have been used to determine the occurrences of failures so that appropriate remedy actions can be taken.

One common approach for fault detection, known as the model-based approach, is illustrated in Figure 6. The fault detection problem can be divided into two steps: The first step is to design a filter based on a model of the plant to generate a vector known as the residual. The residual should ideally be zero (or zero mean) under no-fault conditions. The second step is to make decisions on whether a fault has occurred. This step is usually done using statistical tools to test if the residual has significantly deviated from zero. This fault detection method could be extended to fault detection and isolation (FDI) for multiple faults using a bank of residual generation filters in parallel.

It has been shown the the SLHS is useful in modeling practical hybrid systems that have stochastic discrete state (or mode) transitions which are depenedent on the continuous state. However, most existing quantatitive model-based fault detection methods, such as the observer-based methods or the Kalman filter methods, have so far considered systems with continuous state dynamics only. Hence, we have proposed a FDI algorithm for the SLHS. We have proposed an efficient residual generation filter for the SLHS. Furthermore, we have shown that the residual vector has a zero mean and a known covariance when the model matches the true system dynamics. Using the known statistical properties of the residual, we then designed a quantitative FDI scheme using hypothesis tests. We are currently investigating applications of the proposed FDI scheme in an aircraft autolanding system and a cooperative robotic system respectively.

Figure 6: A model-based fault detection scheme.

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