Abstract
This paper investigates the distributed fault detection problem for linear discrete time-varying heterogeneous multi-agent systems under relative output information. Due to the lack of absolute outputs, an augmented model is built by stacking all local relative output information. Then, the fault detection problem consisting of residual-generation and residual-evaluation is handled using the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filtering framework. The residual-generation problem is actually a minimization problem of an indefinite quadratic form, and the Krein space-Kalman filtering theory is applied, which results in a low computational burden despite the time-varying characteristic. Using the Krein space theory, a necessary and sufficient condition for the minimum is derived, and a residual-generation algorithm is developed. Further, a residual-evaluation mechanism is designed by constructing an evaluation function and detecting faults by comparing it with a threshold. Finally, two illustrative examples are given to demonstrate the effectiveness of the proposed fault detection approach.
Highlights
W ITH the increasing complexity of work environments and task scales, it is difficult for traditional research on a single controlled object to meet the actual demand
Control problems of multi-agent systems (MASs) have been extensively studied such as adaptive control [7], [8] and event-triggered control [9]–[11], and many results have been obtained for communication delay [12], [13]
The elements in the Euclidean space are denoted by normal letters such as x, y, w, f, v, while the elements in the Krein space are denoted by bold letters, such as x, y, w, f, v
Summary
W ITH the increasing complexity of work environments and task scales, it is difficult for traditional research on a single controlled object to meet the actual demand. We deal with the distributed fault detection problem for a class of LDTV heterogeneous MASs with relative output information. We construct an augmented model for each agent by stacking all locally obtained relative output information, and apply the Krein space-based H∞ filtering theory to yield a distributed residual-generator and a distributed residual-evaluation mechanism. Relative output information was considered in [42], [43] and [44], the absolute measurements were used for FD in these works; on the other hand, [39] and [40] investigated FD problems for multi-agent networks with only relative state measurements; the systems considered in these studies were all time-invariant, making the obtained results unsuitable for our problem. The elements in the Euclidean space are denoted by normal letters such as x, y, w, f , v, while the elements in the Krein space are denoted by bold letters, such as x, y, w, f, v
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