A novel strategy aimed at cooperatively differentiating a signal among multiple interacting agents is introduced, where none of the agents needs to know which agent is the leader, i.e. the one producing the signal to be differentiated. Every agent communicates only a scalar variable to its neighbors; except for the leader, all agents execute the same algorithm. The proposed strategy can effectively obtain derivatives up to arbitrary $m$-th order in a finite time under the assumption that the $(m+1)$-th derivative is bounded. The strategy borrows some of its structure from the celebrated homogeneous robust exact differentiator by A. Levant, inheriting its exact differentiation capability and robustness to measurement noise. Hence, the proposed strategy can be said to perform robust exact distributed differentiation. In addition, and for the first time in the distributed leader-observer literature, sampled-data communication and bounded measurement noise are considered, and corresponding steady-state worst-case accuracy bounds are derived. The effectiveness of the proposed strategy is verified numerically for second- and fourth-order systems, i.e., for estimating derivatives of up to first and third order, respectively.

As engineered systems grow in complexity, there is an increasing need for automatic methods that can detect, diagnose, and even correct transient anomalies that inevitably arise and can be difficult or impossible to diagnose and fix manually. Among the most sensitive and complex systems of our civilization are the detectors that search for incredibly small variations in distance caused by gravitational waves -- phenomena originally predicted by Albert Einstein to emerge and propagate through the universe as the result of collisions between black holes and other massive objects in deep space. The extreme complexity and precision of such detectors causes them to be subject to transient noise issues that can significantly limit their sensitivity and effectiveness. In this work, we present a demonstration of a method that can detect and characterize emergent transient anomalies of such massively complex systems. We illustrate the performance, precision, and adaptability of the automated solution via one of the prevalent issues limiting gravitational-wave discoveries: noise artifacts of terrestrial origin that contaminate gravitational wave observatories' highly sensitive measurements and can obscure or even mimic the faint astrophysical signals for which they are listening. Specifically, we demonstrate how a highly interpretable convolutional classifier can automatically learn to detect transient anomalies from auxiliary detector data without needing to observe the anomalies themselves. We also illustrate several other useful features of the model, including how it performs automatic variable selection to reduce tens of thousands of auxiliary data channels to only a few relevant ones; how it identifies behavioral signatures predictive of anomalies in those channels; and how it can be used to investigate individual anomalies and the channels associated with them.