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We present counts-level fits to the multi-instrument (keV–GeV) data of the early afterglow (4 ks, 22 ks) of the brightest gamma-ray burst detected to date, GRB 221009A. The complexity of the data reduction, due to the unprecedented brightness and the location in the Galactic plane, is critically addressed. The energy spectrum is found to be well described by a smoothly broken power law with a break energy at a few keV. Three interpretations (slow/fast cooling or the transition between these) within the framework of forward shock synchrotron emission, from accelerated and subsequently cooled electrons, are found. The physical implications for each of these scenarios are discussed.

 

Modern nonlinear control theory seeks to endow systems with properties such as stability and safety, and has been deployed successfully across various domains. Despite this success, model uncertainty remains a significant challenge in ensuring that model-based controllers transfer to real world systems. This paper develops a data-driven approach to robust control synthesis in the presence of model uncertainty using Control Certificate Functions (CCFs), resulting in a convex optimization based controller for achieving properties like stability and safety. An important benefit of our framework is nuanced data-dependent guarantees, which in principle can yield sample-efficient data collection approaches that need not fully determine the input-to-state relationship. This work serves as a starting point for addressing important questions at the intersection of nonlinear control theory and non-parametric learning, both theoretical and in application. We demonstrate the efficiency of the proposed method with respect to input data in simulation with an inverted pendulum in multiple experimental settings.