Abstract
This is an overview paper on the relationship between risk-averse designs based on exponential loss functions with or without an additional unknown (adversarial) term and some classes of stochastic games. In particular, the paper discusses the equivalences between risk-averse controller and filter designs and saddle-point solutions of some corresponding risk-neutral stochastic differential games with different information structures for the players. One of the by-products of these analyses is that risk-averse controllers and filters (or estimators) for control and signal-measurement models are robust, through stochastic dissipation inequalities, to unmodeled perturbations in controlled system dynamics as well as signal and the measurement processes. The paper also discusses equivalences between risk-sensitive stochastic zero-sum differential games and some corresponding risk-neutral three-player stochastic zero-sum differential games, as well as robustness issues in stochastic nonzero-sum differential games with finite and infinite populations of players, with the latter belonging to the domain of mean-field games.
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This research was supported in part by the Air Force Office of Scientific Research (AFOSR) under Grant FA9550-19-1-0353, and in part by the Army Research Office MURI Grant AG285.
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This research was supported in part by the Air Force Office of Scientific Research (AFOSR) under Grant No. FA9550-19-1-0353, and in part by the Army Research Office MURI under Grant No. AG285.
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Başar, T. Robust Designs Through Risk Sensitivity: An Overview. J Syst Sci Complex 34, 1634–1665 (2021). https://doi.org/10.1007/s11424-021-1242-6
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DOI: https://doi.org/10.1007/s11424-021-1242-6