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Peak estimation bounds extreme values of a function of state along trajectories of a dynamical system. This paper focuses on extending peak estimation to continuous and discrete settings with timeindependent and time-dependent uncertainty. Techniques from optimal control are used to incorporate uncertainty into an existing occupation measure-based peak estimation framework, which includes special consideration for handling switching uncertainties. The resulting infinite-dimensional linear programs can be solved approximately with Linear Matrix Inequalities arising from the moment-SOS hierarchy.

The Hittite composition known as Paskuwatti’s Ritual (CTH 406) has long been understood as a rite designed to help a man to overcome sexual impotence. The present paper, in contrast, attempts to demonstrate that it is more convincingly interpreted as an antidote to homosexual behavior, apparently seeking to cure its patient of his proclivity for passive sexual acquiescence and to replace it with an inclination toward normative male, i.e. penetrative behavior.

This work proposes an algorithm to bound the minimum distance between points on trajectories of a dynamical system and points on an unsafe set. Prior work on certifying safety of trajectories includes barrier and density methods, which do not provide a margin of proximity to the unsafe set in terms of distance. The distance estimation problem is relaxed to a Monge-Kantorovich type optimal transport problem based on existing occupation-measure methods of peak estimation. Specialized programs may be developed for polyhedral norm distances (e.g. L1 and Linfinity) and for scenarios where a shape is traveling along trajectories (e.g. rigid body motion). The distance estimation problem will be correlatively sparse when the distance objective is separable.