{"ID":2852787,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.17551","arxiv_id":"2510.17551","title":"Towards Optimal Control and Algorithmic Structure of Decompression Schedules","abstract":"We formalise decompression planning as an optimal control problem with gas feasibility windows (ppO$_2$, END), affine ceilings, and convex penalties in normalised oversaturation. The depth trajectory is constrained to be a monotone ascent, matching operational decompression practice. In this setting we prove relaxed existence, derive bang-bang structure for the vertical rate control, and obtain nonsmooth dwell time KKT conditions. For finite stop grids we give resource constrained dynamic programming and label setting formulations with explicit discretisation error bounds, while also stating the tissue state quantisation or label growth assumptions needed for pseudo-polynomial complexity. The time risk attainable set is generally nonconvex because gas, stop, and switching choices are discrete. We also isolate the precise scope of the two segment exchange argument. It orders terminal tissue tension under monotone inert fraction ordering, but it does not prove that re-descents are dominated for the oversaturation only penalty used here.","short_abstract":"We formalise decompression planning as an optimal control problem with gas feasibility windows (ppO$_2$, END), affine ceilings, and convex penalties in normalised oversaturation. The depth trajectory is constrained to be a monotone ascent, matching operational decompression practice. In this setting we prove relaxed ex...","url_abs":"https://arxiv.org/abs/2510.17551","url_pdf":"https://arxiv.org/pdf/2510.17551v4","authors":"[\"Benjamin Marsh\"]","published":"2025-10-20T14:00:51Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}