{"ID":2864769,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.23367","arxiv_id":"2509.23367","title":"Efficient Norm-Based Reachable Sets via Iterative Dynamic Programming","abstract":"In this work, we present a numerical optimal control framework for reachable set computation using \\emph{normotopes}, a new set representation as a norm ball with a shaping matrix. In reachable set computations, we expect to continuously vary the shape matrix as a function of time. Incorporating the shape dynamics as an input, we build a \\emph{controlled embedding system} using a linear differential inclusion overapproximating the dynamics of the system, where a single forward simulation of this embedding system always provides an overapproximating reachable set of the system, no matter the choice of \\emph{hypercontrol}. By iteratively solving a linear quadratic approximation of the nonlinear optimal hypercontrol problem, we synthesize less conservative final reachable sets, providing a natural tradeoff between runtime and accuracy. Terminating our algorithm at any point always returns a valid reachable set overapproximation.","short_abstract":"In this work, we present a numerical optimal control framework for reachable set computation using \\emph{normotopes}, a new set representation as a norm ball with a shaping matrix. In reachable set computations, we expect to continuously vary the shape matrix as a function of time. Incorporating the shape dynamics as a...","url_abs":"https://arxiv.org/abs/2509.23367","url_pdf":"https://arxiv.org/pdf/2509.23367v1","authors":"[\"Akash Harapanahalli\",\"Samuel Coogan\"]","published":"2025-09-27T15:26:36Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"eess.SY\"]","methods":"[]","has_code":false}