{"ID":2848594,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.25513","arxiv_id":"2510.25513","title":"Sum-of-Squares Certificates for Almost-Sure Reachability of Stochastic Polynomial Systems","abstract":"In this paper, we present a computational approach to certify almost sure reachability for discrete-time polynomial stochastic systems by turning drift--variant criteria into sum-of-squares (SOS) programs solved with standard semidefinite solvers. Specifically, we provide an SOS method based on two complementary certificates: (i) a drift certificate that enforces a radially unbounded function to be non-increasing in expectation outside a compact set of states; and (ii) a variant certificate that guarantees a one-step decrease with positive probability and ensures the target contains its nonpositive sublevel set. We transform these conditions to SOS constraints. For the variant condition, we enforce a robust decrease over a parameterized disturbance ball with nonzero probability and encode the constraints via an S-procedure with polynomial multipliers. The resulting bilinearities are handled by an alternating scheme that alternates between optimizing multipliers and updating the variant and radius until a positive slack is obtained. Two case studies illustrate the workflow and certifies almost-sure reachability.","short_abstract":"In this paper, we present a computational approach to certify almost sure reachability for discrete-time polynomial stochastic systems by turning drift--variant criteria into sum-of-squares (SOS) programs solved with standard semidefinite solvers. Specifically, we provide an SOS method based on two complementary certif...","url_abs":"https://arxiv.org/abs/2510.25513","url_pdf":"https://arxiv.org/pdf/2510.25513v1","authors":"[\"Arash Bahari Kordabad\",\"Rupak Majumdar\",\"Sadegh Soudjani\"]","published":"2025-10-29T13:36:55Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"eess.SY\"]","methods":"[]","has_code":false}