Unsafe probabilities and risk contours for stochastic processes using convex optimization
When evaluating safety specifications for trajectories of a dynamical system, it is vital to be able to bound the worst-case probability of unsafety (constraint violation) Certifications of stochastic safety and worst-case probabilities of unsafety can be expressed as infinite-dimensional linear programs (e.g. stochastic barrier functions, occupation measure problems) This paper proves that the infinite-dimensional linear programs and their finite-dimensional Moment-Sum-of-Squares truncations are nonconservative (to the true probability of unsafety) under compactness and regularity conditions in stochastic dynamics. Unsafe-probability estimates and risk contours are generated for example stochastic processes.
Authors
- Mario Sznaier (ORCID: https://orcid.org/0000-0003-4439-3988)
- Didier Henrion (ORCID: https://orcid.org/0000-0001-6735-7715)
- Jared Miller (ORCID: https://orcid.org/0000-0003-4948-4918)
- Matteo Tacchi
Institutions
- University of Stuttgart (DE)
- Institut polytechnique de Grenoble (FR)
- Northeastern University (US)
- Centre National de la Recherche Scientifique (FR)
- Université Fédérale de Toulouse Midi-Pyrénées (FR)
- Laboratoire d'Analyse et d'Architecture des Systèmes (FR)
- Stuttgart Technical University of Applied Sciences (DE)
- GIPSA-Lab (FR)
- Université Grenoble Alpes (FR)
Publication Details
- Journal
- Automatica
- Published
- 2026-03-31
- DOI
- https://doi.org/10.1016/j.automatica.2026.112939
- Primary Topic
- Risk and Portfolio Optimization
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- U.S. Department of Homeland Security
- Deutsche Forschungsgemeinschaft
- Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
- Office of Naval Research
- Air Force Office of Scientific Research