Abstract
In the paper, we study the so-called p-safety of a random dynamical system. We generalize the existing results for safety barrier certificates for deterministic dynamical systems and Markov processes. Moreover, we consider the case of random obstacles, modelled as random sets. This leads to the necessity of using integrals with respect to lower and upper distributions. We prove that if there exists at least one barrier certificate then the random dynamical system is safe. The barrier certificates are also defined using such nonlinear distributions. Furthermore, when the family of stochastic Koopman operators has the semigroup property, the barrier certificates are solutions for some type of Dirichlet problems.
| Original language | English |
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| Title of host publication | 2021 American Control Conference (ACC) |
| Place of Publication | Piscataway, NJ |
| Publisher | IEEE |
| Pages | 1340-1345 |
| Number of pages | 6 |
| ISBN (Electronic) | 9781665441971 |
| DOIs | |
| Publication status | Published - 28 Jul 2021 |
| Event | 2021 American Control Conference - Virtual, New Orleans, United States Duration: 25 May 2021 → 28 May 2021 https://acc2021.a2c2.org/ |
Publication series
| Name | Proceedings of the American Control Conference |
|---|---|
| Publisher | IEEE |
| ISSN (Print) | 0743-1619 |
| ISSN (Electronic) | 2378-5861 |
Conference
| Conference | 2021 American Control Conference |
|---|---|
| Abbreviated title | ACC 2021 |
| Country/Territory | United States |
| City | New Orleans |
| Period | 25/05/21 → 28/05/21 |
| Internet address |
Keywords
- Koopman operator
- barrier certificates
- hitting measure
- occupation measure
- p-safety
- random dynamical system
- random set
- supermedian function