Towards Learning and Verifying Maximal Lyapunov-Barrier Functions with a Zubov PDE Formulation
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909899583127552 |
|---|---|
| author | Meng, Yiming Liu, Jun |
| author_facet | Meng, Yiming Liu, Jun |
| contents | Verifying stability and safety guarantees for nonlinear systems has received considerable attention in recent years. This property serves as a fundamental building block for specifying more complex system behaviors and control objectives. However, estimating the domain of attraction under safety constraints and constructing a Lyapunov-barrier function remain challenging tasks for nonlinear systems. To address this problem, we propose a Zubov PDE formulation with a Dirichlet boundary condition for autonomous nonlinear systems and show that a physics-informed neural network solution, once formally verified, can serve as a Lyapunov-barrier function that jointly certifies stability and safety. This approach extends existing converse Lyapunov-barrier theorems by introducing a PDE-based framework with boundary conditions defined on the safe set, yielding a near-optimal certified under-approximation of the true safe domain of attraction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09523 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Towards Learning and Verifying Maximal Lyapunov-Barrier Functions with a Zubov PDE Formulation Meng, Yiming Liu, Jun Dynamical Systems Verifying stability and safety guarantees for nonlinear systems has received considerable attention in recent years. This property serves as a fundamental building block for specifying more complex system behaviors and control objectives. However, estimating the domain of attraction under safety constraints and constructing a Lyapunov-barrier function remain challenging tasks for nonlinear systems. To address this problem, we propose a Zubov PDE formulation with a Dirichlet boundary condition for autonomous nonlinear systems and show that a physics-informed neural network solution, once formally verified, can serve as a Lyapunov-barrier function that jointly certifies stability and safety. This approach extends existing converse Lyapunov-barrier theorems by introducing a PDE-based framework with boundary conditions defined on the safe set, yielding a near-optimal certified under-approximation of the true safe domain of attraction. |
| title | Towards Learning and Verifying Maximal Lyapunov-Barrier Functions with a Zubov PDE Formulation |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2511.09523 |