Adaptive Meshing for CPA Lyapunov Function Synthesis
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917103795175424 |
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| author | Strong, Amy K. Akinwande, Samuel Bridgeman, Leila |
| author_facet | Strong, Amy K. Akinwande, Samuel Bridgeman, Leila |
| contents | Continuous piecewise affine (CPA) Lyapunov function synthesis is one method to perform Lyapunov stability analysis for nonlinear systems. This method first generates a mesh over the region of interest in the system's state space and then solves a linear program (LP), which enforces constraints on each vertex of the mesh, to synthesize a Lyapunov function. Finer meshes broaden the class of Lyapunov function candidates, but CPA function synthesis is more computationally expensive for finer meshes -- particularly so in higher dimensional systems. This paper explores methods to mesh the region of interest more efficiently so that a Lyapunov function can be synthesized using less computational effort. Three methods are explored -- adaptive meshing, meshing using knowledge of the system model, and a combination of the two. Numerical examples for two and three dimensional nonlinear dynamical systems are used to compare the efficacy of the three methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20443 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Adaptive Meshing for CPA Lyapunov Function Synthesis Strong, Amy K. Akinwande, Samuel Bridgeman, Leila Systems and Control Continuous piecewise affine (CPA) Lyapunov function synthesis is one method to perform Lyapunov stability analysis for nonlinear systems. This method first generates a mesh over the region of interest in the system's state space and then solves a linear program (LP), which enforces constraints on each vertex of the mesh, to synthesize a Lyapunov function. Finer meshes broaden the class of Lyapunov function candidates, but CPA function synthesis is more computationally expensive for finer meshes -- particularly so in higher dimensional systems. This paper explores methods to mesh the region of interest more efficiently so that a Lyapunov function can be synthesized using less computational effort. Three methods are explored -- adaptive meshing, meshing using knowledge of the system model, and a combination of the two. Numerical examples for two and three dimensional nonlinear dynamical systems are used to compare the efficacy of the three methods. |
| title | Adaptive Meshing for CPA Lyapunov Function Synthesis |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2511.20443 |