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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.19504 |
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Table of Contents:
- This paper extends sliding-mode control theory to nonlinear systems evolving on smooth manifolds. Building on differential geometric methods, we reformulate Filippov's notion of solutions, characterize well-defined vector fields on quotient spaces, and provide a consistent geometric definition of higher-order sliding modes. We generalize the regular form to non-Euclidean settings and design explicit first- and second-order sliding-mode controllers that respect the manifold structure. Particular attention is given to the role of topological obstructions, which are illustrated through examples on the cylinder, Möbius bundle, and 2-sphere. Our results highlight how geometric and topological properties fundamentally influence sliding dynamics and suggest new directions for robust control in nonlinear spaces.