Data-Driven Tube-Based Zonotopic Predictive Control With Nonconvex Layered Terminal Sets
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918425652101120 |
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| author | Zhang, Zhen Gheorghe, Bogdan Stoican, Florin Alanwar, Amr |
| author_facet | Zhang, Zhen Gheorghe, Bogdan Stoican, Florin Alanwar, Amr |
| contents | This paper presents a data-driven tube-based zonotopic predictive control (DTZPC) framework with nonconvex layered terminal sets. Existing DTZPC schemes with closed-loop guarantees typically rely on a single ellipsoidal terminal set, which can be conservative and thereby limit feasibility. We propose a layered terminal-set design that decouples stability certification, feasibility enlargement, and motion-region screening into three components with distinct roles. First, an offline-designed feedback gain together with a contractive constrained zonotope provides a terminal ingredient for stability certification, while avoiding probabilistic feedback synthesis in high-dimensional DTZPC. Second, we derive a data-driven characterization of the inverse admissible closed-loop model set, avoiding the conservatism of interval-matrix relaxation and inversion. Combined with exact set multiplication, this yields inner and outer approximations of the maximal robust positively invariant (MRPI) set under fixed closed-loop dynamics. The inner approximation serves as a nonconvex terminal set to enlarge feasibility, whereas the outer approximation provides certified motion-region descriptions for fast screening and monitoring. Numerical examples demonstrate tighter inverse-set enclosures and improved feasibility over existing convex-terminal DTZPC schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_02159 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Data-Driven Tube-Based Zonotopic Predictive Control With Nonconvex Layered Terminal Sets Zhang, Zhen Gheorghe, Bogdan Stoican, Florin Alanwar, Amr Optimization and Control This paper presents a data-driven tube-based zonotopic predictive control (DTZPC) framework with nonconvex layered terminal sets. Existing DTZPC schemes with closed-loop guarantees typically rely on a single ellipsoidal terminal set, which can be conservative and thereby limit feasibility. We propose a layered terminal-set design that decouples stability certification, feasibility enlargement, and motion-region screening into three components with distinct roles. First, an offline-designed feedback gain together with a contractive constrained zonotope provides a terminal ingredient for stability certification, while avoiding probabilistic feedback synthesis in high-dimensional DTZPC. Second, we derive a data-driven characterization of the inverse admissible closed-loop model set, avoiding the conservatism of interval-matrix relaxation and inversion. Combined with exact set multiplication, this yields inner and outer approximations of the maximal robust positively invariant (MRPI) set under fixed closed-loop dynamics. The inner approximation serves as a nonconvex terminal set to enlarge feasibility, whereas the outer approximation provides certified motion-region descriptions for fast screening and monitoring. Numerical examples demonstrate tighter inverse-set enclosures and improved feasibility over existing convex-terminal DTZPC schemes. |
| title | Data-Driven Tube-Based Zonotopic Predictive Control With Nonconvex Layered Terminal Sets |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2604.02159 |