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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.18374 |
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| _version_ | 1866913108853784576 |
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| author | Sun, Jiaxun Xue, Hengyu Zhao, Yuyang |
| author_facet | Sun, Jiaxun Xue, Hengyu Zhao, Yuyang |
| contents | We derive a computable closed-form upper bound on the Hausdorff distance between a truncated minimal robust positively invariant (mRPI) set and its infinite-horizon limit. The bound depends only on a disturbance-set size measure and an induced-norm contraction factor of the system matrix, and it yields an explicit, fully analytic horizon-selection rule that guarantees a prescribed approximation tolerance without iterative set computations. The choice of vector norm enters as a design lever: norm shaping -- through diagonal or Lyapunov-based weighting -- tightens both the contraction factor and the resulting certificate, with direct consequences for robust invariant-set approximation and tube-based model predictive control (MPC) constraint tightening. Numerical examples illustrate the accuracy, scalability, and practical impact of the proposed bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18374 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Explicit Bounds on the Hausdorff Distance for Truncated mRPI Sets via Norm-Dependent Contraction Rates Sun, Jiaxun Xue, Hengyu Zhao, Yuyang Robotics Systems and Control Dynamical Systems We derive a computable closed-form upper bound on the Hausdorff distance between a truncated minimal robust positively invariant (mRPI) set and its infinite-horizon limit. The bound depends only on a disturbance-set size measure and an induced-norm contraction factor of the system matrix, and it yields an explicit, fully analytic horizon-selection rule that guarantees a prescribed approximation tolerance without iterative set computations. The choice of vector norm enters as a design lever: norm shaping -- through diagonal or Lyapunov-based weighting -- tightens both the contraction factor and the resulting certificate, with direct consequences for robust invariant-set approximation and tube-based model predictive control (MPC) constraint tightening. Numerical examples illustrate the accuracy, scalability, and practical impact of the proposed bound. |
| title | Explicit Bounds on the Hausdorff Distance for Truncated mRPI Sets via Norm-Dependent Contraction Rates |
| topic | Robotics Systems and Control Dynamical Systems |
| url | https://arxiv.org/abs/2511.18374 |