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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.07225 |
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| _version_ | 1866917461947842560 |
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| author | Wembe, Emmanuel Junior Wafo Saoud, Adnane |
| author_facet | Wembe, Emmanuel Junior Wafo Saoud, Adnane |
| contents | In this paper, we revisit the computation of controlled invariant sets for linear discrete-time systems through a trajectory-based viewpoint. We begin by introducing the notion of convex feasible points, which provides a new characterization of controlled invariance using finitely long state trajectories. We further show that combining this notion with the classical backward fixed-point algorithm allows for the computation of the maximal controlled invariant set. Building on these results, we propose a model predictive control (MPC) scheme that guarantees recursive feasibility without relying on precomputed terminal sets. Finally, we formulate the search for convex feasible points as an optimization problem, yielding a practical computational method for constructing controlled invariant sets. The effectiveness of the approach is illustrated through numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07225 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Trajectory-Based Approach to Controlled Invariance and Recursively Feasible MPC Wembe, Emmanuel Junior Wafo Saoud, Adnane Optimization and Control Systems and Control In this paper, we revisit the computation of controlled invariant sets for linear discrete-time systems through a trajectory-based viewpoint. We begin by introducing the notion of convex feasible points, which provides a new characterization of controlled invariance using finitely long state trajectories. We further show that combining this notion with the classical backward fixed-point algorithm allows for the computation of the maximal controlled invariant set. Building on these results, we propose a model predictive control (MPC) scheme that guarantees recursive feasibility without relying on precomputed terminal sets. Finally, we formulate the search for convex feasible points as an optimization problem, yielding a practical computational method for constructing controlled invariant sets. The effectiveness of the approach is illustrated through numerical examples. |
| title | A Trajectory-Based Approach to Controlled Invariance and Recursively Feasible MPC |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2604.07225 |