Recursive feasibility for stochastic MPC and the rationale behind fixing flat tires
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910918205505536 |
|---|---|
| author | Fiacchini, Mirko Mammarella, Martina Dabbene, Fabrizio |
| author_facet | Fiacchini, Mirko Mammarella, Martina Dabbene, Fabrizio |
| contents | In this paper, we address the problem of designing stochastic model predictive control (SMPC) schemes for linear systems affected by unbounded disturbances. The contribution of the paper is rooted in a measured-state initialization strategy. First, due to the nonzero probability of violating chance-constraints in the case of unbounded noise, we introduce ellipsoidal-based probabilistic reachable sets and we include constraint relaxations to recover recursive feasibility conditioned to the measured state. Second, we prove that the solution of this novel SMPC scheme guarantees closed-loop chance constraints satisfaction under minimum relaxation. Last, we demonstrate that, in expectation, the need of relaxing the constraints vanishes over time, which leads the closed-loop trajectories steered towards the unconstrained LQR invariant region. This novel SMPC scheme is proven to satisfy the recursive feasibility conditioned to the state realization, and its superiority with respect to open-loop initialization schemes is shown through numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17718 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Recursive feasibility for stochastic MPC and the rationale behind fixing flat tires Fiacchini, Mirko Mammarella, Martina Dabbene, Fabrizio Optimization and Control Systems and Control In this paper, we address the problem of designing stochastic model predictive control (SMPC) schemes for linear systems affected by unbounded disturbances. The contribution of the paper is rooted in a measured-state initialization strategy. First, due to the nonzero probability of violating chance-constraints in the case of unbounded noise, we introduce ellipsoidal-based probabilistic reachable sets and we include constraint relaxations to recover recursive feasibility conditioned to the measured state. Second, we prove that the solution of this novel SMPC scheme guarantees closed-loop chance constraints satisfaction under minimum relaxation. Last, we demonstrate that, in expectation, the need of relaxing the constraints vanishes over time, which leads the closed-loop trajectories steered towards the unconstrained LQR invariant region. This novel SMPC scheme is proven to satisfy the recursive feasibility conditioned to the state realization, and its superiority with respect to open-loop initialization schemes is shown through numerical examples. |
| title | Recursive feasibility for stochastic MPC and the rationale behind fixing flat tires |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2504.17718 |