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Measured‐State Conditioned Recursive Feasibility for Stochastic Model Predictive Control.

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Title: Measured‐State Conditioned Recursive Feasibility for Stochastic Model Predictive Control.
Authors: Fiacchini, Mirko1 (AUTHOR) mirko.fiacchini@gipsa-lab.fr, Mammarella, Martina2 (AUTHOR), Dabbene, Fabrizio2 (AUTHOR)
Source: International Journal of Robust & Nonlinear Control. 7/25/2026, Vol. 36 Issue 11, p5964-5981. 18p.
Subjects: Predictive control systems, Linear dynamical systems, Constraints (Physics), Closed loop systems
Abstract: 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 on 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 to relax the constraints vanishes over time, which leads the closed‐loop trajectories steered toward the unconstrained LQR invariant region. This novel SMPC scheme is proven to satisfy the recursive feasibility conditioned on the state realization, and its superiority with respect to open‐loop initialization schemes is shown through numerical examples. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Robust & Nonlinear Control is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
An: 194403487
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  Data: Measured‐State Conditioned Recursive Feasibility for Stochastic Model Predictive Control.
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  Data: <searchLink fieldCode="AR" term="%22Fiacchini%2C+Mirko%22">Fiacchini, Mirko</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> mirko.fiacchini@gipsa-lab.fr</i><br /><searchLink fieldCode="AR" term="%22Mammarella%2C+Martina%22">Mammarella, Martina</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Dabbene%2C+Fabrizio%22">Dabbene, Fabrizio</searchLink><relatesTo>2</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Robust+%26+Nonlinear+Control%22">International Journal of Robust & Nonlinear Control</searchLink>. 7/25/2026, Vol. 36 Issue 11, p5964-5981. 18p.
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  Data: <searchLink fieldCode="DE" term="%22Predictive+control+systems%22">Predictive control systems</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+dynamical+systems%22">Linear dynamical systems</searchLink><br /><searchLink fieldCode="DE" term="%22Constraints+%28Physics%29%22">Constraints (Physics)</searchLink><br /><searchLink fieldCode="DE" term="%22Closed+loop+systems%22">Closed loop systems</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: 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 on 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 to relax the constraints vanishes over time, which leads the closed‐loop trajectories steered toward the unconstrained LQR invariant region. This novel SMPC scheme is proven to satisfy the recursive feasibility conditioned on the state realization, and its superiority with respect to open‐loop initialization schemes is shown through numerical examples. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of International Journal of Robust & Nonlinear Control is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1002/rnc.70565
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      – Code: eng
        Text: English
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        PageCount: 18
        StartPage: 5964
    Subjects:
      – SubjectFull: Predictive control systems
        Type: general
      – SubjectFull: Linear dynamical systems
        Type: general
      – SubjectFull: Constraints (Physics)
        Type: general
      – SubjectFull: Closed loop systems
        Type: general
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      – TitleFull: Measured‐State Conditioned Recursive Feasibility for Stochastic Model Predictive Control.
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            NameFull: Fiacchini, Mirko
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            NameFull: Mammarella, Martina
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            – D: 25
              M: 07
              Text: 7/25/2026
              Type: published
              Y: 2026
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            – TitleFull: International Journal of Robust & Nonlinear Control
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