A stability governor for constrained linear–quadratic MPC without terminal constraints
This paper introduces a supervisory unit, called the stability governor (SG), that provides improved guarantees of stability for constrained linear systems under Model Predictive Control (MPC) without terminal constraints. At each time step, the SG alters the setpoint command supplied to the MPC pro...
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| Published in | Automatica (Oxford) Vol. 164; p. 111650 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.06.2024
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0005-1098 1873-2836 |
| DOI | 10.1016/j.automatica.2024.111650 |
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| Abstract | This paper introduces a supervisory unit, called the stability governor (SG), that provides improved guarantees of stability for constrained linear systems under Model Predictive Control (MPC) without terminal constraints. At each time step, the SG alters the setpoint command supplied to the MPC problem so that the current state is guaranteed to be inside of the region of attraction for an auxiliary equilibrium point. The proposed strategy is shown to be recursively feasible and asymptotically stabilizing for all initial states sufficiently close to any equilibrium of the system. Thus, asymptotic stability of the target equilibrium can be guaranteed for a large set of initial states even when a short prediction horizon is used. A numerical example demonstrates that the stability governed MPC strategy can recover closed-loop stability in a scenario where a standard MPC implementation without terminal constraints leads to divergent trajectories. |
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| AbstractList | This paper introduces a supervisory unit, called the stability governor (SG), that provides improved guarantees of stability for constrained linear systems under Model Predictive Control (MPC) without terminal constraints. At each time step, the SG alters the setpoint command supplied to the MPC problem so that the current state is guaranteed to be inside of the region of attraction for an auxiliary equilibrium point. The proposed strategy is shown to be recursively feasible and asymptotically stabilizing for all initial states sufficiently close to any equilibrium of the system. Thus, asymptotic stability of the target equilibrium can be guaranteed for a large set of initial states even when a short prediction horizon is used. A numerical example demonstrates that the stability governed MPC strategy can recover closed-loop stability in a scenario where a standard MPC implementation without terminal constraints leads to divergent trajectories. |
| ArticleNumber | 111650 |
| Author | Leung, Jordan Kolmanovsky, Ilya V. Permenter, Frank |
| Author_xml | – sequence: 1 givenname: Jordan surname: Leung fullname: Leung, Jordan email: jmleung@umich.edu organization: University of Michigan, Ann Arbor, MI 48109, USA – sequence: 2 givenname: Frank surname: Permenter fullname: Permenter, Frank email: frank.permenter@tri.global organization: Toyota Research Institute, Cambridge, MA 02139, USA – sequence: 3 givenname: Ilya V. surname: Kolmanovsky fullname: Kolmanovsky, Ilya V. email: ilya@umich.edu organization: University of Michigan, Ann Arbor, MI 48109, USA |
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| Cites_doi | 10.23919/ECC.2018.8550438 10.1109/LCSYS.2020.3044977 10.1109/TAC.2013.2275667 10.1109/TAC.2006.875014 10.1016/j.automatica.2023.110942 10.1016/S0005-1098(99)00214-9 10.1016/j.automatica.2008.01.023 10.1016/S0005-1098(01)00028-0 10.1016/j.ifacol.2020.12.073 10.1109/MED.2014.6961399 10.1109/TAC.2021.3123224 10.1109/9.83532 10.1109/TCST.2009.2017934 10.23919/ACC53348.2022.9867484 10.23919/ECC.2019.8796239 |
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| SubjectTerms | Asymptotic stabilization Control of constrained systems Model predictive control Tracking |
| Title | A stability governor for constrained linear–quadratic MPC without terminal constraints |
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