Time-Optimal Model Predictive Control for Linear Time-Variant Systems Based on Configuration-Constrained Backward Reachability
This paper presents a robust formulation of Time-Optimal Model Predictive Control for Linear Time-Variant systems that leverages backward reachability analysis for time-optimality while achieving constraint handling and disturbance rejection. The formulation minimizes the time required to reach a te...
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IEEE
2025-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/11097310/ |
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| author | Michael Fink Annalena Daniels Dirk Wollherr Marion Leibold |
| author_facet | Michael Fink Annalena Daniels Dirk Wollherr Marion Leibold |
| author_sort | Michael Fink |
| collection | DOAJ |
| description | This paper presents a robust formulation of Time-Optimal Model Predictive Control for Linear Time-Variant systems that leverages backward reachability analysis for time-optimality while achieving constraint handling and disturbance rejection. The formulation minimizes the time required to reach a terminal set while maintaining recursive feasibility and robustness. Unlike most Time-Optimal Model Predictive Control approaches that depend on time-scaling or iterative horizon reduction, the proposed framework computes a backward reachable tube offline. Each reachable set contains the largest set of states that can reach the terminal set within a fixed number of steps. A controller that constrains the state to remain within the backward reachable tube achieves time-optimality while ensuring real-time applicability and feasibility under disturbances, also with a short prediction horizon. The central innovation lies in the use of configuration-constrained polytopes to construct backward reachable tubes offline with fixed complexity, which permits propagation over long time horizons without growing computational cost. Notably, our method introduces a containment check that dynamically identifies the set in the tube that contains the current system state and lies closer to the terminal set, thereby providing an updated time index for the controller. This effectively replaces the originally planned initial constraint with one that reflects the actual progress. As a result, the controller exploits favorable disturbance realizations, accelerates convergence to the terminal set, and significantly reduces conservatism without compromising robustness. The approach is validated in a vertical farming application, where the objective is to drive crop growth toward desired biomass and ripeness levels as quickly as possible. |
| format | Article |
| id | doaj-art-dc99628aef7348ac8ac7e64efe7121d6 |
| institution | Kabale University |
| issn | 2169-3536 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IEEE |
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| spelling | doaj-art-dc99628aef7348ac8ac7e64efe7121d62025-08-20T03:59:31ZengIEEEIEEE Access2169-35362025-01-011313371113372310.1109/ACCESS.2025.359298111097310Time-Optimal Model Predictive Control for Linear Time-Variant Systems Based on Configuration-Constrained Backward ReachabilityMichael Fink0https://orcid.org/0000-0003-4197-5464Annalena Daniels1https://orcid.org/0000-0002-3680-7610Dirk Wollherr2https://orcid.org/0000-0003-2810-6790Marion Leibold3https://orcid.org/0000-0002-2802-5600Chair of Automatic Control Engineering, Technical University of Munich, Munich, GermanyChair of Automatic Control Engineering, Technical University of Munich, Munich, GermanyChair of Automatic Control Engineering, Technical University of Munich, Munich, GermanyChair of Automatic Control Engineering, Technical University of Munich, Munich, GermanyThis paper presents a robust formulation of Time-Optimal Model Predictive Control for Linear Time-Variant systems that leverages backward reachability analysis for time-optimality while achieving constraint handling and disturbance rejection. The formulation minimizes the time required to reach a terminal set while maintaining recursive feasibility and robustness. Unlike most Time-Optimal Model Predictive Control approaches that depend on time-scaling or iterative horizon reduction, the proposed framework computes a backward reachable tube offline. Each reachable set contains the largest set of states that can reach the terminal set within a fixed number of steps. A controller that constrains the state to remain within the backward reachable tube achieves time-optimality while ensuring real-time applicability and feasibility under disturbances, also with a short prediction horizon. The central innovation lies in the use of configuration-constrained polytopes to construct backward reachable tubes offline with fixed complexity, which permits propagation over long time horizons without growing computational cost. Notably, our method introduces a containment check that dynamically identifies the set in the tube that contains the current system state and lies closer to the terminal set, thereby providing an updated time index for the controller. This effectively replaces the originally planned initial constraint with one that reflects the actual progress. As a result, the controller exploits favorable disturbance realizations, accelerates convergence to the terminal set, and significantly reduces conservatism without compromising robustness. The approach is validated in a vertical farming application, where the objective is to drive crop growth toward desired biomass and ripeness levels as quickly as possible.https://ieeexplore.ieee.org/document/11097310/Backward reachabilityconfiguration-constrained polytopeslinear time-variant systemsmodel predictive controlreachability analysisrobust control |
| spellingShingle | Michael Fink Annalena Daniels Dirk Wollherr Marion Leibold Time-Optimal Model Predictive Control for Linear Time-Variant Systems Based on Configuration-Constrained Backward Reachability IEEE Access Backward reachability configuration-constrained polytopes linear time-variant systems model predictive control reachability analysis robust control |
| title | Time-Optimal Model Predictive Control for Linear Time-Variant Systems Based on Configuration-Constrained Backward Reachability |
| title_full | Time-Optimal Model Predictive Control for Linear Time-Variant Systems Based on Configuration-Constrained Backward Reachability |
| title_fullStr | Time-Optimal Model Predictive Control for Linear Time-Variant Systems Based on Configuration-Constrained Backward Reachability |
| title_full_unstemmed | Time-Optimal Model Predictive Control for Linear Time-Variant Systems Based on Configuration-Constrained Backward Reachability |
| title_short | Time-Optimal Model Predictive Control for Linear Time-Variant Systems Based on Configuration-Constrained Backward Reachability |
| title_sort | time optimal model predictive control for linear time variant systems based on configuration constrained backward reachability |
| topic | Backward reachability configuration-constrained polytopes linear time-variant systems model predictive control reachability analysis robust control |
| url | https://ieeexplore.ieee.org/document/11097310/ |
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