A data-driven robust optimization approach to scenario-based stochastic model predictive control
•A novel data-driven approach is proposed for stochastic model predictive control.•Support vector clustering is adopted to learn an uncertainty set from scenarios.•A calibration procedure is developed to provide desirable probabilistic guarantees.•Finally, an uncertainty set-induced robust optimizat...
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| Published in: | Journal of process control Vol. 75; pp. 24 - 39 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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01.03.2019
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| ISSN: | 0959-1524, 1873-2771 |
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| Abstract | •A novel data-driven approach is proposed for stochastic model predictive control.•Support vector clustering is adopted to learn an uncertainty set from scenarios.•A calibration procedure is developed to provide desirable probabilistic guarantees.•Finally, an uncertainty set-induced robust optimization problem is solved.•The proposed method requires less scenarios and can reduce conservatism.
Stochastic model predictive control (SMPC) has been a promising solution to complex control problems under uncertain disturbances. However, traditional SMPC approaches either require exact knowledge of probabilistic distributions, or rely on massive scenarios that are generated to represent uncertainties. In this paper, a novel scenario-based SMPC approach is proposed by actively learning a data-driven uncertainty set from available data with machine learning techniques. A systematical procedure is then proposed to further calibrate the uncertainty set, which gives appropriate probabilistic guarantee. The resulting data-driven uncertainty set is more compact than traditional norm-based sets, and can help reducing conservatism of control actions. Meanwhile, the proposed method requires less data samples than traditional scenario-based SMPC approaches, thereby enhancing the practicability of SMPC. Finally the optimal control problem is cast as a single-stage robust optimization problem, which can be solved efficiently by deriving the robust counterpart problem. The feasibility and stability issue is also discussed in detail. The efficacy of the proposed approach is demonstrated through a two-mass-spring system and a building energy control problem under uncertain disturbances. |
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| AbstractList | •A novel data-driven approach is proposed for stochastic model predictive control.•Support vector clustering is adopted to learn an uncertainty set from scenarios.•A calibration procedure is developed to provide desirable probabilistic guarantees.•Finally, an uncertainty set-induced robust optimization problem is solved.•The proposed method requires less scenarios and can reduce conservatism.
Stochastic model predictive control (SMPC) has been a promising solution to complex control problems under uncertain disturbances. However, traditional SMPC approaches either require exact knowledge of probabilistic distributions, or rely on massive scenarios that are generated to represent uncertainties. In this paper, a novel scenario-based SMPC approach is proposed by actively learning a data-driven uncertainty set from available data with machine learning techniques. A systematical procedure is then proposed to further calibrate the uncertainty set, which gives appropriate probabilistic guarantee. The resulting data-driven uncertainty set is more compact than traditional norm-based sets, and can help reducing conservatism of control actions. Meanwhile, the proposed method requires less data samples than traditional scenario-based SMPC approaches, thereby enhancing the practicability of SMPC. Finally the optimal control problem is cast as a single-stage robust optimization problem, which can be solved efficiently by deriving the robust counterpart problem. The feasibility and stability issue is also discussed in detail. The efficacy of the proposed approach is demonstrated through a two-mass-spring system and a building energy control problem under uncertain disturbances. |
| Author | You, Fengqi Shang, Chao |
| Author_xml | – sequence: 1 givenname: Chao surname: Shang fullname: Shang, Chao email: c-shang@tsinghua.edu.cn organization: Beijing National Research Center for Information Science and Technology, and Department of Automation, Tsinghua University, Beijing 100084, China – sequence: 2 givenname: Fengqi surname: You fullname: You, Fengqi email: fengqi.you@cornell.edu organization: Robert Frederick Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY 14853, USA |
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| Keywords | Chance constraints Stochastic model predictive control Robust model predictive control Scenario programs Machine learning |
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| SubjectTerms | Chance constraints Machine learning Robust model predictive control Scenario programs Stochastic model predictive control |
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