Data-driven robust optimization based on kernel learning

Chen, Shang; Huang, Xiaolin; You, Fengqi

doi:10.1016/j.compchemeng.2017.07.004

Cited by 176 publications

(68 citation statements)

References 38 publications

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“…and the ADF policy are adopted in the optimal control problem (12). Here different budget parameters Ω are used in the uncertainty set (48), that is, Ω ∈ {0, 0.01, 0.05, 0.1, 0.25, 0.5, 1, 1.5, 2}, thereby giving rise to a variety of tradeoffs between efficiency and robustness.…”

Section: Resultsmentioning

confidence: 99%

Robust Model Predictive Control of Irrigation Systems With Active Uncertainty Learning and Data Analytics

Chen

Stroock

et al. 2020

IEEE Trans. Contr. Syst. Technol.

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We develop a novel data-driven robust model predictive control (DDRMPC) approach for automatic control of irrigation systems. The fundamental idea is to integrate both mechanistic models, which describe dynamics in soil moisture variations, and data-driven models, which characterize uncertainty in forecast errors of evapotranspiration and precipitation, into a holistic systems control framework. To better capture the support of uncertainty distribution, we take a new learningbased approach by constructing uncertainty sets from historical data. For evapotranspiration forecast error, the support vector clustering-based uncertainty set is adopted, which can be conveniently built from historical data. As for precipitation forecast errors, we analyze the dependence of their distribution on forecast values, and further design a tailored uncertainty set based on the properties of this type of uncertainty. In this way, the overall uncertainty distribution can be elaborately described, which finally contributes to rational and efficient control decisions. To assure the quality of data-driven uncertainty sets, a training-calibration scheme is used to provide theoretical performance guarantees. A generalized affine decision rule is adopted to obtain tractable approximations of optimal control problems, thereby ensuring the practicability of DDRMPC. Case studies using real data show that, DDRMPC can reliably maintain soil moisture above the safety level and avoid crop devastation. The proposed DDRMPC approach leads to a 40% reduction of total water consumption compared to the fine-tuned open-loop control strategy. In comparison with the carefully tuned rulebased control and certainty equivalent model predictive control, the proposed DDRMPC approach can significantly reduce the total water consumption and improve the control performance.

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Section: Resultsmentioning

confidence: 99%

Robust Model Predictive Control of Irrigation Systems With Active Uncertainty Learning and Data Analytics

Chen

Stroock

et al. 2020

IEEE Trans. Contr. Syst. Technol.

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“…To account for asymmetric distributions, forward and backward deviation vectors were utilized in the uncertainty set, which was further integrated with robust optimization models. A data-driven static robust optimization framework based on support vector clustering that aims to find the hypersphere with minimal volume to enclose uncertainty data was proposed [157]. The adopted piecewise linear kernel incorporates the covariance information, thus effectively capturing the correlation among uncertainties.…”

Section: Data-driven Robust Optimizationmentioning

confidence: 99%

Optimization under uncertainty in the era of big data and deep learning: When machine learning meets mathematical programming

Ning

You

2019

Computers & Chemical Engineering

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261

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This paper reviews recent advances in the field of optimization under uncertainty via a modern data lens, highlights key research challenges and promise of data-driven optimization that organically integrates machine learning and mathematical programming for decision-making under uncertainty, and identifies potential research opportunities. A brief review of classical mathematical programming techniques for hedging against uncertainty is first presented, along with their wide spectrum of applications in Process Systems Engineering. A comprehensive review and classification of the relevant publications on data-driven distributionally robust optimization, data-driven chance constrained program, data-driven robust optimization, and data-driven scenario-based optimization is then presented. This paper also identifies fertile avenues for future research that focuses on a closed-loop data-driven optimization framework, which allows the feedback from mathematical programming to machine learning, as well as scenario-based optimization leveraging the power of deep learning techniques. Perspectives on online learningbased data-driven multistage optimization with a learning-while-optimizing scheme is presented.

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“…We first introduce an efficient approach to data-based construction of W t (D), which is proposed by [25]. From a machine learning perspective, estimating the high-density…”

Section: Uncertainty Set Learning With Support Vector Clusteringmentioning

confidence: 99%

“…where matrix Q and the scalar L are kernel parameters that can be determined from data. Typically one can set Q as the sphering matrix Q Σ − 1 2 where Σ is the covariance matrix of w, and value of L shall be sufficiently large [25] 3 . By substituting (25) into (22), we can arrive at the following data-driven uncertainty set:…”

Section: Uncertainty Set Learning With Support Vector Clusteringmentioning

confidence: 99%

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A data-driven robust optimization approach to scenario-based stochastic model predictive control

Chen

You

2019

Journal of Process Control

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115

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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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Data-driven robust optimization based on kernel learning

Cited by 176 publications

References 38 publications

Robust Model Predictive Control of Irrigation Systems With Active Uncertainty Learning and Data Analytics

Robust Model Predictive Control of Irrigation Systems With Active Uncertainty Learning and Data Analytics

Optimization under uncertainty in the era of big data and deep learning: When machine learning meets mathematical programming

A data-driven robust optimization approach to scenario-based stochastic model predictive control

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