Stochastic data-driven model predictive control using gaussian processes

Bradford, Eric; Imsland, Lars; Zhang, Dongda; Chanona, Ehecatl Antonio del Río

doi:10.1016/j.compchemeng.2020.106844

Cited by 87 publications

(72 citation statements)

References 42 publications

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“…In the ESI, we provide figures that show the solution point and objective function value over the number of data points for this problem (Figs. [8][9][10][11]. Interestingly, the objective function value is overestimated considerably for all problems.…”

Section: Illustrative Example and Scaling Of The Algorithmmentioning

confidence: 99%

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Deterministic global optimization with Gaussian processes embedded

et al. 2021

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Gaussian processes (Kriging) are interpolating data-driven models that are frequently applied in various disciplines. Often, Gaussian processes are trained on datasets and are subsequently embedded as surrogate models in optimization problems. These optimization problems are nonconvex and global optimization is desired. However, previous literature observed computational burdens limiting deterministic global optimization to Gaussian processes trained on few data points. We propose a reduced-space formulation for deterministic global optimization with trained Gaussian processes embedded. For optimization, the branch-and-bound solver branches only on the free variables and McCormick relaxations are propagated through explicit Gaussian process models. The approach also leads to significantly smaller and computationally cheaper subproblems for lower and upper bounding. To further accelerate convergence, we derive envelopes of common covariance functions for GPs and tight relaxations of acquisition functions used in Bayesian optimization including expected improvement, probability of improvement, and lower confidence bound. In total, we reduce computational time by orders of magnitude compared to state-of-the-art methods, thus overcoming previous computational burdens. We demonstrate the performance and scaling of the proposed method and apply it to Bayesian optimization with global optimization of the acquisition function and chance-constrained programming. The Gaussian process models, acquisition functions, and training scripts are available open-source within the “MeLOn—MachineLearning Models for Optimization” toolbox (https://git.rwth-aachen.de/avt.svt/public/MeLOn).

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Section: Illustrative Example and Scaling Of The Algorithmmentioning

confidence: 99%

“…Probabilistic constraints are relevant in engineering and science [18] and GPs have been used in the previous literature to formulate chance constraints, e.g., in model predictive control [11] or production planning [87].…”

Section: Chance-constrained Programmingmentioning

confidence: 99%

Deterministic global optimization with Gaussian processes embedded

et al. 2021

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“…The primary challenge in designing nonlinear SMPC (NSMPC) algorithms lies in inefficient uncertainty propagation methods through nonlinear dynamics. Based on different uncertainty propagation methods, NSMPC can be categorized into the following techniques: the generalized polynomial chaos expansions (gPCEs) approach [23] and the Gaussian-mixture (GM) approximation approach [24,25]. In the gPCEs-based approach, polynomial chaos expansions are used to obtain a surrogate for the nonlinear dynamics, which provides an efficient way to predict the state evolution.…”

Section: (Iii) Nonlinear Smpc Approachmentioning

confidence: 99%

Stochastic model predictive control framework for resilient cyber-physical systems: review and perspectives

Chen

Shi

2021

Phil. Trans. R. Soc. A.

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In the era of Industrial 4.0, the next-generation control system regards the cyber-physical system (CPS) as the core ingredient thanks to the comprehensive integration of physical systems, online computation, networking and control. A reliable, stable and resilient CPS should pledge robustness and safety. A significant concern in CPS development arises from security issues since the CPS is vulnerable to physical constraints, ubiquitous uncertainties and malicious cyber attacks. The integration of the stochastic model predictive control (MPC) framework and the resilient mechanism is a possible approach to guarantee robustness in the presence of stochastic uncertainties and enable resilience against cyber attacks. This review paper aims to offer a detailed overview of existing stochastic MPC algorithms and their CPS applications. More specifically, we first review existing stochastic MPC algorithms for both linear and nonlinear systems subject to probabilistic constraints. We then discuss how to extend the stochastic MPC framework to incorporate resilience mechanisms for constrained CPS under various malicious attacks. Finally, we present an architectural stochastic MPC-based framework for resilient CPS and identify future research challenges. This article is part of the theme issue ‘Towards symbiotic autonomous systems’.

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“…An 'ideal' methodology would solve the optimization problem described in (7)(8)(9)(10). However such an approach is intractable for the following reasons: 1) The real system is not known and 2) the expectation and probabilities are in general intractable integrals.…”

Section: Proposed Frameworkmentioning

confidence: 99%

“…Nevertheless, GP has extensively be used in the area of optimal control, where the prior models and black-box techniques are combined to describe the system. GP may be coupled with approximate method for propagating the uncertainty as unscented Kalman Filter [29], exact moment matching [22,14], linearization [22] and scenario-based approaches [63,9]. Recently, GPs have been used in hybrid modeling rational, where they are coupled with the prior (nominal) model that is assumed for the system, and learning is conducted only for the GP [15,24].…”

Section: Introductionmentioning

confidence: 99%

Safe model-based design of experiments using Gaussian processes

Petsagkourakis

Galvanin

2021

Computers & Chemical Engineering

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This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Stochastic data-driven model predictive control using gaussian processes

Cited by 87 publications

References 42 publications

Deterministic global optimization with Gaussian processes embedded

Deterministic global optimization with Gaussian processes embedded

Stochastic model predictive control framework for resilient cyber-physical systems: review and perspectives

Safe model-based design of experiments using Gaussian processes

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