Chance-constrained sets approximation: A probabilistic scaling approach

Mammarella, Martina; Mirasierra, Victor; Lorenzen, Matthias; Álamo, T.; Dabbene, Fabrizio

doi:10.1016/j.automatica.2021.110108

Cited by 10 publications

(5 citation statements)

References 61 publications

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“…As discussed in [2], this result may be alternatively derived by applying the scenario approach with discarded constraints [8,6]. Adaptations of this result have been used in the context of chance constrained optimization [4,20], and stochastic model predictive control [17,15,19].…”

Section: Uncertainty Quantification Using Probabilistic Maximizationmentioning

confidence: 99%

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Prediction error quantification through probabilistic scaling -- EXTENDED VERSION

Mirasierra¹,

Mammarella²,

Dabbene³

et al. 2021

Preprint

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In this paper, we address the probabilistic error quantification of a general class of prediction methods. We consider a given prediction model and show how to obtain, through a sample-based approach, a probabilistic upper bound on the absolute value of the prediction error. The proposed scheme is based on a probabilistic scaling methodology in which the number of required randomized samples is independent of the complexity of the prediction model. The methodology is extended to address the case in which the probabilistic uncertain quantification is required to be valid for every member of a finite family of predictors. We illustrate the results of the paper by means of a numerical example.

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Section: Uncertainty Quantification Using Probabilistic Maximizationmentioning

confidence: 99%

“…We now state a result, which has been presented in a different context in [17] and [20], that shows how to obtain N in such a way that (2) is satisfied for the particular choice r = εN 2 . Lemma 2.1.…”

Section: Uncertainty Quantification Using Probabilistic Maximizationmentioning

confidence: 99%

Prediction error quantification through probabilistic scaling -- EXTENDED VERSION

Mirasierra¹,

Mammarella²,

Dabbene³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…12.5.2], our objective is to show that (26) holds for some τ > 0 and β > 1 2 . Then, by inspecting (30) and using (31), to achieve this it is sufficient to guarantee…”

Section: Proof Of Lemmamentioning

confidence: 99%

“…Besides the game-theoretic context, alternative methodologies for set-oriented probabilistic feasibility guarantees have been proposed in the seminal works [5,15], which a priori characterise probabilistic feasibility regions constructed out of sampled constraints using statistical learning theoretic results. More recently, the so called probabilistic scaling [4,31] has been proposed to obtain a posteriori guarantees on the probability that a polytope generated out of samples is a subset of some chance-constrained feasibility region. Following an approach similar to [36], the works [16,17] deliver tighter probabilistic feasibility guarantees by focusing on variational-inequality (VI) solution sets.…”

Section: Introductionmentioning

confidence: 99%

A posteriori probabilistic feasibility guarantees for Nash equilibria in uncertain multi-agent games

2020

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“…It should be noted that a compact uncertainty set could reduce the conservatism of optimization and control performances 17 . The data‐driven uncertainty sets are designed in the works of literatures 17–20 to apply to optimization problems. To capture the relationship among the uncertain variables, the data‐driven uncertainty set is proposed by using principal component analysis (PCA) and kernel smoothing methods, 19 and it is further integrated into the MPC framework in the literature 21.…”

Section: Introductionmentioning

confidence: 99%

A chance‐constrained tube‐based model predictive control for tracking linear systems using data‐driven uncertainty sets

Zhang,

Jia,

et al. 2023

Intl J Robust & Nonlinear

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This article presents a chance‐constrained tube‐based model predictive control (MPC) method for tracking linear time‐invariant systems based on data‐driven uncertainty sets. By defining the terminal admissible set to consider all the possible steady‐states and reformulating the stochastic tube‐based MPC framework, the proposed method can systematically hedge against the impact of uncertainties and ensure tracking for all reachable operating setpoints. To reduce the conservatism of control performance while enlarging the feasible region, a data‐driven polyhedral uncertainty set is constructed by using the principal component analysis technique, which can effectively capture correlations among uncertain variables. Since state constraint violations in a certain probability are allowed, a probability uncertainty set is constructed by using statistic limit and cutting plane methods to formulate a stochastic tube to ensure constraint satisfaction. The recursive feasibility and stability can be guaranteed if the uncertainties are bounded. The effectiveness of the proposed method is verified by numerical examples and tracking problems of a thickening process.

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Chance-constrained sets approximation: A probabilistic scaling approach

Cited by 10 publications

References 61 publications

Prediction error quantification through probabilistic scaling -- EXTENDED VERSION

Prediction error quantification through probabilistic scaling -- EXTENDED VERSION

A posteriori probabilistic feasibility guarantees for Nash equilibria in uncertain multi-agent games

A chance‐constrained tube‐based model predictive control for tracking linear systems using data‐driven uncertainty sets

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