Robust Design Through Probabilistic Maximization

Álamo, T.; Manzano, J.M.; Camacho, Eduardo F.

doi:10.1007/978-3-030-04630-9_7

Cited by 9 publications

(18 citation statements)

References 29 publications

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“…The probabilistic scaling approach was presented in the conference papers (Alamo, Mirasierra, Dabbene, & Lorenzen, 2019;Mammarella, Alamo, Dabbene, & Lorenzen, 2020) and it is based on recent results on order statistics (Alamo, Manzano, & Camacho, 2018). The present work extends Alamo et al (2019), Mammarella et al (2020) in several directions.…”

Section: Introductionmentioning

confidence: 88%

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Chance-constrained sets approximation: A probabilistic scaling approach

et al. 2022

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Section: Introductionmentioning

confidence: 88%

“…The following definition is borrowed from the field of order statistics (Alamo et al, 2018;Mirasierra, Mammarella, Dabbene, & Alamo, 2022).…”

Section: Notationmentioning

confidence: 99%

Chance-constrained sets approximation: A probabilistic scaling approach

et al. 2022

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“…This will allow us to reduce the conservativeness that follows from the use of the standard notion of max function. See also Section 3 of Alamo et al (2018).…”

Section: Preliminaries: Probabilistic Upper Bound Of a Random Variablementioning

confidence: 99%

A probabilistic validation approach for penalty function design in Stochastic Model Predictive Control

Mammarella¹,

Álamo²,

Lucia³

et al. 2020

Preprint

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In this paper, we consider a stochastic Model Predictive Control able to account for effects of additive stochastic disturbance with unbounded support, and requiring no restrictive assumption on either independence nor Gaussianity. We revisit the rather classical approach based on penalty functions, with the aim of designing a control scheme that meets some given probabilistic specifications. The main difference with previous approaches is that we do not recur to the notion of probabilistic recursive feasibility, and hence we do not consider separately the unfeasible case. In particular, two probabilistic design problems are envisioned. The first randomization problem aims to design offline the constraint set tightening, following an approach inherited from tube-based MPC. For the second probabilistic scheme, a specific probabilistic validation approach is exploited for tuning the penalty parameter, to be selected offline among a finite-family of possible values. The simple algorithm here proposed allows designing a single controller, always guaranteeing feasibility of the online optimization problem. The proposed method is shown to be more computationally tractable than previous schemes. This is due to the fact that the sample complexity for both probabilistic design problems depends on the prediction horizon in a logarithmic way, unlike scenario-based approaches which exhibit linear dependence. The efficacy of the proposed approach is demonstrated with a numerical example.

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“…See [16], [17], [18] and references therein. Also, probabilistic validation methods can be used to assess the performance of the interval predictors [19], [20], [21], [22].…”

Section: Introductionmentioning

confidence: 99%

“…This is due to the fact that estimating the probability of rare events requires a large number of samples. For example, the number of independent identically distributed samples required to obtain the 1 − ϵ quantile of a monovariable random variable grows with 1 ϵ (see [31], [20] and [21]). This paper presents a new methodology for the computation of interval predictions of a dynamical system.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Interval Predictor Based on Dissimilarity Functions

Carnerero

Ramı́rez

Álamo

2022

IEEE Trans. Automat. Contr.

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This work presents a new methodology to obtain probabilistic interval predictions of a dynamical system. The proposed strategy uses stored past system measurements to estimate the future evolution of the system. The method relies on the use of dissimilarity functions to estimate the conditional probability density function of the outputs. A family of empirical probability density functions, parameterized by means of two scalars, is introduced. It is shown that the proposed family encompasses the multivariable normal probability density function as a particular case. We show that the presented approach constitutes a generalization of classical estimation methods. A validation scheme is used to tune the two parameters on which the methodology relies. In order to prove the effectiveness of the presented methodology, some numerical examples and comparisons are provided.

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Robust Design Through Probabilistic Maximization

Cited by 9 publications

References 29 publications

Chance-constrained sets approximation: A probabilistic scaling approach

Chance-constrained sets approximation: A probabilistic scaling approach

A probabilistic validation approach for penalty function design in Stochastic Model Predictive Control

Probabilistic Interval Predictor Based on Dissimilarity Functions

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