Advanced probabilistic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mi>μ</mml:mi></mml:math>-analysis techniques for AOCS validation

Biannic, Jean‐Marc; Roos, Clément; Bennani, Samir; Boquet, Fabrice; Preda, Valentin; Girouart, Bénédicte

doi:10.1016/j.ejcon.2021.06.019

Cited by 11 publications

(12 citation statements)

References 16 publications

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“…The last step of the end-to-end design process is the V&V campaign in order to provide a guarantee of robust stability and performance. In this section we propose some analyses run with the MATLAB routine wcgain of the Robust Control Toolbox and the routines available in the SMAC Toolbox developed by Biannic et al (2016) and the STOchastic Worst-case Analysis Toolbox (STOWAT), which was first introduced by Thai et al ( 2019) and Biannic et al (2021).The analyses proposed in this articles have to be considered as simple examples while researchers are challenged to use the proposed benchmark to highlight the performance and check the limits of their own V&V algorithms.…”

Section: Robust Control Analysismentioning

confidence: 99%

Satellite Dynamics Toolbox Library: a tool to model multi-body space systems for robust control synthesis and analysis

Sanfedino¹,

Alazard²,

Kassarian³

et al. 2023

Preprint

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The level of maturity reached by robust control theory techniques nowadays contributes to a considerable minimization of the development time of an end-to-end control design of a spacecraft system. The advantage offered by this framework is twofold: all system uncertainties can be included from the very beginning of the design process; the validation and verification (V&V) process is improved by fast detection of worst-case configurations that could escape to a classical sample-based Monte Carlo simulation campaign. Before proceeding to the control synthesis and analysis, a proper uncertain plant model has to be available in order to push these techniques to their limits of performance. In this spirit, the Satellite Dynamics Toolbox Library (SDTlib) offers many features to model a spacecraft system in a multi-body fashion on SIMULINK. Parametric models can be easily built in a Linear Fractional Transformation (LFT) form by including uncertainties and varying parameters with minimal number of repetitions. Uncertain Linear Time Invariant (LTI) and uncertain Linear Parameter-Varying (LPV) controllers can then be synthesized and analyzed in a straightforward way. The authors present in this article a tutorial, that can be downloaded at https://nextcloud.isae. fr/index.php/s/XDfRfHntejHTmmp, to show how to deal with an end-to-end robust design of a spacecraft mission and to provide to researchers a benchmark to test their own algorithms.

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Section: Robust Control Analysismentioning

confidence: 99%

Satellite Dynamics Toolbox Library: a tool to model multi-body space systems for robust control synthesis and analysis

Sanfedino¹,

Alazard²,

Kassarian³

et al. 2023

Preprint

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“…Here, the matrix M depends on the internal structure of the uncertainty structure determined by (7) and the controller C.…”

Section: Motivating Examplementioning

confidence: 99%

“…Theorem 2. Let H denote the multivariable system at frequency 𝜔 of the form (7) with its input w and output z. The inequalities in (38) hold if and only if (36) holds with the performance matrices…”

Section: Magnitude and Phase Descriptionmentioning

confidence: 99%

“…It has led to approaches that consider parametric uncertainty that is directly applicable to

{\mathscr{H}}_{\infty }

optimization 5 . In References 6 and 7, connections to the prediction error framework have been established. Besides the use of parameter uncertainty, uncertainty structures in robust control have been further developed towards system identification.…”

Section: Introductionmentioning

confidence: 99%

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Comparing multivariable uncertain model structures for data‐driven robust control: Visualization and application to a continuously variable transmission

Tacx

Oomen

2023

Intl J Robust & Nonlinear

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The selection of uncertainty structures is an important aspect of system identification for robust control. The aim of this paper is to provide insight into uncertain multivariable systems for robust control. A unified method for visualizing model sets is developed by generating Bode plots of multivariable uncertain systems, both in magnitude and phase. In addition, these model sets are compared from the viewpoint of the control objective, allowing a quantitative analysis as well. An experimental case study on an automotive transmission application demonstrates these connections and confirms the importance of the developed framework for control applications. In addition, the experimental results provide new insights into the shape of associated model sets by using the presented visualization procedure. Both the theoretical and experimental results confirm that a recently developed robust-control-relevant uncertainty structure outperforms general dual-Youla-Kučera uncertainty, which in turn outperforms traditional uncertainty structures, including additive uncertainty.

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“…Models for probabilistic robust control have been developed for probabilistic extension of µ analysis ( [13,2,4]), disk margins ( [24]), scenario optimization [5], and the methods reviewed in [6]. Unlike for Bayesian system identification, these models usually place severe structural restrictions on the form of the unknown model, including a finite (known) bound on the order.…”

mentioning

confidence: 99%

Data-Driven Reachable Set Computation using Adaptive Gaussian Process Classification and Monte Carlo Methods

Devonport

Arcak

2020

2020 American Control Conference (ACC)

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Complex-valued Gaussian processes are commonly used in Bayesian frequencydomain system identification as prior models for regression. If each realization of such a process were an H∞ function with probability one, then the same model could be used for probabilistic robust control, allowing for robustly safe learning. We investigate sufficient conditions for a general complex-domain Gaussian process to have this property. For the special case of processes whose Hermitian covariance is stationary, we provide an explicit parameterization of the covariance structure in terms of a summable sequence of nonnegative numbers. We then establish how an H∞ Gaussian process can serve as a prior for Bayesian system identification and as a probabilistic uncertainty model for probabilistic robust control. In particular, we compute formulas for refining the uncertainty model by conditioning on frequency-domain data and for upper-bounding the probability that the realizations of the process satisfy a given integral quadratic constraint.

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Advanced probabilistic μ-analysis techniques for AOCS validation

Cited by 11 publications

References 16 publications

Satellite Dynamics Toolbox Library: a tool to model multi-body space systems for robust control synthesis and analysis

Satellite Dynamics Toolbox Library: a tool to model multi-body space systems for robust control synthesis and analysis

Comparing multivariable uncertain model structures for data‐driven robust control: Visualization and application to a continuously variable transmission

Data-Driven Reachable Set Computation using Adaptive Gaussian Process Classification and Monte Carlo Methods

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