Probabilistic gain, phase and disk margins with application to AOCS validation

Somers, Franca; Thai, Sovanna; Roos, Clément; Biannic, Jean‐Marc; Bennani, Samir; Preda, Valentin; Sanfedino, Francesco

doi:10.1016/j.ifacol.2022.09.314

Cited by 7 publications

(11 citation statements)

References 7 publications

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“…During the past 5 years, a significant effort has been put in the development of probabilistic μ theory and its implementation in the Matlab STOchastic Worst-case Analysis Toolbox (STOWAT) [9]. Stability and 𝐻 ∞ performance were studied first [7,8], followed by gain/phase/disk margins [10] and more recently delay margin [11]. The theory behind μ-analysis is not presented in this paper due to space limitations, but the interested reader can for example refer to [1,2,12] and [3][4][5][6][7][8][9][10][11] for the classical and the probabilistic versions respectively.…”

Section: Problem 1 (Probabilistic Robust Stability)mentioning

confidence: 99%

“…Stability and 𝐻 ∞ performance were studied first [7,8], followed by gain/phase/disk margins [10] and more recently delay margin [11]. The theory behind μ-analysis is not presented in this paper due to space limitations, but the interested reader can for example refer to [1,2,12] and [3][4][5][6][7][8][9][10][11] for the classical and the probabilistic versions respectively. Only a few facts are briefly recalled below to facilitate the understanding of the paper.…”

Section: Problem 1 (Probabilistic Robust Stability)mentioning

confidence: 99%

“…smaller) than the desired threshold 𝜙, it is then checked whether the margin requirement is satisfied (resp. violated) on the entire domain ℬ 𝛿 , using sufficient conditions involving μ upper bound computations (see Propositions 3.1 and 3.3 of [10] for gain/phase/disk margins, and Propositions 4.1 and 4.3 of [11] for delay margin). If this cannot be guaranteed, ℬ 𝛿 is finally partitioned into smaller boxes and this process is repeated until each box has guaranteed sufficient/insufficient margin, or is small enough to be neglected.…”

Section: Problem 1 (Probabilistic Robust Stability)mentioning

confidence: 99%

“…At that time indeed, no practical tool offering both good reliability and reasonable computational time was available, making this technique hardly usable in an industrial context. More recently, following the work carried out in [6,7], significant improvements have been achieved by ONERA supported by ESA and CNES to develop the STOchastic Worst-case Analysis Toolbox (STOWAT) [8,9,10]. With the help of this new Matlab toolbox, probabilistic µ-analysis may now be considered as a very good candidate for integration in the aerospace V&V process in a near future, finding its place between Monte Carlo simulationsuseful for quantifying the probability of sufficiently frequent phenomena -and worst-case μ-analysis -relevant for detecting extremely rare events.…”

Section: Introductionmentioning

confidence: 99%

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Attitude control laws validation through probabilistic µ-analysis : application to a microsatellite control laws

Evain,

Casati,

Roos

et al. 2023

Papers of ESA GNC-ICATT 2023

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During the development of a new attitude control system for ambitious satellite missions, the validation & verification phase represents a large part of the process. One difficulty is to detect worst case configurations. In such cases, when applicable, µ-analysis [1] offers a nice additional tool to be used before launching the Monte Carlo simulation campaign, but does not provide any quantification of the probability of occurrence of the identified worst-cases. A control system can then be invalidated on the basis of unlikely events. Probabilistic µ-analysis was introduced in this context 20 years ago to bridge the gap between the two techniques. It has been used for the first time in [2] in the challenging context of validation of launcher thrust vector control systems. But it appeared to be computationally very expensive. At that time indeed, no practical tool offering both good reliability and reasonable computational time was available, making this technique hardly usable in an industrial context. After the preliminary work of [3,4], strong improvements have been achieved by ONERA supported by ESA and CNES to develop the STOchastic Worst-case Analysis Toolbox (STOWAT). With the help of this new Matlab toolbox, probabilistic µ-analysis may now be considered as a very good candidate for integration in the aerospace V&V process in a near future, finding its place between Monte Carlo simulations – useful for quantifying the probability of sufficiently frequent phenomena – and worst-case μ-analysis – relevant for detecting extremely rare events. Recently tested on a series of AOCS benchmarks of increasing complexity [5,6,7], the most recent version of the toolbox is now evaluated for the first time on a more challenging and realistic attitude control problem. The analysis focuses both on the normal mode (MNO) and on the orbit control mode (MCO) of the CNES MicroCarb mission [8,9]. The paper compares and discusses the results which have been obtained with different V&V techniques, critically assessing the advantages of the innovative method with respect to more classical procedures. [1] C. Roos. Systems Modeling, Analysis and Control (SMAC) toolbox: an insight into the robustness analysis library. Proceedings of the IEEE CACSD Conference, Hyderabad, India, 2013. [2] A. Marcos, S. Bennani, C. Roux. Stochastic µ-analysis for launcher thrust vector control systems. Proceedings of the EuroGNC Conference, Toulouse, France, 2015. [3] A. Falcoz, D. Alazard, C. Pittet. Probabilistic µ-analysis for system performances assessment. Proceedings of the 20th IFAC World Congress, Toulouse, France, 2017. [4] S. Thai, C. Roos, J.M. Biannic. Probabilistic µ-analysis for stability and H∞ performance verification. Proceedings of the ACC, Philadelphia, PA, USA, 2019. [5] J.M. Biannic, C. Roos, S. Bennani, F. Boquet, V. Preda, B. Girouart. Advanced probabilistic µ-analysis techniques for AOCS validation. European Journal of Control, 62 (2021), pp. 120-129. [6] C. Roos, J-M. Biannic, and H. Evain. A new step towards the integration of probabilistic µ in the aerospace V&V process. Proceedings of the EuroGNC Conference, Berlin, Germany, 2022. [7] F. Somers, S. Thai, C. Roos,[ J-M. Biannic, S. Bennani, V. Preda, and F. Sanfedino. Probabilistic gain, phase and disk margins with application to AOCS validation. Proceedings of the IFAC ROCOND Symposium, Kyoto, Japan, 2022. [8] Arnaud Varinois and al., “MICROCARB: A micro-satellite for atmospheric CO2 monitoring”, 4S 2016 [9] Genin, F. and Viaud, F. “An innovative control law for Microcarb microsatellite”, 32nd annual AAS Guidance and Control Conference, 2018

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Section: Problem 1 (Probabilistic Robust Stability)mentioning

confidence: 99%

Section: Problem 1 (Probabilistic Robust Stability)mentioning

confidence: 99%

Section: Problem 1 (Probabilistic Robust Stability)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Attitude control laws validation through probabilistic µ-analysis : application to a microsatellite control laws

Evain,

Casati,

Roos

et al. 2023

Papers of ESA GNC-ICATT 2023

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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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A μ-analysis based approach to probabilistic delay margin analysis of uncertain linear systems*

Somers,

Roos,

Sanfedino

et al. 2023

2023 IEEE Conference on Control Technology and Applications (CCTA)

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Probabilistic gain, phase and disk margins with application to AOCS validation

Cited by 7 publications

References 7 publications

Attitude control laws validation through probabilistic µ-analysis : application to a microsatellite control laws

Attitude control laws validation through probabilistic µ-analysis : application to a microsatellite control laws

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

A μ-analysis based approach to probabilistic delay margin analysis of uncertain linear systems*

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