A new step towards the integration of probabilistic $$\mu$$ in the aerospace V&V process

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

“…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].…”

“…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.…”

“…In particular, evaluating the worst-case combination of uncertainties can be tedious if a large number of uncertainties are present, and may lead to mistakes if the worst combination of parameters expected does not correspond to boundary values of the parameters. However, µ-analysis does not provide time performance information, so we limit the comparison of the classical validation approach at CNES with the use of the SMART [21] and STOWAT [9] toolboxes developed at ONERA to robust stability and frequency analyses.…”

“…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.…”

“…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. Recently tested on a series of AOCS benchmarks of increasing complexity [9], the most recent version of the toolbox is now evaluated on a challenging and realistic attitude control problem that was faced in a microsatellite project at CNES.…”