CEAS Space Journal

, Volume 7, Issue 2, pp 303–318 | Cite as

An overview of the RFCS project V&V framework: optimization-based and linear tools for worst-case search

  • A. Marcos
  • P. RosaEmail author
  • C. Roux
  • M. Bartolini
  • S. Bennani
Original Paper


This article presents the application of nonlinear (simulation-based) and linear (structured singular value) worst-case tools to the VEGA launcher Verification and Validation process, during atmospheric ascent. The simulation-based worst-case evaluation is performed by minimizing a set of cost functions that capture the launcher’s performance objectives, using the Worst-Case Analysis Optimization Tool and a high-fidelity nonlinear simulator of VEGA. The linear worst-case search uses the structured singular value (\(\mu \)) and a linear fractional transformation model representing the yaw rigid motion of the VEGA launcher but numerically evaluated using time simulation data from the VEGA simulator. To facilitate the analysis of the worst-case results as well as the comparison between the two analysis tools, a selection of the most critical uncertainties is performed using sensitivity analysis based on selected nonlinear simulator time responses. It is highlighted that the presented analysis tools are complementary to traditional Monte Carlo approaches in that they strive to identify worst-case uncertainty combinations as opposed to providing probabilistic guarantees on performance metric satisfaction. In addition, as it will be shown, these approaches require only a fraction of the time required to perform a Monte Carlo campaign.


Verification & Validation Worst-case search LFT model μ-analysis VEGA launcher 


  1. 1.
    Balas, G.J., Doyle, J.C., Glover, K., Packard, A., Smith, R.: \(\mu \)-analysis and synthesis toolbox. MUSYN Inc. and The MathWorks, Natick (1998)Google Scholar
  2. 2.
    Bateman, A., Ward, D., Balas, G.: Robust/worst-case analysis and simulation tools. In: Proc. AIAA Guidance, Navigation, and Control Conference (2005)Google Scholar
  3. 3.
    Belcastro, C.M., Belcastro, C.M.: On the validation of safety critical aircraft systems, part i: an overview of analytical & simulation methods. In: AIAA Guidance, Navigation and Control Conference, vol. 20. Austin, Texas (2003)Google Scholar
  4. 4.
    Doyle, J., Packard, A., Zhou, K.: Review of LFTs, LMIs, and \(\mu \). In: Decision and Control, 1991, Proceedings of the 30th IEEE Conference on, pp. 1227–1232. IEEE (1991)Google Scholar
  5. 5.
    Ferreres, G., Magni, J.F., Biannic, J.M.: Robustness analysis of flexible structures: practical algorithms. Int. J. Robust Nonlinear Control 13(8), 715–733 (2003)zbMATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Fielding, C., Varga, A., Bennani, S., Selier, M.: Advanced techniques for clearance of flight control laws, vol. 283. Springer (2002)Google Scholar
  7. 7.
    Hanson, J.M., Beard, B.B.: Applying monte carlo simulation to launch vehicle design and requirements verification. J. Spacecr. Rockets 49(1), 136–144 (2012)CrossRefGoogle Scholar
  8. 8.
    Hansson, J.: Using Linear Fractional Transformations for Clearance of Flight Control Laws. MS Thesis, Linkoping University, Sweden (2003)Google Scholar
  9. 9.
    Jacklin, S.A., Schumann, J.M., Gupta, P.P., Richard, R., Guenther, K., Soares, F.: Development of advanced verification and validation procedures and tools for the certification of learning systems in aerospace applications. In: Proceedings of Infotech Aerospace Conference. Arlington (2005)Google Scholar
  10. 10.
    Lambrechts, P., Terlouw, J., Bennani, S., Steinbuch, M.: Parametric uncertainty modeling using LFTs. In: American Control Conference, pp. 267–272. IEEE (1993)Google Scholar
  11. 11.
    Lawrence, C.T., Tits, A.L., Van Dooren, P.: A fast algorithm for the computation of an upper bound on the \(\mu \)-norm. Automatica 36(3), 449–456 (2000)zbMATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    Magni, J.F.: Linear fractional representation toolbox for use with matlab., (2006)
  13. 13.
    Marcos, A., Balas, G.J.: Development of linear-parameter-varying models for aircraft. J. Guid. Control Dyn 27(2), 218–228 (2004)CrossRefGoogle Scholar
  14. 14.
    Marcos, A., Bates, D.G., Postlethwaite, I.: A symbolic matrix decomposition algorithm for reduced order linear fractional transformation modelling. Automatica 43(7), 1211–1218 (2007)zbMATHMathSciNetCrossRefGoogle Scholar
  15. 15.
    Marcos, A., De Marina, H.G., Mantini, V., Roux, C., Bennani, S.: Optimization-based worst-case analysis of a launcher during the atmospheric ascent phase. In: AIAA Guidance, Navigation, and Control Conference and Exhibit (2013)Google Scholar
  16. 16.
    Marcos, A., Mantini, V., Roux, C., Bennani, S.: Bridging the gap between linear and nonlinear worst-case analysis: An application case to the atmospheric phase of the vega launcher. IFAC Autom. Control Aerosp. Würzburg Ger. 19(1), 42–47 (2013)Google Scholar
  17. 17.
    Marcos, A., Roux, C., Rotunno, M., Joos, H.D., Bennani, S., Penín, L.F., Caramagno, A.: The V&V problematic for launchers: current practice and potential advantages on the application of modern analysis techniques. In: ESA Guidance, Navigation and Control Conference, Karlovy Vary. Czech Republic (2011)Google Scholar
  18. 18.
    Menon, P.P., Postlethwaite, I., Bennani, S., Marcos, A., Bates, D.: Robustness analysis of a reusable launch vehicle flight control law. Control Eng. Pract. 17(7), 751–765 (2009)CrossRefGoogle Scholar
  19. 19.
    Storn, R., Price, K.: Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J. Global Optim. 11(4), 341–359 (1997)zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© CEAS 2015

Authors and Affiliations

  • A. Marcos
    • 1
    • 2
  • P. Rosa
    • 3
    Email author
  • C. Roux
    • 4
  • M. Bartolini
    • 4
  • S. Bennani
    • 5
  1. 1.Deimos Space S.L.U.MadridSpain
  2. 2.Aerospace Engineering DepartmentUniversity of BristolBristolUK
  3. 3.Deimos EngenhariaLisbonPortugal
  4. 4.ELVRomeItaly
  5. 5.ESA_ESTECNoordwijkThe Netherlands

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