Advertisement

Global Optimization of \(H_\infty \) Problems: Application to Robust Control Synthesis Under Structural Constraints

  • Dominique MonnetEmail author
  • Jordan Ninin
  • Benoit Clement
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9582)

Abstract

In this paper, a new technique to compute a synthesis structured Robust Control Law is developed. This technique is based on global optimization methods using a Branch-and-Bound algorithm. The original problem is reformulated as a min/max problem with non-convex constraint. Our approach uses interval arithmetic to compute bounds and accelerate the convergence.

References

  1. 1.
    Apkarian, P., Noll, D.: Nonsmooth \(H_{\infty }\) synthesis. IEEE Trans. Autom. Control 51(1), 71–86 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Arzelier, D., Clement, B., Peaucelle, D.: Multi-objective \(H_2\)/\(H_\infty \)/impulse-to-peak control of a space launch vehicle. Eur. J. Control 12(1), 57–70 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM, vol. 15. SIAM, Philadelphia (1994)CrossRefzbMATHGoogle Scholar
  4. 4.
    Petersen, I.R., Tempo, R.: Robust control of uncertain systems: classical results and recent developments. Automatica 50(5), 1315–1335 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Hurwitz, A.: Ueber die Bedingungen, unter welchen eine Gleichung nur Wurzeln mit negativen reellen Theilen besitzt. Math. Ann. 46(2), 273–284 (1895)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Jaulin, L., Kieffer, M., Didrit, O., Walter, E.: Applied Interval Analysis, with Examples in Parameter and State Estimation Robust Control and Robotics. Springer, London (2001)zbMATHGoogle Scholar
  7. 7.
    Ninin, J.: Optimisation Globale basée sur l’Analyse d’Intervalles: Relaxation Affine et Limitation de la Mémoire. PhD thesis, Institut National Polytechnique de Toulouse, Toulouse (2010)Google Scholar
  8. 8.
    Trombettoni, G., Chabert, G.: Constructive interval disjunction. In: Principles and Practice of Constraint Programming–CP 2007, pp. 635–650. Springer (2007)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Dominique Monnet
    • 1
    Email author
  • Jordan Ninin
    • 1
  • Benoit Clement
    • 1
  1. 1.Lab-STICC, IHSEV TeamENSTA-BretagneBrestFrance

Personalised recommendations