LPV Approaches for Varying Sampling Control Design: Application to Autonomous Underwater Vehicles

  • Emilie RocheEmail author
  • Olivier Sename
  • Daniel Simon
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 437)


This chapter deals with the robust control of an Autonomous Underwater Vehicle (AUV) subject to computation or communication constraints. The aim is the design of a gain-scheduled varying sampling controller using non periodic measurements, where the varying sampling rate is considered as a known parameter. First a Linear Parameter Varying (LPV) model of the AUV is developed to keep some non-linearities of the plant in the model, thus enlarging the model’s domain of validity around nominal conditions. The weighting templates are also made bandwidth dependent to take into account the dependencies between the achievable control performances and the sampling interval. From this model a LPV controller is synthesized in continuous time and then discretized over the range of predefined sampling rates. The approach is applied to the altitude control of an AUV, where depth measurements are asynchronously supplied by acoustic sensors.


Pitch Angle Autonomous Underwater Vehicle Forward Velocity Linear Parameter Vary Control Engineer Practice 
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  1. 1.
    Apkarian, P., Gahinet, P.: A convex characterisation of gain-scheduled \(\mathcal{H}_{\infty}\) controllers. IEEE Transaction on Automatic Control 40, 853–864 (1995)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Apkarian, P., Gahinet, P., Becker, G.: Self-scheduled \(\mathcal{H}_\infty\) control of linear parameter-varying systems: a design example. Automatica 31(9), 1251–1261 (1995)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Bokor, J., Balas, G.: Detection filter design for LPV systems–a geometric approach. Automatica 40(3), 511–518 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Briat, C., Sename, O., Lafay, J.F.: Memory-resilient gain-scheduled state-feedback control of uncertain LTI/LPV systems with time-varying delays. Systems and Control Letters 59(8), 451–459 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Feng, Z., Allen, R.: Reduced order \(\mathcal{H}_{\infty}\) control of an autonomous underwater vehicle. Control Engineering Practice 12, 1511–1520 (2004)CrossRefGoogle Scholar
  6. 6.
    Fossen, T.I.: Guidance and Control of Ocean Vehicles. John Wiley & Sons (1994)Google Scholar
  7. 7.
    Gaspar, P., Szabo, Z., Bokor, J.: LPV design of fault-tolerant control for road vehicles. In: 2010 Conference on Control and Fault-Tolerant Systems (SysTol), pp. 807–812 (October 2010)Google Scholar
  8. 8.
    Healey, A.J., Lienard, D.: Multivariable sliding mode control for autonomous diving and steering of unmanned underwater vehicles. Oceanic Engineering 18(3), 327–339 (1993)CrossRefGoogle Scholar
  9. 9.
    Heemels, W.P.M.H., Daafouz, J., Millerioux, G.: Observer-based control of discrete-time LPV systems with uncertain parameters. IEEE Transactions on Automatic Control 55(9), 2130–2135 (2010)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Hetel, L., Kruszewski, A., Perruquetti, W., Richard, J.-P.: Discrete and intersample analysis of systems with aperiodic sampling. IEEE Transactions on Automatic Control 56(7), 1696–1701 (2011)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Leveille, E.A.: Analysis, redesign and verification of the iver2 autonomous underwater vehicle motion controller. Master’s thesis, University of Massachusetts Dartmouth (2007)Google Scholar
  12. 12.
    Lofberg, J.: YALMIP: A toolbox for modeling and optimization in MATLAB. In: Proceedings of the CACSD Conference, Taipei, Taiwan (2004)Google Scholar
  13. 13.
    Miyamaoto, S., Aoki, T., Maeda, T., Hirokawa, K., Ichikawa, T., Saitou, T., Kobayashi, H., Kobayashi, E., Iwasaki, S.: Maneuvering control system design for autonomous underwater vehicle. In: MTS/IEEE Conference and Exhibition, vol. 1, pp. 482–489 (November 2001)Google Scholar
  14. 14.
    Opderbecke, J.: Description of the scientific mission scenario(s) to be investigated for the marine application. deliverable D08.01, FeedNetBack project (2009),
  15. 15.
    Pellanda, P.C., Apkarian, P., Tuan, H.D., Alazard, D.: Missile autopilot design via a multi-channel LFT/LPV control method. In: 15th IFAC World Congress, Barcelona, Spain (2002)Google Scholar
  16. 16.
    Poussot-Vassal, C., Sename, O., Dugard, L., Gáspár, P., Szabó, Z., Bokor, J.: Attitude and handling improvements through gain-scheduled suspensions and brakes control. Control Engineering Practice 19(3), 252–263 (2011)CrossRefGoogle Scholar
  17. 17.
    Poussot-Vassal, C., Sename, O., Dugard, L., Gáspár, P., Szabó, Z., Bokor, J.: A new semi-active suspension control strategy through LPV technique. Control Engineering Practice 16(12), 1519–1534 (2008)CrossRefGoogle Scholar
  18. 18.
    Robert, D.: Contribution à l’interconnection commande / ordonnancement. PhD thesis, Institut National Polytechnique de Grenoble (2007)Google Scholar
  19. 19.
    Robert, D., Sename, O., Simon, D.: An h  ∞  LPV design for sampling varying controllers: experimentation with at inverted pendulum. IEEE Transactions on Control Systems Technology 18(3), 741–749 (2010)CrossRefGoogle Scholar
  20. 20.
    Roche, E., Sename, O., Simon, D.: LPV / \(\mathcal{H}_{\infty}\) varying sampling control for autonomous underwater vehicles. In: Proceedings of the IFAC SSSC, Ancona, Italy (2010)Google Scholar
  21. 21.
    Roche, E., Sename, O., Simon, D.: A hierarchical varying sampling \(\mathcal{H}_{\infty}\) control of an AUV. In: Proceedings of the IFAC World Congress, Milano, Italy (2011)Google Scholar
  22. 22.
    Santos, A.S.: Contribution à la conception des sous-marins autonomes: architecture des capteurs d’altitude, et commande référencées capteurs. PhD thesis, Ecole nationale supérieure des Mines de Paris (1995) (in French)Google Scholar
  23. 23.
    Scherer, C.W.: LPV control and full block multipliers. Automatica 37(3), 361–375 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  24. 24.
    Shirazi, F.A., Mohammadpour Velni, J., Grigoriadis, K.M.: An LPV design approach for voltage control of an electrostatic MEMS actuator. Journal of Microelectromechanical Systems 20(1), 302–311 (2011)CrossRefGoogle Scholar
  25. 25.
    Silvestre, C., Pascoal, A.: Control of the INFANTE AUV using gain scheduled static output feedback. Control Engineering Practice 12(12), 1501–1509 (2004)CrossRefGoogle Scholar
  26. 26.
    Silvestre, C., Pascoal, A.: Depth control of the INFANTE AUV using gain-scheduled reduced order output feedback. Control Engineering Practice 15(7), 883–895 (2007)CrossRefGoogle Scholar
  27. 27.
    Simon, D., Robert, D., Sename, O.: Robust control/scheduling co-design: application to robot control. In: 11th IEEE Real Time and Embedded Technology and Applications Symposium, RTAS 2005, pp. 118–127 (March 2005)Google Scholar
  28. 28.
    Sturm, J.F.: Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optim. Methods Softw. 11/12(1-4), 625–653 (1999), Interior point methodsMathSciNetCrossRefGoogle Scholar
  29. 29.
    Tóth, R., Heuberger, P.S.C., Van den Hof, P.M.J.: Discretisation of linear parameter-varying state-space representations. IET Control Theory and Applications 4(10), 2082–2096 (2010)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Wei, X., del Re, L.: Gain scheduled \(\mathcal{H}_{\infty}\) control for air path systems of diesel engines using LPV techniques. IEEE Transactions on Control Systems Technology 15(3), 406–415 (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.INRIA RASaint Ismier CedexFrance

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